RRB Group D Previous Year Paper (Held on: 19 Sept 2022 Shift 3)

Given:

160 × 8 + 12 - 6 ÷ 180 × 6 - 4 = ?

Concept Used:

Follow BODMAS rule to solve this question, as per the order given below,

Calculation:

⇒ 160 × 8 + 12 - 6 ÷ 180 × 6 - 4

When signs are interchanged,

⇒ 160 ÷ 8 – 12 + 6 × 180 ÷ 6 + 4

⇒ 20 – 12 + 6 × 30 + 4

⇒ 20 – 12 + 180 + 4

⇒ 24 – 12 + 180

⇒ 12 + 180 = 192

Therefore, the required value of the expression is 192.

Hence, the correct answer is option 3).

The logic followed is:

Given:

Five students are sitting in a straight row facing the north.

 

 A and B are sitting at the extreme left and the extreme right end of the row, respectively.

D is an immediate neighbour of B.

C is an immediate neighbour of D and second to the right of A.

E is an immediate neighbour of A.

According to the arrangement, C is sitting in the third position from the extreme right end.

Hence the correct answer is 'C'.

Given :

38 ÷ 10 × 5 - 7 + 10 × 2 

Concept used:

BODMAS table:

Decoding the information, 

 

After replacing the signs from left to right and using the BODMAS rule,

⇒ 38 + 10 ÷ 5 × 7 - 10 ÷ 2 

⇒ 38 + 2 × 7 - 5

⇒ 38 + 14 - 5

⇒ 52 - 5

⇒ 47

Hence, the correct answer is '47'.

The word arranged in alphabetical order is:

Thus, the total 3 letter positions remained unchanged.

Hence, the correct answer is 'option 3'.

The position of the letters according to the English alphabet series:

The logic followed here is as follows:

The code for the 1^st and 2^nd letters of one part in the letter-cluster pair is the previous and the subsequent letter gives the other part of the letter-cluster pair according to the English alphabet series.

According to the question:

ON : NPMO

and,

IN : HJMO

Similarly,

Hence, the correct answer is option 2.

The Venn diagram according to the given statements we have:

Conclusions:

I. Some engines are stoves → Follow (Since given that all jugs are cans and all cans are engines and some jugs are stoves. Thus, some engines are stoves is true.)

II. Some cans are jugs.→ Follow (Since given all jugs are cans and so some cans are jugs is true.)

Thus, both conclusion I and II follows.

Hence, the correct answer is 'Option 3'.

We follow the given table and code the given combination:

Given combination: 6 % $ 8 5

Since first and last elements are numbers, first condition will be applied which says 'If the first and last elements are numbers, then the last element will be replaced by the symbol @.' so the code will contain '@' at last.

Now none of the other conditions apply so the code becomes:

Hence, the correct answer is option 3).

Statements:

All creepers are vegetables.

All vegetables are fruits.

Some fruits are flowers.

Venn Diagram:

Conclusions:

I. Some creepers are flowers → Does not follow → We have no information which suggests the relationship between creepers and flowers so we cannot assume anything and thus the conclusion does not follow.

II. Some fruits are creepers→ Follow → Since all creepers are fruits, they both are directly related to each other & the same can be seen in the Venn diagram so we can say that some fruits are creepers therefore the conclusion follows.

III. All vegetables are flowers→ Does not follow → We have 'All vegetables are fruits' and 'Some fruits are flowers' which means vegetables and flowers are directly not related to each other so the conclusion does not follow.

So only conclusion II follows.

Hence, the correct answer is option 2).

According to the given condition the series becomes:

Now we have, 2 as third from left and 8 as second from right.

Sum = 2 + 8 = 10

Hence, the correct answer is option 1).

According to the English alphabets and their positional values:

After applying the condition, the word becomes:

Now we arrange the word in alphabetical order, we get:

Here Q is the second letter from right.

Hence the correct answer is option 1)

The Positional value Table:

In a forward direction : RU 

In a backward direction : PR and BE

 

Thus, there are three pairs of words have as many letters between them as there are in the English alphabetical order.

Hence, the correct answer is Option 2.

Statement:

It is reported that heavy and erratic rainfall has destroyed many agricultural crops and farmers are in debt.

Conclusions:

I. Farmers need not repay the debt → Does not follow → From the given statement there is no information that tells us about the repayment of debt so we cannot assume anything so the conclusion does not follow.

II. Prices of groceries and other essential food items such as lentils and grains will surge → Follow → Since the farmers are in debt and their crops has been destroyed, there will be an increase in the price of upcoming crops by the farmers so that they can make a good amount of money to pay their debt, we can see that this conclusion directly justifies the statement, therefore, the conclusion follow.

So only conclusion II follows.

Hence the correct answer is option 4)

From the given information:

Step 1: Falak, who is third to the left of Aman, is standing at one of the extreme ends. Fatima is fourth to the right of Falak.

  

 

Falak is at the extreme end but Fatima is 4^rd to the right of Falak which means Falak has to be at the left end.

Step 2: Chandan is to the immediate right of Fatima. 

Here we place Chandan to the right of Fatima.

Step 3: Manoj is an immediate neighbour of both Aman and Bony.

 

Now we place Manoj next to Aman and Bony next to Manoj.

So the only person left is Mahima at the right end.

Now we consider the given options:

Option 1) To the immediate left of Chandan: False.

Option 2) To the immediate left of Bony: False.

Option 3) Immediate neighbour of Bony and Fatima: False.

Option 4) Fourth to the right of Manoj: True.

Hence the correct answer is option 4)

We follow the given table and code the given combination:

Given combination: + # 7 & 6

Since the first element is a symbol and a last element is a number, the first condition will be applied which says 'If the first element is a symbol and the last is a number, the codes for these two (the first and last elements) are to be interchanged.'

Now, none of the other conditions apply so the code becomes:

Hence the correct answer is option 1)$

From the given information:

Step 1: Ajay is driving in the east direction and covers a distance of 2.5 km and then takes a turn in the left direction and travels a distance of 3 km.

Step 2: Further, he turns to the right and travels a distance of 4.5 km. Lastly, he turns to his right and travels a distance of 3 km.

Total distance = 2.5 + 4.5 = 7 km

Hence the correct answer is option 3)

The pattern followed in the given series is:

The difference between the terms is -1 of the previous difference.

Hence, the correct answer is option 3).

The pattern followed in the given series is:

(First term)² = Second term

Now we apply the pattern to the given series:

6 : 36 :: 13 : 169 :: 17 : 289 :: 23 : ?

(6)² = 36

36 = 36

6 : 36 :: 13 : 169 :: 17 : 289 :: 23 : ?

(13)2 = 169

169 = 169

6 : 36 :: 13 : 169 :: 17 : 289 :: 23 : ?

(17)2 = 289

289 = 289

6 : 36 :: 13 : 169 :: 17 : 289 :: 23 : ?

(23)2 = ?

529 = Answer

Hence, the correct answer is option 3).

Statements:

Some pouches are combs.

All combs are reds.

All reds are sticks.

Venn diagram:

Conclusions:

I. All pouches are sticks→ Does not follow → From the given statements 'All combs are reds.' & 'All reds are sticks.' which means all combs are sticks but only some pouches are combs, therefore, some pouches are sticks so the conclusion does not follow.

II. All combs are sticks→ Follow → Since 'All combs are reds.' & 'All reds are sticks.' we can say that all combs are sticks and the same can be seen in the Venn diagram so the conclusion follows.

III. Some reds are combs→ Follow → We have 'all combs are reds' which means reds and combs are directly related so it is safe to say that some reds are combs thus the conclusion follows.

IV. Some sticks are pouches→ Follow → From the diagram and the statements it can be clearly seen that some part of sticks is shared with pouches and we can say that some sticks are pouches, therefore the conclusion follows.

So only conclusions II, III, and IV follow.

Hence the correct answer is option 4)

From the given information:

Total number of students in a class = 100

Students with marks more than Sharmistha = 24

Students with marks less than Amit = 18 

Total = 24 + 18 = 42

Now we have to find out the number of students who score lesser marks than Sharmistha but more marks than Amit: 

100 - 42 - 2 (Sharmistha & Amit) ⇒ 100 - 44 = 56

Hence the correct answer is option 3)

From the given information:

Step 1: Mohan drives 6 km towards the south and takes a turn to the right at 90°.

Step 2: After driving a distance of 3 km, he turns to the right and drives further 3 km.

From the diagram we can see that, Mohan is towards south-west from the starting point.

Hence the correct answer is option 3)

In the given series, there are only two symbols which are immediately preceded and immediately followed by a vowel:

The 2 symbols are @ and &.

Hence the correct answer is option 3)

From the given information:

People till Manish = 18

People till Aman = 12 

People between Aman & Manish = 8

Total people = 18 + 12 + 8 = 38

Since Aman is behind Manish we don't have to calculate anything else.

Hence the correct answer is option 1)

The pattern followed in the given series is:

The series breaks down into triads and then each triad have a difference with increasing natural number and the first term of each triad is +2 of the first term of previous triad.

Hence, the correct answer is option 2).

Given:

J > K = L, M $\ge$ N < K, O < J < P, N > Q > R

Conclusions:

I. P > M → False

We have P > J and J > K which means P > K

also M $\ge$ N < K so relation between P and M cannot be determined.

II. N < P → True

We have P > J and J > K which means P > K also N < K (given)

when we combine both the relations we get, P > K > N so P > N.

So only conclusion II is true.

Hence, the correct answer is Option 4.

Given: 

Step 1: M's night shift duty is on Saturday & Q's night shift duty is on Wednesday.

Step 2: O's nightshift duties are on the day immediately before P but it is not on Monday. 

There are two weekdays reserved for O and P but not Monday-Tuesday it cannot be Tuesday-Wednesday(Q) and also not Wednesday(Q)-Thursday and therefore it is Thursday-Friday so O's is Thursday & P's is Friday.

Step 3: L's nightshift duties are on the day immediately after N

We have only two weekdays left i.e., Monday and Tuesday since N's duties come before N works on Monday and L works on Tuesday.

From the chart, we can see that, L has nightshift duties on Tuesday.

Hence the correct answer is Option 1.

Given: 

K P _ L Z _ P _ MZK _ B _ Z _ PB _ Z

Let's check each option:

1)  B K B P N P O → K P B /L Z/ K P B/ MZ/K P B /N Z/ P PB /O Z

2)  B K B P N K O → K P B /L Z /K P B /MZ/K P B /N Z /K PB /O Z

So, In option 2 "KPB - L/M/N/O - Z" is repeating itself.

3.  B K B P N K P → K P B /L Z/ K P B/ MZ/K P B/ N Z/ K PB/ P Z

4)  B K P P O K P → K P B /L Z/ K P P/MZ/K P B/ O Z /K PB/ P Z

Hence, ‘B K B P N K O’ is the correct answer.

The logic followed here is:

Logic: (1^st number)² + (3^rd number)² + 1^st number × 3^rd number = 2^nd number.

Now,

(7, 127, 6)

→ (7)² + (6)2 + 7 × 6

→ 49 + 36 + 42 = 127.

(8, 129, 5)

→ (8)2 + (5)2 + 8 × 5

→ 64 + 25 + 40 = 129.

Similarly, for (10, 156, 4)

→ (10)2 + (4)2 + 10 × 4

→ 100 + 16 + 40 = 156.

Hence, the correct answer is "Option 1".

From the given information:

Step 1: S is taller than only two other friends.

             _ > _ > _ > S > _ > _

Step 2: R is shorter than only one friend.

            _ > R > _ > S > _ > _

Step 3: P is shorter than S but taller than Q.

            _ > R > _ > S > P > Q

Step 4: T is shorter than U.

           U > R > T > S > P > Q

From the arrangement, we can see that Q is the shortest among all the friends.

Hence the correct answer is option 4.

Shortcut Trick

Surface area is proportional to the square of the edge length (Area ∝ side²).

Successive percentage formula: x + y + (x × y)/100

Here, x = 50 and y = 50 ⇒ 50 + 50 + (50 × 50)/100

⇒ 100 + 25 = 125%

∴ The correct answer is 125%.

Alternate Method

Given: Let the initial edge length of the cube be a = 10 units.

Formula Used: Total Surface Area (TSA) = 6 × a²

⇒ Initial Surface Area = 6 × 10² = 600 sq. units.

⇒ New Edge length = 10 + 50% of 10 = 10 + 5 = 15 units.

⇒ New Surface Area = 6 × 15² = 6 × 225 = 1350 sq. units.

⇒ Increase in Area = 1350 − 600 = 750 sq. units.

⇒ Percentage Increase = (750 ÷ 600) × 100

⇒ Percentage Increase = 1.25 × 100 = 125%

∴ The correct answer is 125%.

Additional Information

Volume Increase of Cube

If the edge is increased by x%, the volume increases by [(1 + x/100)³ − 1] × 100%.

Diagonal of a Cube

The length of the longest rod that can be placed in a cube is its diagonal, given by d = a√3.

Ratio Method for Area

If side ratio is x : y, then surface area ratio is x² : y² and volume ratio is x³ : y³.

Shortcut Trick Given ratio: (x + z)2 / (y + z)2 = x / y Expanding and cross-multiplying: y(x2 + 2xz + z2) = x(y2 + 2yz + z2) yx2 + 2xyz + yz2 = xy2 + 2xyz + xz2 By canceling 2xyz: yx2 − xy2 = xz2 − yz2 ⇒ xy(x − y) = z2(x − y) Since x ≠ y, we get xy = z2. Given x : a :: a : y ⇒ a2 = xy ⇒ a2 = z2. ∴ The correct answer is Z. Alternate Method Given:

1. (x + z)2 : (y + z)2 = x : y
2. x : a :: a : y (where a > 0, z > 0, x ≠ y) Formula Used: ⇒ If p : q :: r : s, then p/q = r/s ⇒ If a is the mean proportional between x and y, then a2 = xy

Calculations: ⇒ (x + z)2 / (y + z)2 = x / y ⇒ y(x + z)2 = x(y + z)2 ⇒ y(x2 + 2xz + z2) = x(y2 + 2yz + z2) ⇒ x2y + 2xyz + yz2 = xy2 + 2xyz + xz2 ⇒ x2y − xy2 + yz2 − xz2 = 0 ⇒ xy(x − y) − z2(x − y) = 0 ⇒ (xy − z2)(x − y) = 0 ⇒ Since x ≠ y, then (x − y) ≠ 0, ∴ xy − z2 = 0 ⇒ xy = z2 ⇒ From the condition x : a :: a : y, we have a2 = xy ⇒ Substituting xy = z2 into a2 = xy, we get a2 = z2 ⇒ Since a > 0 and z > 0, taking square root on both sides: a = z ∴ The correct answer is Z. Additional Information Mean Proportional The mean proportional between two numbers x and y is given by √(xy). If x, a, y are in continued proportion, then a2 = xy. Ratio and Proportion Basics For a proportion x : a :: b : y, the product of means equals the product of extremes, i.e., ab = xy. Algebraic Identities The square of a binomial (x + z)2 expands to x2 + 2xz + z2, which is essential for simplifying proportional equations.

Shortcut Trick

For a mixed recurring decimal like 0.abc…, the fraction is (Number − Non-repeating part) ÷ (9 for each repeating digit and 0 for each non-repeating digit).

Value = 0.335

Numerator = 335 − 3 = 332

Denominator = 99 (for two repeating digits) followed by 0 (for one non-repeating digit) = 990

∴ The correct answer is 332/990.

Alternate Method

Given: x = 0.3353535...

⇒ Multiply by 10: 10x = 3.353535... — (Eq. 1)

⇒ Multiply Eq. 1 by 100: 1000x = 335.353535... — (Eq. 2)

⇒ Subtract (Eq. 1) from (Eq. 2): 1000x − 10x = 335.3535... − 3.3535...

⇒ 990x = 332

⇒ x = 332/990

∴ The correct answer is 332/990.

Additional Information

Pure Recurring Decimal

If all digits after the decimal repeat (e.g., 0.ab), the fraction is ab/99.

Mixed Recurring Decimal

If some digits are non-repeating (e.g., 0.abc), the fraction is (abc − a)/990.

Rational Numbers

Numbers that can be expressed as P/Q where P, Q are integers and Q ≠ 0. All recurring decimals are rational.

Shortcut Trick

For a number to be divisible by 33, it must be divisible by both 3 and 11.

Divisibility by 3: Sum of digits must be a multiple of 3.

Divisibility by 11: Difference between sum of digits at odd places and even places must be 0 or a multiple of 11.

Checking 25080: Sum = 2+5+0+8+0 = 15 (Divisible by 3). Alternating sum = (2+0+0) − (5+8) = 2 − 13 = −11 (Divisible by 11).

∴ The correct answer is 25080.

Alternate Method

Given: Number must be divisible by 33.

Formula Used: Divisibility rules for composite numbers (33 = 3 × 11).

Calculations:

Option 1: 25080

⇒ Sum of digits = 2 + 5 + 0 + 8 + 0 = 15. Since 15 is divisible by 3, 25080 is divisible by 3.

⇒ Diff of alternating digits = (2 + 0 + 0) − (5 + 8) = 2 − 13 = −11. Since −11 is divisible by 11, 25080 is divisible by 11.

Option 2: 19679

⇒ Sum of digits = 1 + 9 + 6 + 7 + 9 = 32. Not divisible by 3.

Option 3: 73205

⇒ Sum of digits = 7 + 3 + 2 + 0 + 5 = 17. Not divisible by 3.

Option 4: 27441

⇒ Sum of digits = 2 + 7 + 4 + 4 + 1 = 18. (Divisible by 3).

⇒ Diff of alternating digits = (2 + 4 + 1) − (7 + 4) = 7 − 11 = −4. Not divisible by 11.

∴ The correct answer is 25080.

Additional Information

Divisibility by 11

A number is divisible by 11 if the difference of the sum of digits in odd positions and the sum of digits in even positions is 0 or a multiple of 11.

Divisibility by 3

A number is divisible by 3 if the sum of its digits is divisible by 3.

Composite Divisibility

If a number is divisible by two co-prime numbers a and b, then it is also divisible by their product (a × b).

Shortcut Trick

The sum of all interior angles of a quadrilateral is always 360°.

Sum of three given angles = 110° + 55° + 125° = 290°.

Fourth angle = 360° − 290° = 70°.

∴ The correct answer is 70°.

Alternate Method

Given:

Three angles of a quadrilateral are 110°, 55°, and 125°.

Let the fourth angle be x.

Formula Used:

Sum of interior angles of a quadrilateral = (n − 2) × 180° = (4 − 2) × 180° = 360°

Calculations:

⇒ Angle A + Angle B + Angle C + Angle D = 360°

⇒ 110° + 55° + 125° + x = 360°

⇒ 290° + x = 360°

⇒ x = 360° − 290°

⇒ x = 70°

Option Analysis:

⇒ Option 1 (60°): If the fourth angle is 60°, the sum of angles would be 290° + 60° = 350° ≠ 360°. Thus, it is incorrect.

⇒ Option 2 (90°): If the fourth angle is 90°, the sum of angles would be 290° + 90° = 380° ≠ 360°. Thus, it is incorrect.

⇒ Option 4 (110°): If the fourth angle is 110°, the sum of angles would be 290° + 110° = 400° ≠ 360°. Thus, it is incorrect.

∴ The correct answer is 70°.

Additional Information

Sum of Interior Angles of a Polygon

For any n-sided polygon, the sum of all interior angles is given by the formula (n − 2) × 180°.

Sum of Exterior Angles

The sum of the exterior angles of any convex polygon (including a quadrilateral) is always 360°.

Cyclic Quadrilateral Property

In a cyclic quadrilateral, the sum of opposite interior angles is always equal to 180°.

Shortcut Trick

Check options: If Raju's present age is 38 years.

Age after 30 years = 38 + 30 = 68 years.

Age 4 years ago = 38 − 4 = 34 years.

Condition: 68 = 2 × 34 (True).

∴ The correct answer is 38 years.

Alternate Method

Let Raju's present age be x years.

Age after 30 years = x + 30

Age 4 years ago = x − 4

According to the question:

⇒ x + 30 = 2 × (x − 4)

⇒ x + 30 = 2x − 8

⇒ 2x − x = 30 + 8

⇒ x = 38

∴ The correct answer is 38 years.

Additional Information

Linear Equations in Ages

Most age problems can be solved by assuming the present age as 'x' and forming an equation based on past or future conditions.

Age Ratio Property

The difference between the ages of two people remains constant throughout their lives, regardless of the number of years passed.

Shortcut Trick

For any set of numbers, the product of HCF and LCM is NOT simply the product of the numbers if there are more than two numbers.

HCF of (4, 20, 28) → 4 is the largest number dividing all.

LCM of (4, 20, 28) → 4 × 5 × 7 = 140.

Product = 4 × 140 = 560.

∴ The correct answer is 560.

Alternate Method

Given: Numbers are 4, 20, and 28.

Prime Factorization:

⇒ 4 = 2²

⇒ 20 = 2² × 5¹

⇒ 28 = 2² × 7¹

Calculations:

⇒ HCF (Highest Common Factor) = 2² = 4

⇒ LCM (Least Common Multiple) = 2² × 5¹ × 7¹ = 4 × 5 × 7 = 140

⇒ Product of HCF and LCM = 4 × 140

⇒ Product = 560

∴ The correct answer is 560.

Additional Information

HCF and LCM Property for Two Numbers

For any two numbers A and B, HCF(A, B) × LCM(A, B) = A × B. This property does not necessarily apply to three or more numbers.

Definition of HCF

The Highest Common Factor is the product of the lowest powers of all common prime factors.

Definition of LCM

The Least Common Multiple is the product of the highest powers of all prime factors involved in the numbers.

Shortcut Trick

Given Slant height (l) = 28 cm and Radius (r) = 21 cm.

Using the ratio of sides (r : l) = 21 : 28 = 3 : 4.

Height ratio factor = √(4² − 3²) = √7. Actual Height (h) = 7 × √7 = 7√7 cm.

Volume = 1/3 × 22/7 × 21 × 21 × 7√7 = 22 × 21 × 7√7 = 3234√7 cm³.

∴ The correct answer is 3234√7 cm³.

Alternate Method

Given:

Radius (r) of the cone = 21 cm

Slant height (l) of the cone = 28 cm

Formula Used:

1. Slant height relation: l² = r² + h²
2. Volume of cone = (1/3)πr²h

Calculations:

⇒ h² = l² − r²

⇒ h² = 28² − 21²

⇒ h² = (28 − 21)(28 + 21) = 7 × 49

⇒ Height (h) = √(7 × 49) = 7√7 cm

⇒ Volume (V) = (1/3) × (22/7) × 21 × 21 × 7√7

⇒ V = (1/3) × 22 × 3 × 21 × 7√7

⇒ V = 22 × 21 × 7√7

⇒ V = 462 × 7√7

⇒ V = 3234√7 cm³

∴ The correct answer is 3234√7 cm³.

Additional Information

Curved Surface Area (CSA)

The lateral area of a cone is given by πrl, where r is the radius and l is the slant height.

Total Surface Area (TSA)

The total area includes the base: TSA = πrl + πr² = πr(l + r).

Slant Height Calculation

For a right circular cone, the relation between height (h), radius (r), and slant height (l) is always governed by the Pythagoras Theorem: l = √(r² + h²).

Given:

Calculation:

⇒ Number of students passed from U, T, P, and Q = 70 + 90 + 120 + 100

⇒ Number of students passed from U, T, P, and Q = 380

⇒ Number of students passed from S and R = 85 + 60 = 145

Difference = 380 – 145 = 235

Therefore, Students passed from institutions U, T, P, and Q together is 235 more than that institutes S and R together.

Hence, the correct answer is option 3).

Shortcut Trick

Total sum of all interior angles of a quadrilateral is always 360°.

Sum of the three equal angles = 360° − 120° = 240°.

Measure of each of the three equal angles = 240° ÷ 3 = 80°.

∴ The correct answer is 80°.

Alternate Method

Given:

Measure of one angle = 120°

Measure of the other three angles = Equal (Let each be x)

Formula Used:

The sum of the interior angles of a quadrilateral is 360°.

 

 

Calculations:

Let the measure of each of the three equal angles be x.

According to the angle sum property of a quadrilateral:

⇒ 120° + x + x + x = 360°

⇒ 120° + 3x = 360°

⇒ 3x = 360° − 120°

⇒ 3x = 240°

⇒ x = 240° ÷ 3

⇒ x = 80°

∴ The correct answer is 80°.

Additional Information

Angle Sum Property of Polygons

The sum of interior angles of any polygon with n sides is calculated as (n − 2) × 180°.

Cyclic Quadrilateral

In a cyclic quadrilateral (vertices on a circle), the sum of opposite interior angles is always 180°.

Regular Quadrilateral

A quadrilateral with all sides and all angles equal is called a Square, where each interior angle is 90°.

Shortcut Trick

Selling Price (SP) = Profit × (100 + Profit%) ÷ Profit%

⇒ SP = 1840 × (123 ÷ 23) = ₹9,840

Marked Price (MP) = SP × 100 ÷ (100 − Discount%)

⇒ MP = 9840 × (100 ÷ 82) = ₹12,000

∴ The correct answer is ₹12,000.

Alternate Method

Given:

Discount = 18%

Profit = 23%

Gain (Profit amount) = ₹1,840

Formula Used:

Profit = (Profit% ÷ 100) × CP

SP = CP + Profit

SP = MP × (100 − Discount%) ÷ 100

Calculations:

⇒ 23% of CP = 1840

⇒ CP = (1840 × 100) ÷ 23 = ₹8,000

⇒ SP = CP + Profit = 8000 + 1840 = ₹9,840

⇒ We know that SP = MP × (100 − 18) ÷ 100

⇒ 9840 = MP × (82 ÷ 100)

⇒ 9840 = 0.82 × MP

⇒ MP = 9840 ÷ 0.82

⇒ MP = ₹12,000

∴ The correct answer is ₹12,000.

Additional Information

Relation between CP and MP

The ratio of Cost Price to Marked Price can be directly found using: CP/MP = (100 − Discount%) ÷ (100 + Profit%).

Successive Discounts

If two successive discounts of a% and b% are given, the equivalent single discount is (a + b − a × b ÷ 100)%.

Dishonest Dealer

When a dealer sells goods at CP but uses a false weight, the Profit% = (Error ÷ True Value − Error) × 100.

Given:

Imports in 2009 = 420 crore

Calculation:

Let the export for the company in 2009 be x.

According to the ratio,

⇒ $\frac{420}{x}=1.4$

⇒ x = $\frac{420}{1.4}$

⇒ x = 300

Therefore, the export for the company in 2009 was 300 crore.

Shortcut Trick

Put A = 45° to verify the identity quickly.

m = cot 45° + cos 45° = 1 + 1/√2 and n = cot 45° − cos 45° = 1 − 1/√2

m² − n² = (m + n)(m − n) = (2)(2/√2) = 2√2 ⇒ (m² − n²)² = (2√2)² = 8

Check 16mn = 16(1 − 1/2) = 16(1/2) = 8. Since 8 = 8, the relation holds.

∴ The correct answer is (m² − n²)² = 16 mn.

Alternate Method

Given: m = cot A + cos A and n = cot A − cos A

Formula Used: (a + b)(a − b) = a² − b²

⇒ m + n = 2 cot A and m − n = 2 cos A

⇒ m² − n² = (2 cot A)(2 cos A) = 4 cot A cos A

⇒ (m² − n²)² = 16 cot² A cos² A

⇒ mn = (cot A + cos A)(cot A − cos A) = cot² A − cos² A

⇒ mn = (cos² A / sin² A) − cos² A = cos² A (1/sin² A − 1) = cos² A ((1 − sin² A)/sin² A)

⇒ mn = cos² A (cos² A / sin² A) = cos² A cot² A

⇒ 16 mn = 16 cot² A cos² A

⇒ Comparing both sides, (m² − n²)² = 16 mn

∴ The correct answer is (m² − n²)² = 16 mn.

Additional Information

Trigonometric Identity for cot and cos

A very common identity used in competitive exams: cot² A − cos² A = cot² A × cos² A.

Tan and Sec Relation

If tan A + sin A = m and tan A − sin A = n, then the same result holds: (m² − n²)² = 16 mn.

Value Substitution Method

For identities involving cot, tan, sin, or cos, substituting standard angles like 45° or 30° is often the fastest way to eliminate wrong options.

Shortcut Trick

For a hollow cylinder, Curved Surface Area (CSA) = 2πh(R + r).

Total Surface Area (TSA) = CSA + 2 × Area of Base Ring = 2πh(R + r) + 2π(R² − r²).

Ratio = 2πh(R + r) ÷ [2π(R + r)(h + R − r)] = h ÷ (h + R − r).

∴ The correct answer is h : (h + R - r).

Alternate Method

Given: Height = h, Outer Radius = R, Inner Radius = r.

Formula Used:

⇒ Curved Surface Area (CSA) = 2πRh + 2πrh = 2πh(R + r)

⇒ Total Surface Area (TSA) = CSA + 2 × Area of circular ends = 2πh(R + r) + 2π(R² − r²)

Calculations:

⇒ Ratio = CSA ÷ TSA

⇒ Ratio = [2πh(R + r)] ÷ [2πh(R + r) + 2π(R − r)(R + r)]

⇒ Ratio = [2π(R + r) × h] ÷ [2π(R + r) × (h + R − r)]

⇒ Ratio = h ÷ (h + R − r)

∴ The correct answer is h : (h + R - r).

Additional Information

Volume of Hollow Cylinder

The amount of material in a hollow cylinder is given by V = πh(R² − r²).

Lateral Surface Area

For a solid cylinder, CSA = 2πrh, whereas for a hollow cylinder, it includes both inner and outer surfaces: 2πh(R + r).

Base Area of Ring

The area of the cross-section (ring) is Area = π(R² − r²).

Shortcut Trick

Recognize the perfect square trinomial form: a² + 2ab + b² = (a + b)².

Identify a = 5m and b = 4n, then 25m² + 40mn + 16n² → (5m + 4n)².

Substitute m = −9 and n = 13: (5 × (−9) + 4 × 13)² → (−45 + 52)².

Calculated value: 7² = 49.

∴ The correct answer is 49.

Alternate Method

Given: m = −9 and n = 13.

Formula Used: (a + b)² = a² + 2ab + b²

⇒ The given expression is 25m² + 40mn + 16n².

⇒ This can be rewritten as (5m)² + 2 × (5m) × (4n) + (4n)².

⇒ Applying the algebraic identity, we get (5m + 4n)².

⇒ Substituting the values: (5 × (−9) + 4 × 13)²

⇒ (−45 + 52)²

⇒ (7)² = 49

∴ The correct answer is 49.

Additional Information

Perfect Square Identities

(a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b² are fundamental quadratic identities used to simplify complex algebraic terms.

Product of Sum and Difference

The identity a² − b² = (a − b)(a + b) is helpful for factoring expressions that are a difference of two squares.

Substitution Strategy

In quantitative aptitude, always factorize or condense an algebraic expression before substituting variable values to minimize calculation errors.

Shortcut Trick

Weighted Average method: Average Speed = (s₁×t₁ + s₂×t₂) ÷ (t₁ + t₂)

Average Speed = (30 × 6 + 45 × 4) ÷ (6 + 4)

Average Speed = (180 + 180) ÷ 10 = 360 ÷ 10

Average Speed = 36 km/h.

∴ The correct answer is 36 km/h.

Alternate Method

Given:

Speed 1 (s₁) = 30 km/h, Time 1 (t₁) = 6 hours

Speed 2 (s₂) = 45 km/h, Time 2 (t₂) = 4 hours

Formula Used:

Average Speed = Total Distance ÷ Total Time

Distance = Speed × Time

Calculations:

⇒ Distance 1 = 30 × 6 = 180 km

⇒ Distance 2 = 45 × 4 = 180 km

⇒ Total Distance = 180 + 180 = 360 km

⇒ Total Time = 6 + 4 = 10 hours

⇒ Average Speed = 360 ÷ 10 = 36 km/h

∴ The correct answer is 36 km/h.

Additional Information

Average Speed for Equal Distances

If a journey covers two equal distances at speeds 'a' and 'b', the average speed is given by (2ab) ÷ (a + b).

Unit Conversion

To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Relative Speed

When two objects move in the same direction, relative speed is (s₁ − s₂). In opposite directions, it is (s₁ + s₂).

Given:

(3.7)3 - 3 × (3.7)2 × (0.7) + 3(3.7) × (0.7)2 - (0.7)³

Concept Used:

(a – b)³ = a³ – b³ – 3a²b + 3ab²

Calculation:

For the given expression, comparing it with the formula of (a – b)³,

⇒ (3.7)3 - 3 × (3.7)2 × (0.7) + 3(3.7) × (0.7)2 - (0.7)³

⇒ a = 3.7 and b = 0.7

⇒ (3.7)3 - 3 × (3.7)2 × (0.7) + 3(3.7) × (0.7)2 - (0.7)³ = (3.7 – 0.7)³

⇒ (3.7 – 0.7)³ = 3³ = 27

Therefore, the required value is 27.

Shortcut Trick

When two objects start at the same time and meet, Time (t) is constant.

Ratio of Speeds = 85 : 105 = 17 : 21.

Since Time is constant, Distance ratio = Speed ratio = 17 : 21.

Difference in distance units = 21 − 17 = 4 units → 200 km (Given).

Total distance (A to B) = (17 + 21) units = 38 units = 38 × (200 ÷ 4) = 38 × 50 = 1900 km.

∴ The correct answer is 1900 km.

Alternate Method

Given: Speed of Train A = 85 kmph, Speed of Train B = 105 kmph, Difference in distance = 200 km.

Formula: Distance = Speed × Time

⇒ Let Time taken to meet be t hours.

⇒ Distance by Train A (D_A) = 85 × t

⇒ Distance by Train B (D_B) = 105 × t

⇒ Difference: D_B − D_A = 105t − 85t = 200

⇒ 20t = 200 ⇒ t = 10 hours.

⇒ Total Distance = D_A + D_B = (85 + 105) × 10

⇒ Total Distance = 190 × 10 = 1900 km.

∴ The correct answer is 1900 km.

Additional Information

Relative Speed

When two objects move towards each other, their Relative Speed is the sum of their individual speeds (S₁ + S₂).

Proportionality in Motion

If time is constant, Distance is directly proportional to Speed (D₁/D₂ = S₁/S₂).

Meeting Point Distance

Difference in distance = (S_large − S_small) × Time to meet. Total distance = (S₁ + S₂) × Time to meet.

Given:

$40 - [3 - { 4 - (6 - \overline {6 - 4} )}]$

Concept Used:

Follow BODMAS rule to solve this question, as per the order given below,

Calculation:

⇒ $40 - [3 - { 4 - (6 - \overline {6 - 4} )}]$

⇒ 40 – [3 – {4 – (6 – 2)]

⇒ 40 – [3 – {4 – 4}]

⇒ 40 – 3 = 37

Therefore, the value of the given expression is 37.

Shortcut Trick

Total Amount Paid = ₹4,000 + ₹4,350 = ₹8,350

Total Interest = Total Paid − Principal = 8,350 − 7,000 = ₹1,350

Total Product (Principal × Time) = (7,000 × 3) + (3,000 × 2) = 21,000 + 6,000 = 27,000

Rate (R) = (Total Interest × 100) ÷ Total Product

R = (1,350 × 100) ÷ 27,000 = 5%

∴ The correct option is C.

Alternate Method

Given:

Initial Principal (P₁) = ₹7,000

Repayment after 3 years = ₹4,000

New Principal for next 2 years (P₂) = 7,000 − 4,000 = ₹3,000

Total Time = 5 years (3 years + 2 years)

Final Settlement Payment = ₹4,350

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Year 0 Year 3 Year 5

P = ₹7,000

P = ₹3,000 Repay ₹4,000

Final: ₹4,350

Calculations:

⇒ Total Payment = 4,000 + 4,350 = ₹8,350

⇒ Total Interest = 8,350 − 7,000 = ₹1,350

⇒ Total Interest = (P₁ × R × T₁)/100 + (P₂ × R × T₂)/100

⇒ 1,350 = (7,000 × R × 3)/100 + (3,000 × R × 2)/100

⇒ 1,350 = 210R + 60R

⇒ 1,350 = 270R

⇒ R = 1,350 ÷ 270

⇒ R = 5%

∴ The correct option is C.

Additional Information

Simple Interest on Installments

When parts of the principal are repaid, the interest for the subsequent period is calculated only on the remaining balance of the principal.

Effective Principal Method

Total Interest = (Sum of [Principal × Time for each period] × Rate) ÷ 100. This is useful for multiple repayments.

Difference between SI and CI

In Simple Interest, the principal remains constant unless explicitly repaid. In Compound Interest, interest is added to the principal at the end of each period.

Shortcut Trick

Calculate the Discriminant (D) using D = b² − 4ac.

Here, D = (4√3)² − 4(1)(3) = 48 − 12 = 36.

Since D > 0, the roots are unequal.

Since the coefficient 'b' is irrational (4√3) and √D (6) is rational, the roots will be irrational.

∴ The correct answer is irrational and unequal.

Alternate Method

Given Equation: x² + 4√3x + 3 = 0

Formula: The nature of roots is determined by D = b² − 4ac and roots are x = [−b ± √D] / 2a.

⇒ Comparing with ax² + bx + c = 0, we get a = 1, b = 4√3, c = 3.

⇒ D = (4√3)² − 4 × 1 × 3

⇒ D = (16 × 3) − 12 = 48 − 12 = 36

⇒ x = [−4√3 ± √36] / (2 × 1)

⇒ x = [−4√3 ± 6] / 2

⇒ Root 1 = −2√3 + 3

⇒ Root 2 = −2√3 − 3

⇒ Since √3 is a non-terminating non-repeating decimal, both roots are irrational and clearly unequal.

∴ The correct answer is irrational and unequal.

Additional Information

Discriminant and Nature of Roots

If D > 0, roots are real and unequal. If D = 0, roots are real and equal. If D < 0, roots are imaginary.

Rational vs Irrational Roots

For rational coefficients, if D is a perfect square, roots are rational. If D is not a perfect square, roots are irrational and occur in conjugate pairs.

Irrational Coefficients

If any coefficient (a, b, or c) is irrational, the roots can be irrational even if D is a perfect square. Always use the quadratic formula to check.

Shortcut Trick

Total Work (LCM of 4 and 6) = 12 units.

Efficiency: Sony = 3, Mary = 2.

In 2 days (Mary + Sony): 2 + 3 = 5 units.

In 4 days: 5 × 2 = 10 units. Remaining: 12 − 10 = 2 units.

Day 5: Mary completes remaining 2 units (2 ÷ 2 = 1 day).

∴ The correct answer is 5 days.

Alternate Method

Given: Time taken by Sony = 4 days; Time taken by Mary = 6 days.

Calculations:

⇒ Total work = LCM(4, 6) = 12 units.

⇒ Mary starts on Day 1: Work done = 2 units.

⇒ Sony works on Day 2: Work done = 3 units.

⇒ Total work in 1 cycle (2 days) = 2 + 3 = 5 units.

⇒ Number of complete cycles = 12 ÷ 5 = 2 cycles (with remainder).

⇒ Work done in 2 cycles (4 days) = 2 × 5 = 10 units.

⇒ Remaining work = 12 − 10 = 2 units.

⇒ On Day 5, it is Mary's turn. Time taken for remaining work = 2 ÷ 2 = 1 day.

⇒ Total time = 4 + 1 = 5 days.

∴ The correct answer is 5 days.

Additional Information

Alternate Day Concept

In alternate work problems, identify the repeating cycle and calculate the total work done per cycle before finding the remaining work for the next individual.

Efficiency and Time

Efficiency is inversely proportional to time: Efficiency = Total Work ÷ Time.

Work & Wages

Wages are generally distributed in the ratio of work done or efficiency when the duration of work is the same for all.

Shortcut Trick

Sum of present ages = 58 + 5 + 5 = 68 years.

Difference (B − 8) − (A + 8) = 16 ⇒ B − A = 32 years.

A = (Sum − Diff) ÷ 2 = (68 − 32) ÷ 2 = 18 years.

B = (Sum + Diff) ÷ 2 = (68 + 32) ÷ 2 = 50 years.

Ratio A : B = 18 : 50 = 9 : 25.

∴ The correct answer is 9 : 25.

Alternate Method

Let the present ages of A and B be A and B respectively.

According to first condition:

⇒ (A − 5) + (B − 5) = 58

⇒ A + B − 10 = 58

⇒ A + B = 68 --- (eq i)

According to second condition:

⇒ (B − 8) − (A + 8) = 16

⇒ B − 8 − A − 8 = 16

⇒ B − A = 32 --- (eq ii)

Adding (eq i) and (eq ii):

⇒ 2B = 100 ⇒ B = 50

Subtracting (eq ii) from (eq i):

⇒ 2A = 36 ⇒ A = 18

⇒ Ratio A : B = 18 : 50 = 9 : 25

∴ The correct answer is 9 : 25.

Additional Information

Age Sum Property

If the sum of ages of 'n' people is S now, then 'x' years ago the sum was S − (n × x).

Age Difference Constant

The difference between the ages of two individuals remains constant at any point in time.

Ratio and Proportion

To find the ratio of two quantities, they must be in the same unit and simplified to their lowest terms.

Shortcut Trick

Total Cost Price (CP) of 100 apples = ₹700 ⇒ CP of 1 apple = ₹7.

Selling Price (SP) of 12 apples = ₹96 ⇒ SP of 1 apple = 96 ÷ 12 = ₹8.

Profit per apple = 8 − 7 = ₹1.

Profit percentage = (Profit ÷ CP) × 100 = (1 ÷ 7) × 100 = 14²/₇%.

∴ The correct answer is 14(2)/(7) %.

Alternate Method

Given: CP of 100 apples = ₹700, SP of 12 apples (one dozen) = ₹96. Formulas: Profit = SP − CP | Profit% = (Profit ÷ CP) × 100.

⇒ CP of 100 apples = ₹700. ⇒ SP of 12 apples = ₹96. ⇒ SP of 1 apple = 96 ÷ 12 = ₹8. ⇒ SP of 100 apples = 8 × 100 = ₹800. ⇒ Total Profit = 800 − 700 = ₹100. ⇒ Profit % = (100 ÷ 700) × 100 = 100 ÷ 7 = 14²/₇%.

∴ The correct answer is 14(2)/(7) %.

Additional Information

Fraction to Percentage Conversion

The fraction 1/7 is equal to 14.28% or 14²/₇% in mixed fraction form.

Profit and Loss Basics

Profit occurs when Selling Price is greater than Cost Price. The percentage is always calculated on the Cost Price unless specified otherwise.

Shortcut Trick

Present ages of A and B are 7x and 3x.

According to condition: (7x − 4) / (3x + 4) = 2 / 1

⇒ 7x − 4 = 6x + 8 ⇒ x = 12.

Difference required = (7x + 4) − (3x − 4) = 4x + 8.

⇒ 4(12) + 8 = 48 + 8 = 56 years.

∴ The correct answer is 56 years.

Alternate Method

Given: Present age ratio A : B = 7 : 3.

Formula Used: Ratio and linear equation method.

Let the present ages be 7x and 3x.

A's age 4 years ago = 7x − 4.

B's age 4 years hence = 3x + 4.

⇒ (7x − 4) / (3x + 4) = 2 / 1

⇒ 7x − 4 = 2 × (3x + 4)

⇒ 7x − 4 = 6x + 8

⇒ 7x − 6x = 8 + 4

⇒ x = 12.

A's age 4 years hence = 7(12) + 4 = 84 + 4 = 88 years.

B's age 4 years ago = 3(12) − 4 = 36 − 4 = 32 years.

⇒ Difference = 88 − 32 = 56 years.

∴ The correct answer is 56 years.

Additional Information

Age Ratio Concept

If the ratio of ages is a : b, then actual ages are ax and bx where x is the common multiplier.

Time Shift Rule

For a person with present age P, age after 'n' years is P + n and age 'n' years ago was P − n.

Difference Invariance

The difference between the ages of two people remains constant throughout their lives.

Given:

22x - 10 × 2x + 16 = 0

Calculation:

Splitting the middle terms to form factors,

⇒ 22x – 8.2x – 2.2^x + 16 = 0

⇒ 2^x(2^x – 8) – 2(2^x – 8) = 0

⇒ (2^x – 2)(2^x – 8) = 0

Now, we have 2^x = 2 and 2^x = 8

⇒ 2^x = 2¹ and 2^x = 2³

Comparing both values, we get x = 1 or x = 3.

Therefore, the roots of the equation are 1 and 3.

Shortcut Trick Use the Empirical Formula: Mode = 3 × Median − 2 × Mean Given Median = 55 and Mean = 58 Mode = 3 × 55 − 2 × 58 = 165 − 116 = 49 ∴ The correct answer is 49.

Alternate Method Given: Median of the observations = 55 Arithmetic Mean of the observations = 58 Formula Used: The relationship between Mean, Median, and Mode for a moderately skewed distribution is: Mode = 3(Median) − 2(Mean)

Calculations: ⇒ Mode = (3 × 55) − (2 × 58) ⇒ Mode = 165 − 116 ⇒ Mode = 49 ∴ The correct answer is 49.

Additional Information Empirical Relationship For a frequency distribution, the Mode is approximately equal to the difference between three times the Median and twice the Mean. Symmetrical Distribution If the distribution is perfectly symmetrical, then Mean = Median = Mode. Skewness Property In a negatively skewed distribution, Mean < Median < Mode. In this specific question, Mode (49) < Median (55) < Mean (58), indicating the distribution is positively skewed.

The correct answer is It has no unit.

Key Points

• Magnification has no units because it is a length ratio.
• Magnification is the increase (or reduction) in the size of an optical system-produced picture relative to its actual size.
• Although angular magnification is seldom encountered, linear magnification is the most often used type of magnification.
• the standard representation of power as a measure of magnification.
• Calculating the overall magnification of an image you are looking at using a microscope is actually quite simple.

Additional Information

• Dioptre
• The optical power of a lens or curved mirror is measured in units of 1 dioptre, which is equal to the reciprocal of the focal length ($f$).
• In metres, the focal length is expressed.
• The dioptre, which has a focal length of one metre and is represented by the symbol $D$, is the SI unit of lens power.
• Newton
• ​In the International System of Units (SI units), the letter N stands for newton, an absolute measure of force. It is described as the amount of force required to accelerate a mass of one kilogramme by one metre per second.
• Newton was given its name in honour of Sir Isaac Newton, whose second rule of motion defines the modifications that a force might make to a body's motion.
• Centimeter
• Centimeters, which are metric units of measurement, are used to determine an object's length.The abbreviation is cm.
• 100 centimetres make to a metre.
• The unit of measure changes to cm² when determining an object's surface area.
• The measurement unit changes to cm³ for determining an object's volume.

The correct answer is an insoluble ionic solid.

Key Points

• When cations and anions in an aqueous solution come together to produce an insoluble ionic solid called a precipitate, this process is known as a precipitation reaction.
• Whether or not such a reaction occurs can be determined using the solubility principles for typical ionic solids.
• Before calculating the state of the products and creating a net ionic equation, one must refer to the solubility criteria because not all aqueous reactions produce precipitates.

 Additional Information

• Precipitation reactions
• The word "precipitation reaction" is defined as a "chemical reaction occurring in an aqueous solution when two ionic bonds join, resulting in the production of an insoluble salt." Precipitates are the insolusalts created during precipitation reactions.
• Properties of Precipitates and Precipitation reaction
• ​In ionic or aqueous solutions, the precipitation reaction takes place.
• Ions present in the aqueous solutions interact and react to generate the product.
• Precipitates that are insoluble in aqueous solutions are the byproducts of the precipitation reaction.
• Since the ions actively participate in the reaction and produce the product, precipitation reactions are also referred to as ionic reactions.
• Temperature, solution concentration, buffer solution, and other factors all affect how these reactions behave.
• Applications of Precipitation reaction
• ​The precipitation reaction aids in identifying a specific element that is present in the supplied solution. When a chemical is introduced to solutions, these reactions also keep an eye on the precipitate that results. These are employed in the process of removing magnesium from saltwater. The responses between antigens and antibodies occur in the human body as well.

The correct answer is option c)+6

Given:

Convex mirror whose $u=-21cm$,$v=+7cm$

Formula:

Mirror equation: ${1 \over f}={1 \over u}+{1 \over v}$

Calculations:

${1 \over f}={1 \over -21}+{1 \over 7}$

$={7-21 \over -21*7}$

=${2 \over 21}$

Now for object distance to be $u=-14cm$ we have the image distance:

${2 \over 21}={1 \over -14}+{1 \over v}$

${1 \over v}={2 \over 21}+{1 \over 14}$

= 7/42

=1/6

Therefore we have the image distance as $v=+6cm$

The correct answer is "Region a".

Key Points

• Collecting Duct System
• ​Connecting tubules and collecting ducts make up the collecting duct system.
• Arcades that drain several nephrons are created when connecting tubules connect the distal convoluted tubules to the cortical collecting ducts. Six nephrons on average drain into a collecting duct.
• Collecting ducts descend into the brain and medulla before successively fusing close to the inner medullary region. As the papillary tip approaches, convergent papillary ducts form about 20 large ducts that empty into the renal pelvis.
• The two cell types that make up the collecting ducts are principal and intercalated cells.

Additional Information

• Nephron
• The nephron is the basic anatomical and functional unit of the kidney.
• They are tiny structures made up of renal tubules and corpuscles. The English term "nephron" derives from the Greek word "nephros," which signifies kidney. There are millions of nephrons in each kidney of a human.
• Nephrons come in two different varieties: cortical and juxtamedullary.
• Functions of Nephron
• The primary functions of nephrons are to filter the blood of all waste materials, including solid wastes and extra water, as well as to reabsorb, secrete, and excrete a variety of substances.
• The tiny molecules are transported into the glomerular capsules and proceed through a twisting network of tubules when the blood is forced through the glomerulus under high pressure.
• The cell found in each tube absorbs various molecules, with the exception of glucose, water, and other advantageous compounds known as ultrafiltrate. More water is removed from the ultrafiltrate before it leaves the nephrons as the ultrafiltrate molecules become increasingly hypertonic as they go down the tubules.

The correct answer is "Embryo".

Key Points

• Seeds contain an embryo that, when nurtured under ideal circumstances, matures into a seedling. The endosperm found inside seeds aids in the formation and expansion of the embryo.
• It has stored nutrition, starch, which enables the embryo's quick growth. Oil is also stored there.
• A seedling is a juvenile sporophyte that has emerged from a plant embryo. The germination of the seed initiates the growth of the seedling.
• The radicle, hypocotyl, and cotyledons are the three primary structural components of a typical early seedling.

Additional Information

• Endosperm- ​The majority of angiosperm seeds have endosperm. The growing embryo receives nutrients from it. Dicotyledons have fleshy cotyledons in place of the endosperm. Endosperm remains and stores nourishment in mature seeds of monocotyledons. In addition to being rich in carbohydrates, the endosperm tissue also contains proteins and lipids.
• Cotyledons- ​The substantial portion of the embryo found inside the seed is referred to as a cotyledon. When the seed germinates, the earliest and most delicate leaf appears. Given that it supplies nutrients to the many components of an embryo, it is also known as the storage unit of seed.
• Seed coat- ​The interior components of a seed are shielded by its coat. Two layers comprise the seed coat. Testa, the term for the thick outer layer, Tegmen, is the name of the innermost, thin layer. The seed is shielded from water and sunlight by a thick seed coat.

The correct answer is Cl2 gas at the anode and H2 gas at the cathode.

Key Points

• H₂ and Cl₂ gas are released when NaCl is electrolyzed. Cl₂ gas is released from the anode and H₂ gas from the cathode.
• Concentration solution of NaCl
• ​NaOH & H₂      →   at Cathode
• Cl₂   →   at Anode
• Dilute solution of NaCl
• ​NaOH  →   at Cathode
• Cl₂    →   at Anode
• The electrolysis of molten sodium chloride results in the production of chlorine gas at the anode.

Additional Information

• The chloride and hydroxide negative ions are drawn to the positively charged anode. While it is simpler to convert hydroxide ions to oxygen than chloride ions to chlorine, chloride ions arrive at the anode in far greater quantities.
• Since the cathode is the negative electrode, hydrogen gas is liberated there and is drawn to the cathode, while oxygen, which is the negative ion, is drawn to the positive electrode anode.
• Electrons from the external circuit interact with steam at the cathode to create hydrogen gas and negatively charged oxygen ions. The oxygen ions cross the solid ceramic membrane, where they react with the anode to produce oxygen gas and electrons for the external circuit.

The correct answer is a White precipitate of silver chloride is produced.

Key Points

• When silver nitrate solution is combined with sodium chloride solution, a white precipitate of silver chloride is generated in addition to the sodium nitrate solution.
• Chemical reaction equation:
• ​$AgNO$₃ $(aq)$ $+$ $NaCl$ $(aq)$ → $AgCl(aq)$ $+ NaNO$₃ $(aq)$
• It is an illustration of a double displacement reaction.

Additional Information

• Double Displacement Reaction
• ​Chemical reactions known as double displacement reactions occur when the reactant ions move around to create new products. Precipitate production often happens as a result of a double displacement process. Covalent or ionic chemical bonds may be present between the reactant.
• For instance, a white precipitate of barium sulphate quickly forms when a solution of barium chloride and sodium sulphate is combined. These are ionic-based reactions. When the reactants are dissolved in water, they turn into ions, and when ions exchange in the solution, a product molecule is created.
• $Ba$²⁺ $(aq) + 2Cl$^- $(aq) + 2Na$⁺ $(aq) + SO$ ₄ ^2- $(aq)$ → 

 $Ba$²⁺ $(aq) + SO$₄ ^2- $(aq) + 2Na$⁺ $(aq) + 2Cl$^- $(aq)$

The correct answer is 1.6cm.

Given:

$u=-45cm,f=-30cm$

$hi=4cm$ of a needle placed in a concave lens.

Formula:

Lens formula: ${1 \over f}={1 \over v}-{1 \over u}$

Calculations:

${1 \over -30}={1 \over v}-{1 \over -45}$

${ 1 \over v}=-({1\over 45}+{1\over30})$

${1 \over v}=-{45+30\over1350}=-{75\over1350}=-{1\over18}$

Therefore, $v=-18cm$ for a concave lens.

Thus we have the height of needle is:

${hi\over ho}={v\over u}$

$hi={v*ho\over u}$

$hi={-18*4\over-45}={72\over45}=1.6cm$

Therefore, the height of the image formed by the needle is 1.6cm.

The correct answer is Sunlight and chlorophyll.

Key Points:

• The following is a basic general equation for photosynthesis: C₆H₁₂O₆ =  6CO₂ + 12 H₂O + photons, which is carbon dioxide + water + light energy.
• We are well aware that plants serve as a means for recycling our surroundings.
• Technology has made so much CO₂ available that plants can't handle it all.
• To commercially make this reaction—which may or may not use sunshine and green plants as the only input—feasible, some thought must have gone into it.
• One may employ alternatives in place of avoiding either or both.

Additional Information:

• Plants absorb water (H₂O) and carbon dioxide (CO₂) from the atmosphere and soil during photosynthesis.
• In the plant cell, carbon dioxide is reduced, which means it receives electrons, whereas water is oxidized, which means it loses electrons.
• As a result, carbon dioxide is transformed into glucose and water into oxygen.
• The plant then releases the oxygen back into the atmosphere after storing energy within the glucose molecules.

The correct answer is less reactive than unsaturated compounds.

Key Points:

• Due to the strong carbon-carbon single bonds, saturated carbon compounds are often not very reactive.
• Alkanes are single-bond C-C saturated carbon compounds.
• A general inertness to various chemical reagents is one of the characteristics of alkanes as a class.
• Strong connections between C and H can be found.
• Unless alkanes are heated to extremely high temperatures, they do not break.
• The bonds between carbon and hydrogen are only marginally polarised because carbon and hydrogen have approximately identical electronegativities.
• They are hence typically unaffected by the majority of bases.
• Alkanes have covalent bonds, which make it difficult for them to break and react.

Additional Information:

• Alkane molecules lack any unshared electrons that an acid could use as a site of attack.
• Alkanes were previously referred to as paraffins because of their poor reactivity toward various chemicals.
• We all know that when the right mixture is burned, alkanes react violently with oxygen.
• For instance, this combustion happens in the cylinders of cars and in oil furnaces.
• Alkanes react violently with fluorine and violently with bromine and chlorine when heated.

The correct answer is different

Key Points

• A time-varying magnetic field produces an electric field
• This is according to Faraday's first law of electromagnetic induction which states that whenever a magnetic flux associated with a conductor changes, it produces an electromotive force.
• Thus, this electromotive force is different for the different coils as the resistances of them are different
• Since resistance and EMF is different we have the current induced in these coils are also different

The correct answer is Diffusion.

Key Points:

• An essential mechanism by which gases are exchanged in a cell is diffusion.
• The difference in concentration pressure is what primarily controls this process.
• As a result, the gases shift from a place of high concentration to one of low concentration.
• The main time that diffusion occurs in plant cells is during photosynthesis when carbon dioxide diffuses into plant cells through the stomata on the leaf.

Additional Information:

• Osmosis is the naturally occurring net movement or diffusion of solvent molecules through a membrane that is selectively permeable, in a direction that tends to balance the solute concentrations on the two sides, from a region of high water potential (region of lower solute concentration) to a region of low water potential (region of higher solute concentration).​
• Endocytosis is ​a process through which cells take in foreign material by enveloping it with their membrane.
• Absorption: The substance being absorbed's molecules, atoms, and ions move into the medium's bulk phase, which might be solid, liquid, or gas. A chemical or physical phenomenon is called absorption. Absorption is the process through which something completely dissolves into another substance.

The correct answer is number of shells increases.

Key Points:

• Atomic sizes drop as a period moves from left to right.
• The same shell receives progressively more electrons.
• As the atomic number rises, so does the nucleus's attraction to the valence b.
• The atomic size grows as one descends the group, top to bottom.
• This is so that more electron shells can be added when the atomic number rises.

Additional Information:

• The chemical elements are arranged in rows and columns on what is known as the periodic table, or periodic table of the (chemical) elements.
• It is frequently used in physics, chemistry, and other sciences and is frequently regarded as a symbol of chemistry.
• It is a visual representation of the periodic law, which claims that the atomic numbers of chemical elements have a roughly periodic relationship with their attributes.
• The table is divided into four blocks that are about rectangular in shape.
• The table's columns are referred to as groups and its rows are known as periods.
• The periodic table's elements in the same group have comparable chemical properties.

The correct answer is Johann Wolfgang Dobereiner.

Key Points:

• Johann Wolfgang Dobereiner, a German scientist, was the first to categorise elements according to John Dalton's claims in the year 1829.
• He created 'Triads,' groups of three elements with identical chemical properties.
• The atomic mass of the middle element served as the defining characteristic of a trio.
• The middle element in a triad had an atomic mass that was about equal to the arithmetic mean of the other two elements when the elements were grouped in order of increasing atomic mass.

Additional Information:

• Henry Moseley:
• The justification of the earlier empirical and chemical concept of the atomic number by physical rules was Henry Gwyn Jeffreys Moseley's contribution to the science of physics.
• This came about as a result of his creation of Moseley's law in X-ray spectra.
• Mendeleev:
• ​Chemist and inventor Dmitri Ivanovich Mendeleev was from Russia.
• The Periodic Law and a modified version of the periodic chart of elements were two of his most famous creations.
• John Newlands:
• British chemist John Alexander Reina Newlands (26 November 1837 – 29 July 1898) focused on the periodicity of elements.

The correct answer is 220.

Given:

The voltage of the supply line, V=220 V,

Power on each bulb, P=10W,

Maximum current allowed, I= 10 A

Formulas:

Ohm's law: $V=IR$

$P={V^2 \over R}=I^2R$

Calculations:

Resistance of each bulb is $R = {V^2 \over P}$

$R = {(220)^2 \over 10}=4840$

Resistance of each bulb is 4840 ohm.:

Assume 'n' bulbs are to be connected in parallel with each other, we have

${1 \over Rp} = {1 \over 4840}+{1 \over 4840}+...n$

${1 \over Rp} = {n \over 4840}$

$Rp = {4840 \over n}ohm$

Applying Ohm's law:

$Rp = {V \over I}$

${4840 \over n} = {220 \over 10}$

$n = {4840\times10 \over 220}=220$

Therefore '220' lamps can be connected

The correct answer is RA = 20 Ω and RB = 15 Ω.

Given: 

Two circuits A and B having six resistors and resistance RA and R_B whose net resistance is minimum.

V=20 V, Current across A, I_A=6A and Current across B, I_B=8A.

Formula used:

Ohm's law: 

$V=IR$

Calculations:

As the net resistance is minimum , the resistors must be connected in parallel.

Therefore,

${1 \over R} = {1 \over Ra}+{1 \over Ra}+{1 \over Ra}+{1 \over Ra}+{1 \over Ra}+{1 \over Ra}$

${1 \over R}={6 \over Ra}$

$R={Ra \over 6}={Rb \over 6}$

Now applying Ohm's law:

${Ra \over 6} = {20 \over 6}$

$Ra={20*6 \over 6}=20Ω$

${Rb \over 6} = {20 \over 8}$

$Rb={20*6 \over 8}=15Ω$

Therefore, the two resistances are RA = 20 Ω and RB = 15 Ω