Mathematics and Science PYQs

Calculation :

By going through options :

\(\left(\frac{-1}{3}\right)^5\) = -1/243

\(\left(\frac{1}{3}\right)^5\) = 1/243

\(\left(\frac{1}{3}\right)^{-5}\) = 243

(3)5  = 243

∴ The correct answer is 243.

Calculation :

 \(\left(\frac{-1}{3}\right)^4\) + \(\left(\frac{-1}{6}\right)^3\) 

⇒ 1/81 - 1/216

⇒ (8 - 3)/648

⇒ 5/ 648

⇒ 0.00771

∴ The correct answer is 0 and 0.5.

Calculation :

Accoridng to question,

⇒ π = 3.14, \(3 \frac{3}{7}\) = 3.42

So, only 3.2857 is the only number between π and \(3 \frac{3}{7}\).

∴ The correct answer is option 1,

Calculations:

(27)⁴/ (125)² = 3¹²/5⁶

(5/9)^-2 = (9/5)²

\(\frac{(27)^4}{(125)^2}\)   / \(\left{\left(\frac{5}{9}\right)^{-2}\left(\frac{3}{5}\right)^6\right} \) = (312/56) / (9/5)2 × (3/5)⁶

= 3¹²  × 5² × 5⁶ / 3⁴ × 3⁶ = 3² × 5² = 225

Hence, The Correct Answer is option 2.

Calculation:

x = (-5)-11. \(\left(\frac{1}{5}\right)^{11}\) + 511. \(\left(\frac{-1}{5}\right)^{11}\)

⇒ 1/-5¹¹ × 1/5¹¹ - 5¹¹/5¹¹

⇒ -1/5²² - 1

⇒ -[(1 + 5²²)/5²²]

∴ The correct answer is option 1.

Calculation :

1.5 kg of chalk

Calcium = 12%, Crabon = 3%

Calculation :

According to question,

Calcium = 12% , Carbon = 3%, Rest = 85%

We know, 100% = 1.5 kg

⇒ 1% = 15 gm

Amount of rest = 85 × 15 = 1275 g

∴ The correct answer is 1275 g.

Calculation :

 \(\frac{x}{6}\) = \(\frac{36}{x^2}\) 

⇒ x³ = 36 × 6 = 216

⇒ x³ = 6³

∴ The correct answer is 6.

Calculation :

⇒ x = \(\frac{(1.75)^2-(1.62)^2}{0.13}\)

⇒ x = [(1.75 - 1.62)(1.75 + 1.62)]/0.13

⇒ x = (0.13 × 3.37)/0.13

⇒ x = 3.37

∴ The correct answer is 3.37.

Formula used :

M₁H₁D₁/W₁ = M₂H₂D₂/W₂

Calculation :

According to question,

⇒ 10 × 8 = 16 × h

⇒ 16 h = 80

⇒ h = 5

∴ The correct answer is 5.

Given: 

x + 10 = 100 

Calculations:

option 1)

x is a natural number less than 100.

suppose x = 99 

so we can't write 99 in the form x + 10 = 100 

because from the above equation x = 90 which contradicts the statement of option 1.

Hence, Option 1 is incorrect.

option 2)

x = 100 - 10 = 90

Hence, x is a  natural number less than 100 by 10

Hence, Option 2 is Correct.

option 3)

x is a natural number greater than 100 by 10.

suppose x = 110 then we can't write it as x + 10 = 100 

because if x = 110 then from above equation 110 + 10 ≠ 100 

Hence, Option 3 is incorrect.

option 4)

10 is a natural number less than 100.

we can't write 10 as x + 10 = 100 

Hence, option 4 is incorrect.

Concept used :

Sum of all the angles of quadrilateral = 360° 

Calculation :

⇒ ∠DAB + ∠ADC + ∠DCB + ∠DCB = 360° 

⇒ 135° + 90° + 60° + ∠DCB = 360° 

⇒ ∠DCB = 360° - 285° = 75° 

  

∴ The correct answer is 75°.

Explanations:

A rectangle is a quadrilateral with four right angles. A square meets this definition as it has four right angles.

A rhombus is a quadrilateral with all sides of equal length. A square meets this definition as it has four equal length sides.

A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. A square meets this definition as its opposite sides are paralleL.

Hence, The Correct option is 4.

Calculation :

∠AOP = ∠BOP = 60° [Vertically Opposite Angle]

Now, ∠BOQ + ∠OQB + ∠OBQ = 180° 

∠OQB + ∠OBQ = 180° - 60° = 120° 

∴ The correct answer is 120°.

Given :

Δ MAT and Δ NOR are congruent.

TM = RO

MA = RN 

∠TMA = 65° 

Calculation: 

Since both triangles are congruent 

So, ∠TMA = ∠ORN

By angle sum property,

∠RON + ∠RNO + ∠ORN = 180° 

Now, ∠RNO + ∠NOR = 180° - 65° = 115° 

∴ The correct answer is 115°.

Calculation :

We know that opposite angle of parallelogram becomes equal.

Here, ∠L = ∠F and ∠I = ∠E 

∴ The correct answer is only parallelogram.

Given:

Sides of rectangle are x and y units.

Perimeter of rectangle = 24 units.

Formula used:

Area of rectangle = length × breadth

Perimeter of rectangle = 2 × (length + breadth)

Calculation:

According to question,

⇒ 2 × (L + B) = 24

⇒ (L + B) = 12

Now, for area to be maximum length must be equal to breadth,

So, Area of rectangle = 6 × 6 = 36 sq. unit.

∴ The correct answer is 36 sq. unit.

Given:

Volume of cuboid = 900 m³

Length = 14.5 m, Breadth = 9.5 m

Formula used:

Voulme of cuboid = l × b × h

Calculation:

According to question,

⇒ 14.5 × 9.5 × h = 900

⇒ h = 900/137.5 = 6.54

∴ The correct answer is 6.54 m.

Given:

Sides of cuboid 3.5, 3.1, 2.1 units.

Side of cube = average of sides of cuboid/

Formula used:

Average = Sum of all observations/ Number of observations

Volume of cuboid = l × b × h

Volume of cube = a³

Calculation:

According to question,

Volume of cuboid = 3.5 × 3.1 × 2.1 = 22.785 unit

Average of side of cuboid = (3.5 + 3.1 + 2.1)/3 = 2.9

Volume of cube = 24.389

Difference in volume = 24.389 - 22.785 = + 1.604 unit

∴ The correct answer is +1.604 unit.

Given:

Average of boys = 12

Average of boys and girls = 13

Number of boys = 10, Number of girls = 5

Formula used :

Average = Sum of all observations/Total number of observations

Calculation:

According to question,

Sum of ages of all boys = 10 × 12 = 120

Sum of ages of all boys and girls = 13 × 15 = 195

Sum of ages of girls = 195 - 120 = 75

Average = 75/5 = 15

∴ The correct answer is 15.

Formula used :

Probability = Num of favourable outcome/Total number of outcome

Calculation :

According to question,

Probabilty = 4/52 = 1/13

∴ The correct answer is 1/13.