Search Previous Year Questions

Shortcut Trick

Assume the number is the LCM of the denominators (2 and 3) = 6 units.

According to the question: 6 units (number) + 3 units (half) + 2 units (one-third) + 27 = 71.

Summing the units: 11 units + 27 = 71.

⇒ 11 units = 71 − 27 = 44.

⇒ 1 unit = 4.

⇒ The number (6 units) = 6 × 4 = 24.

∴ The correct answer is 24.

Alternate Method

Given:

Let the number be x.

Sum of x, x/2, x/3, and 27 is 71.

Formula Used:

Linear equation in one variable: x + (1/2)x + (1/3)x + C = Total

Calculations:

⇒ x + x/2 + x/3 + 27 = 71

⇒ x + x/2 + x/3 = 71 − 27

⇒ x + x/2 + x/3 = 44

⇒ (6x + 3x + 2x) ÷ 6 = 44

⇒ 11x ÷ 6 = 44

⇒ 11x = 44 × 6

⇒ x = (44 × 6) ÷ 11

⇒ x = 4 × 6 = 24

∴ The correct answer is 24.

Additional Information

Linear Equations

An equation involving only linear polynomials with one variable is called a linear equation in one variable, typically in the form ax + b = 0.

Least Common Multiple (LCM) Method

To eliminate fractions in an equation, multiply the entire equation by the LCM of all denominators involved.

Transposition Rule

When a term is moved from one side of the equals sign to the other, its sign changes (+ becomes −, and × becomes ÷).

The correct answer is Both the statements are true. 

Key Points

• Statement I is True, Litmus solution is a purple dye, extracted from lichens, a plant belonging to the Thallophyta division, and is commonly used as an indicator. When litmus solution is neither acidic nor alkaline, its color is purple.
• Statement II is true as there are many natural materials that can indicate the presence of acid or base in a solution.
• Litmus solution is commonly used as a pH indicator in chemistry to determine whether a solution is acidic or basic.
• Lichen is a composite organism that arises from algae or cyanobacteria living among filaments of multiple fungi in a mutualistic relationship, and it is used to extract litmus solution in some cases.

Additional Information

• The pH scale indicates how basic or acidic water is.
• The neutral number is 7, and the range is 0 to 14.
• Acidity is indicated by a pH of less than 7, and baseness is indicated by a pH of greater than 7.
• The relative concentration of free hydrogen and hydroxyl ions in water is what pH actually measures.

Shortcut Trick

Convert Time to years: 3 years 4 months = 3 + 1/3 = 10/3 years.

Calculate interest for 1 year: 840 ÷ (10/3) = (840 × 3) ÷ 10 = ₹252.

Rate = (Interest per year ÷ Principal) × 100.

Rate = (252 ÷ 3600) × 100 = 7%.

∴ The correct answer is 7%.

Alternate Method

Given:

Principal (P) = ₹3,600

Simple Interest (SI) = ₹840

Time (T) = 3 years 4 months = 3 + 4/12 = 3 + 1/3 = 10/3 years

Formula Used:

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

Calculations:

⇒ R = (SI × 100) ÷ (P × T)

⇒ R = (840 × 100) ÷ (3600 × 10/3)

⇒ R = (84000 × 3) ÷ (3600 × 10)

⇒ R = 252000 ÷ 36000

⇒ R = 252 ÷ 36

⇒ R = 7%

∴ The correct answer is 7%.

Additional Information

Simple Interest Concept

Interest calculated only on the initial principal amount throughout the entire period. Formula: SI = P × R × T / 100.

Rate and Time Units

Ensure the Rate of interest and Time are in the same time units (usually per annum and years) before applying the formula.

Amount Calculation

The total amount (A) at the end of the period is the sum of Principal and Simple Interest: A = P + SI = P(1 + RT/100).

Shortcut Trick

Determine the Cost Price (CP) of the mixture: CP = 55.20 ÷ (1 + 0.15) = 55.20 ÷ 1.15 = ₹48 per kg.

Apply the Rule of Allegation between Sugar 1 (₹45) and Sugar 2 (₹52) with Mean Price (₹48).

Ratio = (52 − 48) : (48 − 45) = 4 : 3.

∴ The correct answer is 4 : 3.

Alternate Method

Given: CP₁ = ₹45, CP₂ = ₹52, SP_mix = ₹55.20, Profit% = 15%.

Formulas: CP = [SP × 100] ÷ [100 + Profit%], Allegation Ratio = (CP₂ − CP_m) : (CP_m − CP₁).

⇒ Step 1: Calculate mean CP of mixture = (55.20 × 100) ÷ 115 = ₹48.

⇒ Step 2: Difference between CP₂ and Mean CP = 52 − 48 = 4.

⇒ Step 3: Difference between Mean CP and CP₁ = 48 − 45 = 3.

⇒ Step 4: The required ratio of quantities is 4 : 3.

∴ The correct answer is 4 : 3.

Additional Information

Rule of Alligation

It is used to find the ratio in which two ingredients at given prices must be mixed to produce a mixture of a certain price. All units (CP, SP, or % concentration) must be consistent.

Profit and Loss Relation

The Cost Price is always the base (100%) when calculating Profit or Loss percentages unless stated otherwise.

The correct answer is Wormivet.

Key Points

• The National Innovation Foundation - India is an autonomous body that supports grassroots innovations and traditional knowledge practices.
• Herbal medicine is a natural alternative to chemical drugs and is gaining popularity due to its effectiveness and minimal side effects.
• Wormivet is an indigenous herbal medicine developed by the National Innovation Foundation - India to treat worm infestations in livestock.

Additional Information

• Endoparasite worms in cattle are treated with the Wormivet.
• An inventive patent application has been made.
• The Department of Science and Technology oversees the National Innovation Foundation.
• It strives to assist grassroots inventions.
• Along with the CBSE board, it also hosts the annual IGNITE tournament.

The correct answer is Maharashtra.

Key Points

• Maharashtra is a state in the western region of India, known for its diverse culture, history, and natural beauty.
• Tadoba National Park is one of the largest and oldest national parks in Maharashtra, covering an area of around 625 square kilometers.
• The park is home to a variety of flora and fauna, including tigers, leopards, sloth bears, sambar deer, and Indian bison.

Additional Information

• Uttar Pradesh is a state in northern India, known for its historical monuments, temples, and rich cultural heritage.
• It is home to Dudhwa National Park, Kishanpur Wildlife Sanctuary, Ranipur Wildlife Sanctuary etc.
• Bihar is a state in eastern India, known for its archaeological sites, temples, and festivals.
• It is home to Bhimbandh Sanctuary, Gautam Budha Wildlife Sanctuary, Kaimur Wildlife Sanctuary etc.
• Rajasthan is a state in northwestern India, known for its forts, palaces, and desert landscapes.
• It is home to Keoladeo National Park, Ranthambore National Park, etc.

Shortcut Trick For a Quadratic Equation ax2 + bx + c = 0, the sum of roots (α + β) = −b/a and the product of roots (αβ) = c/a. Sum of roots: −1 + (−2) = −p/3 ⇒ −3 = −p/3 ⇒ p = 9. Product of roots: (−1) × (−2) = q/3 ⇒ 2 = q/3 ⇒ q = 6. Value of 3p − 2q = 3(9) − 2(6) = 27 − 12 = 15. ∴ The correct answer is 15. Alternate Method Given: The equation is 3x2 + px + q = 0 and its solutions are x = −1 and x = −2. Formula Used: If x = a is a root, then substituting x = a in the equation must satisfy it (result in zero).

⇒ Substitute x = −1: 3(−1)2 + p(−1) + q = 0 ⇒ 3 − p + q = 0 ⇒ p − q = 3 ... (i) ⇒ Substitute x = −2: 3(−2)2 + p(−2) + q = 0 ⇒ 12 − 2p + q = 0 ⇒ 2p − q = 12 ... (ii) ⇒ Subtracting equation (i) from (ii): (2p − q) − (p − q) = 12 − 3 ⇒ p = 9. ⇒ Substitute p = 9 in equation (i): 9 − q = 3 ⇒ q = 6. ⇒ Required calculation: 3p − 2q = 3(9) − 2(6) = 27 − 12 = 15. ∴ The correct answer is 15. Additional Information Relationship between Roots and Coefficients For any equation ax2 + bx + c = 0, the sum of roots is −b/a and the product of roots is c/a. Formation of Quadratic Equation If α and β are the roots, the equation is given by x2 − (α + β)x + αβ = 0. Discriminant (D) The nature of roots is determined by D = b2 − 4ac. If D > 0, roots are real and distinct; if D = 0, roots are real and equal.

The correct answer is 0.25 A.

Key Points

• The total resistance in a parallel circuit is given by the formula: 1/Rt = 1/R1 + 1/R2, where R1 and R2 are the resistances of the two parallel branches.
• So, in this case, 1/Rt = 1/20 + 1/30 = 1/12.
• Rearranging the formula, we get Rt = 12/5 = 2.4 ohms.
• This is the equivalent resistance of the parallel combination.
• Using Ohm's Law, we can find the current through the battery, which is given by I = V/Rt, where V is the voltage of the battery.
• In this case, V = 3V, so I = 3/2.4 = 1.25 A.
• However, this is not the final answer because the question asks for the current through the battery, not the equivalent resistance.
• So, we need to find the current through each resistor separately.
• Using Ohm's Law again, we can find the current through resistor A, which is I1 = V/R1 = 3/20 = 0.15 A.
• Similarly, the current through resistor B is I2 = V/R2 = 3/30 = 0.1 A.
• The total current through the battery is the sum of the currents through each resistor, which is I = I1 + I2 = 0.15 + 0.1 = 0.25 A.
• Therefore, 0.25 A is the correct answer.

Additional Information

• The amount of obstruction to current passage in an electrical circuit is measured as resistance.
• Ohms, a unit of measurement for resistance, are represented by the Greek letter omega (Ω).
• Electrical charge carriers, often electrons or atoms with a deficiency in electrons, travel in current.
• The ampere, denoted by the letter A, is the standard unit.

The logic followed here is:

So, '360' will complete the series.

Hence, the correct answer is "Option 4".

The logic followed here is:

Given number: 9345712.

Odd digits is decreased by - 1

and, Even digits is increased by + 2

After arrange the numbers:

9345712 ⇒ 8264604

Now, The largest digits after rearranging the series: 8

And, The smallest digits after rearranging the series: 0

So, the difference between the largest and smallest digits is: 8 - 0 = 8.

Hence, the correct answer is "Option 2".