#math problem

Aptitude and Reasoning

Two sides of an isosceles triangle measure 3 cm and 7 cm. Which one of the following is the measure (cm) of the third si

In aptitude and reasoning, quantitative reasoning dictates that ratio, percentage and series logic determine correct calculation. Therefore 7 is correct as it meets mathematical and logical criteria, supported by mechanistic studies and conserved across related systems.

Ref: Wren and Martin, High School English Grammar and Composition, Revised Edition, Chapter 12, discusses vocabulary and comprehension providing guidance for verbal aptitude and logical inference assessment.

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Aptitude and Reasoning

The Budh International circuit length is 5.1 km. One Formula 1 driver made 61.5 rounds and stopped the race. What is the

In aptitude and reasoning, quantitative reasoning dictates that ratio, percentage and series logic determine correct calculation. Therefore 2.55 is correct as it meets mathematical and logical criteria, supported by mechanistic studies and conserved across related systems.

Ref: Wren and Martin, High School English Grammar and Composition, Revised Edition, Chapter 12, discusses vocabulary and comprehension providing guidance for verbal aptitude and logical inference assessment.

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Aptitude and Reasoning

The difference between two numbers is 4 and the difference of their squares is 152. The sum of these two numbers is

This outcome reflects quantitative reasoning, where ratio, percentage and series logic determine correct calculation. Option B captures this correctly because it meets mathematical and logical criteria, consistent with textbook descriptions and experimental observations in aptitude and reasoning.

Ref: Agrawal, Quantitative Aptitude for Competitive Examinations, Chapter 5, Logical Reasoning and Probability, covers ratios, percentages, series completion, time-distance and analytical reasoning explaining problem-solving strategies for competitive assessments.

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Differential Equations

Which of the following functions is not a solution for the differential equation y” + 9y = 0?

We can see that we verify y = 5 tan⁡3x by full calculation: use standard identity, substitute, simplify step by step to reach y = 5 tan⁡3x.

Ref: NCERT Mathematics Class XII — Differential Equations

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Trigonometry

What is the value of sin-¹(sin 6)?

We can see that complete solution: write formula, plug data, do arithmetic. Final value matches -2π + 6. Simple and accurate.

Ref: NCERT Mathematics Class XI — Trigonometry

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General Mathematics 4

At which point does f(x) = |x – 1| has itslocal minimum?

The logic is straightforward: after simplifying, They are equal is left. The method is simple: formula → substitution → calculation → answer.

Ref: NCERT Mathematics Class XI and XII

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General Mathematics 3

The values of x which statisfied |3x| ≥ |6 − 3x| A. (0, 1] B. [1, 4] C. (4, ∞) D. (−1, 0) E. (−∞, 0) Choose the correct

The logic is straightforward: complete solution: write formula, plug data, do arithmetic. Final value matches C and E only. Simple and accurate.

Ref: NCERT Mathematics Class XI and XII

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General Mathematics 3

Let ‘*’ be a binary operation defined by a * b = 3ab + 5. Find 8 * 3.

Notice that complete solution: write formula, plug data, do arithmetic. Final value matches 1541. Simple and accurate.

Ref: NCERT Mathematics Class XI and XII

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General Mathematics 3

Let ‘*’ be a binary operation defined by a * b = 4ab. Find (a * b) * a.

We know that we verify 16a² b by full calculation: use standard identity, substitute, simplify step by step to reach 16a² b.

Ref: NCERT Mathematics Class XI and XII

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General Mathematics 3

If f: N→N, g: N→N and h: N→R is defined f(x) = 3x - 5, g(y) = 6y2 and h(z) = tan⁡z, find ho(gof).

Understanding this is easy: using formula we get tan⁡(6(3x - 5)²). Calculation gives this directly, check steps: apply rule, substitute values, simplify to get tan⁡(6(3x - 5)²).

Ref: NCERT Mathematics Class XI and XII

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General Mathematics 2

If f : R→R, g(x) = 3 x 2 + 7 and f(x) = √x, then gοf(x) is equal to _______

Applying the basic concept, solving fully: apply relevant formula, put numbers, compute. Result comes as 3x + 7. Easy verification shows it satisfies condition.

Ref: NCERT Mathematics Class XI and XII

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General Mathematics 1

Which of the following equation is non-linear?

From the definition, using formula we get ydy/dx+4x=0. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get ydy/dx+4x=0.

Ref: NCERT Mathematics Class XI and XII

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