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Day 463: JEE Mains Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Inverse Trigonometric Functions. Asked once: 29 Jan 2024

    165
    Let x=mnx =\frac{m}{n} (m, nn are co-prime natural numbers) be a solution of the equation cos⁡(2sin⁡−1x)=19\cos\left( 2\sin^{- 1}x \right)=\frac{1}{9} and let α,β(α>β)\alpha,\beta(\alpha > \beta) be the roots of the equation mx2−nx−mx^{2}- nx - m+n=0m + n = 0. Then the point (α,β)(\alpha,\beta) lies on the line

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  2. Question 2

    Limits and Continuity. Asked once: 7 Apr 2025

    146
    If the function f(x)=tan⁡(tan⁡x)−sin⁡(sin⁡x)tan⁡x−sin⁡xf(x) = \frac{\tan(\tan x) - \sin(\sin x)}{\tan x - \sin x} is continuous at x=0x = 0, then f(0)f(0) is equal to

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  3. Question 3

    Matrices. Asked once: 24 Jan 2026 S2

    51
    Let f(x)=∫ 7x10+9x8(1+x2+2x9)2dx, x >0f(x) =\int_{}^{}\ \frac{7x^{10}+ 9x^{8}}{\left( 1 +x^{2}+ 2x^{9} \right)^{2}}dx,\ x\ > 0, lim⁡x→0f(x)=0\underset{x \rightarrow 0}{\lim} f(x) = 0 and  f(1)=14\ f(1) =\frac{1}{4}. A=[00114f′(1)1α241]A =\begin{bmatrix} 0 & 0 & 1 \\ \frac{1}{4} & f^{'}(1) & 1 \\ \alpha^{2} & 4 & 1 \end{bmatrix} and B=adj(adjA)B = adj(adjA) be such that ∣B∣=81|B| = 81, then α2\alpha^{2} is equal to

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  4. Question 4

    Permutations and Combinations. Asked once: 4 Apr 2025

    149
    Let m and n,(m<n)n,(m < n) be two 2-digit numbers. Then the total numbers of pairs (m,n)(m,n), such that gcd(m,n)=6gcd(m,n) = 6, is.

  5. Question 5

    Probability. Asked once: 21 Jan 2026 S1

    63
    Let the mean and variance of 7 observations 2,4,10,x,12,14,y,x>y2,4,10,x,12,14,y,x > y, be 8 and 16 respectively. Two numbers are chosen from {1,2,3,x−4,y,5}\mathbf{\{ 1,2,3,x - 4,y,5\}} one after another without replacement, then the probability, that the smaller number among the two chosen numbers is less than 4 , is:

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