PYQ Vault
EbooksTutor

Day 453: JEE Mains Maths

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

  1. Question 1

    Differentiation. Asked once: 29 Jan 2025

    130
    Let the function f(x)=(x2−1)∣x2−ax+2∣+cos⁡∣x∣f(x) =\left( x^{2}- 1 \right)\left| x^{2}- ax + 2 \right|+ \cos|x| be not differentiable at the two points x=α=2x = \alpha = 2 and x=βx = \beta. Then the distance of the point (α,β)(\alpha,\beta) from the line 12x+5y+10=012x + 5y + 10 = 0 is equal to :

    Tap an option to check your answer.

  2. Question 2

    Indefinite Integration. Asked once: 22 Jan 2026 S1

    73
    If ∫ (sin⁡x)−112(cos⁡x)−52dx=\int_{}^{}\ (\sin x)^{\frac{- 11}{2}}(\cos x)^{\frac{- 5}{2}}dx = −p1q1(cot⁡x)92−p2q2(cot⁡x)52−p3q3(cot⁡x)12+p4q4(cot⁡x)−32+C- \frac{p_{1}}{q_{1}}(\cot x)^{\frac{9}{2}} - \frac{p_{2}}{q_{2}}(\cot x)^{\frac{5}{2}} - \frac{p_{3}}{q_{3}}(\cot x)^{\frac{1}{2}} + \frac{p_{4}}{q_{4}}(\cot x)^{\frac{- 3}{2}} + C, where pip_{i} and qiq_{i} are positive integers with gcd⁡(pi,qi)=1\gcd\left( p_{i},q_{i} \right) = 1 for i=1,2,3,4i = 1,2,3,4 and C is the constant of integration, then 15p1p2p3p4q1q2q3q4\frac{15p_{1}p_{2}p_{3}p_{4}}{q_{1}q_{2}q_{3}q_{4}} is equal to ____\_\_\_\_ .

  3. Question 3

    Inverse Trigonometric Functions. Asked once: 4 Apr 2024

    167
    Given the inverse trigonometric function assumes principal values only. Let x,yx,y be any two real numbers in [−1,1]\lbrack - 1,1\rbrack such that cos⁡−1x−sin⁡−1y=α,−π2≤α≤π\cos^{- 1}x -\sin^{- 1}y = \alpha,\frac{- \pi}{2}\leq \alpha \leq \pi. Then, the minimum value of x2+y2+2xysin⁡αx^{2}+y^{2}+ 2xy\sin\alpha is

    Tap an option to check your answer.

  4. Question 4

    Limits and Continuity. Asked once: 24 Jan 2026 S1

    51
    If the function f(x)=ex(etan⁡x−x−1)+log⁡e(secx+tan⁡x)−xtan⁡x−xf(x) =\frac{e^{x}\left( e^{\tan x - x}- 1 \right)+\log_{e}(secx + \tan x) - x}{\tan x - x} is Continuous at x=0x = 0, then the value of f(0)f(0) is equal to

    Tap an option to check your answer.

  5. Question 5

    Matrices. Asked once: 2 Apr 2026 S2

    72
    Consider the matrices A=[2−24−2]A = \begin{bmatrix} 2 & - 2 \\ 4 & - 2 \end{bmatrix} and B=[3913]B = \begin{bmatrix} 3 & 9 \\ 1 & 3 \end{bmatrix}. If matrices P and Q are such that PA=PA = B and AQ=BAQ = B, then the absolute value of the sum of the diagonal elements of 2(P+Q)2(P + Q) is ____\_\_\_\_ .