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Day 203: JEE Mains Maths

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

  1. Question 1

    Matrices. Asked once: 2021 Paper 3 (same type asked 2 times) See all 2 of this type

    84
    If A=[0−tan⁡(θ2)tan⁡(θ2)0]A=\begin{bmatrix} 0 & - \tan\left( \frac{\theta}{2} \right) \\ \tan\left( \frac{\theta}{2} \right) & 0 \end{bmatrix} and (I2+A)(I2−A)−1\left( I_{2}+A \right)\left( I_{2}-A \right)^{- 1} =[a−bba]=\begin{bmatrix} a & -b \\ b & a \end{bmatrix}, then 13(a2+b2)13\left( a^{2}+b^{2} \right) is equal to

  2. Question 2

    Permutations and Combinations. Asked once: 26 Jul 2022 (same type asked 2 times) See all 2 of this type

    82
    The number of 5-digit natural numbers, such that the product of their digits is 36, is

  3. Question 3

    Conic Sections. Asked once: 29 Jun 2022 (same type asked 2 times) See all 2 of this type

    88
    Let H:x2a2−y2b2=1,a>0,b>0H:\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}= 1,a > 0,b > 0, be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is 4(22+14)4(2\sqrt{2}+\sqrt{14}). If the eccentricity HH is 112\frac{\sqrt{11}}{2}, then value of a2+b2a^{2}+b^{2} is equal to

  4. Question 4

    Conic Sections. Asked once: 30 Jan 2024 (same type asked 2 times) See all 2 of this type

    160
    Let PP be a point on the hyperbola H:x29−y24=1H:\frac{x^{2}}{9}-\frac{y^{2}}{4}= 1, in the first quadrant such that the area of triangle formed by PP and the two foci of HH is 2132\sqrt{13}. Then, the square of the distance of PP from the origin is

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  5. Question 5

    Binomial Theorem. Asked once: 6 Apr 2024 (same type asked 2 times) See all 2 of this type

    173
    If S(x)=(1+x)+2(1+x)2+3(1+x)3+…S(x) = (1 +x) + 2(1 +x)^{2}+ 3(1 +x)^{3}+ \ldots. +60(1+x)60,x≠0+ 60(1 +x)^{60},x\neq 0, and (60)2S(60)=a(b)b+b(60)^{2}S(60) =a(b)^{b}+b, where a,b∈Na,b \in N, then (a+b)(a + b) equal to