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Day 218: JEE Mains Maths

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

  1. Question 1

    Definite Integration. Asked once: 2021 Paper 22 (same type asked 2 times) See all 2 of this type

    88
    If xϕ(x)=∫5x(3t2−2ϕ′(t))dt,x>−2x\phi(x) =\int_{5}^{x} \left( 3t^{2}- 2\phi^{'}(t) \right)dt,x> - 2, and ϕ(0)=4\phi(0) = 4, then ϕ(2)\phi(2) is

  2. Question 2

    Inverse Trigonometric Functions. Asked once: 2021 Paper 11 (same type asked 2 times) See all 2 of this type

    55
    The number of real roots of the equation tan⁡−1x(x+1)+sin⁡−1x2+x+1=π4\tan^{- 1}\sqrt{x(x + 1)}+\sin^{- 1}\sqrt{x^{2}+ x + 1}=\frac{\pi}{4} is :

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  3. Question 3

    Application of Derivatives. Asked once: 2021 Paper 5 (same type asked 2 times) See all 2 of this type

    87
    If the normal to the curve y(x)=∫0x(2t2−15t+10)dty(x) =\int_{0}^{x} \left( 2t^{2}- 15t+ 10 \right)dt at a point (a,b)(a,b) is parallel to the line x+3y=−5,a>1x+ 3y= - 5,a> 1, then the value of ∣a+6b∣|a+ 6b| is equal to

  4. Question 4

    Permutations and Combinations. Asked once: 25 Jan 2023 (same type asked 2 times) See all 2 of this type

    87
    Let xx and yy be distinct integers where 1≤x≤251 \leq x \leq 25 and 1≤y≤251 \leq y \leq 25. Then, the number of ways of choosing xx and yy such that x+yx+y is divisible by 5, is

  5. Question 5

    Permutations and Combinations. Asked once: 24 Jan 2023 (same type asked 2 times) See all 2 of this type

    86
    The number of 9-digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is