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Day 318: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. Asked once: 25 Jun 2022 (same type asked 5 times) See all 5 of this type

    152
    Let a,b∈Ra,b \in R be such that the equation ax2−2bx+15=0ax^{2}- 2bx + 15 = 0 has a repeated root α\alpha. If α\alpha and β\beta are the roots of the equation x2−2bx+21=0x^{2}- 2bx + 21 = 0, then α2+β2\alpha^{2}+\beta^{2} is equal to:

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  2. Question 2

    Permutations and Combinations. Asked once: 2021 Paper 2 (same type asked 4 times) See all 4 of this type

    82
    The students S1,S2,…,S10S_{1},S_{2},\ldots,S_{10} are to be divided into 3 groups A, B and CC such that each group has at least one student and the group CC has at most 3 students. Then the total number of possibilities of forming such groups is

  3. Question 3

    Complex Numbers. Asked once: 13 Apr 2023 (same type asked 4 times) See all 4 of this type

    154
    Let α,β\alpha,\beta be the roots of the equation x2−2x+2=0x^{2}-\sqrt{2}x + 2 = 0. Then α14+β14\alpha^{14}+\beta^{14} is equal to

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  4. Question 4

    Inverse Trigonometric Functions. Asked once: 2021 Paper 18 (same type asked 4 times) See all 4 of this type

    67
    Let f(x)=cos⁡(2tan⁡−1sin⁡(cot⁡−11−xx))f(x) = \cos\left( 2\tan^{- 1}\sin\left( \cot^{- 1}\sqrt{\frac{1 -x}{x}} \right) \right) 0<x<10 < x < 1. Then:

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  5. Question 5

    Sequences and Series. Asked once: 27 Jul 2022 (same type asked 4 times) See all 4 of this type

    174
    23−131×7+43−33+23−132×11+\frac{2^{3}-1^{3}}{1 \times 7}+\frac{4^{3}-3^{3}+2^{3}-1^{3}}{2 \times 11}+ 63−53+43−33+23−133×15+…..+303−293+283−273+…+23−1315×63\begin{matrix} \frac{6^{3}-5^{3}+4^{3}-3^{3}+2^{3}-1^{3}}{3 \times 15}+ \ldots.. + \\ \frac{30^{3}-29^{3}+28^{3}-27^{3}+ \ldots +2^{3}-1^{3}}{15 \times 63} \end{matrix} is equal to