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Day 150: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. Asked once: 28 Jan 2026 S1 (same type asked 5 times) See all 5 of this type

    75
    Let PQRPQR be a triangle such that PQ→=−2i^−j^+2k^\overrightarrow{PQ} = - 2\widehat{i} - \widehat{j} + 2\widehat{k} and PR→=ai^+bj^−4k^,a,b∈Z\overrightarrow{PR} = a\widehat{i} + b\widehat{j} - 4\widehat{k},a,b \in \mathbb{Z}. Let SS be the point on QR, which is equidistant from the lines PQ and PR. If ∣PR→∣=9|\overrightarrow{PR}| = 9 and PS→=i^−7j^+2k^\overrightarrow{PS} = \widehat{i} - 7\widehat{j} + 2\widehat{k}, then the value of 3a−4b3a - 4b is ____\_\_\_\_ .

  2. Question 2

    Statistics. Asked once: 4 Apr 2025 (same type asked 5 times) See all 5 of this type

    145
    Let the mean and the standard deviation of the observation 2,3,3,4,5,7,a,b2,3,3,4,5,7,a,b be 4 and 2\sqrt{2} respectively. Then the mean deviation about the mode of these observations is :

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  3. Question 3

    Vector Algebra. Asked once: 7 Apr 2025 (same type asked 5 times) See all 5 of this type

    127
    Let a→\overrightarrow{a} and b→\overrightarrow{b} be the vectors of the same magnitude such that ∣a→+b→∣+∣a→−b→∣∣a→+b→∣−∣a→−b→∣=\frac{\left| \overrightarrow{a}+\overrightarrow{b} \right|+\left| \overrightarrow{a}-\overrightarrow{b} \right|}{\left| \overrightarrow{a}+\overrightarrow{b} \right|-\left| \overrightarrow{a}-\overrightarrow{b} \right|}= 2+1\sqrt{2}+ 1. Then ∣a→+b→∣2∣a→∣2\frac{|\overrightarrow{a}+\overrightarrow{b}|^{2}}{|\overrightarrow{a}|^{2}} is:

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  4. Question 4

    Definite Integration. Asked once: 29 Jan 2023 (same type asked 5 times) See all 5 of this type

    78
    Let f(x)=x+aπ2−4sin⁡x+bπ2−4cos⁡x,x∈Rf(x) = x +\frac{a}{\pi^{2}- 4}\sin x +\frac{b}{\pi^{2}- 4}\cos x,x \in R be a function which satisfies f(x)=x+∫0π/2sin⁡(x+f(x) = x +\int_{0}^{\pi/2} \sin(x + y)f(y)dyy)f(y)dy. Then (a+b)(a + b) is equal to

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  5. Question 5

    Relations and Functions. Asked once: 21 Jan 2026 S1 (same type asked 5 times) See all 5 of this type

    51
    If the domain of the function f(x)=cos⁡−1(2x−511−3x)+sin⁡−1(2x2−3x+1)f(x) =\cos^{- 1}\left( \frac{2x - 5}{11 - 3x} \right)+\sin^{- 1}\left( 2x^{2}- 3x + 1 \right) is the interval [α,β]\lbrack\alpha,\beta\rbrack, then α+2β\alpha + 2\beta is equal to :

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