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Day 368: JEE Mains Maths

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

  1. Question 1

    Trigonometric Identities. Asked once: 26 Jun 2022 (same type asked 7 times) See all 7 of this type

    86
    If sin⁡2(10∘)sin⁡(20∘)sin⁡(40∘)sin⁡(50∘)sin⁡(70∘)=α−\sin^{2}\left( 10^{\circ} \right)\sin\left( 20^{\circ} \right)\sin\left( 40^{\circ} \right)\sin\left( 50^{\circ} \right)\sin\left( 70^{\circ} \right)=\alpha- 116sin⁡(10∘)\frac{1}{16}\sin\left( 10^{\circ} \right), then 16+α−116 +\alpha^{- 1} is equal to

  2. Question 2

    Differential Equations. Asked once: 2021 Paper 25 (same type asked 7 times) See all 7 of this type

    84
    If y=y(x)y=y(x) is the solution of the equation esin⁡ycos⁡ydydx+esin⁡ycos⁡x=cos⁡x,y(0)=0e^{\sin y}\cos y\frac{dy}{dx}+e^{\sin y}\cos x= \cos x,y(0) = 0; then 1+y(π6)+32y(π3)+12y(π4)1 +y\left( \frac{\pi}{6} \right)+\frac{\sqrt{3}}{2}y\left( \frac{\pi}{3} \right)+\frac{1}{\sqrt{2}}y\left( \frac{\pi}{4} \right) is equal to

  3. Question 3

    Trigonometric Equations. Asked once: 29 Jun 2022 (same type asked 7 times) See all 7 of this type

    174
    The number of solutions of the equation sin⁡x=\sin x= cos⁡2x\cos^{2}x in the interval (0,10)(0,10) is

  4. Question 4

    Complex Numbers. Asked once: 28 Jun 2022 (same type asked 7 times) See all 7 of this type

    178
    Sum of squares of modulus of all the complex numbers zz satisfying z‾=iz2+z2−z\overline{z}=iz^{2}+z^{2}- z is equal to

  5. Question 5

    Vector Algebra. Asked once: 2021 Paper 20 (same type asked 7 times) See all 7 of this type

    81
    Let a→=i^+5j^+αk^,b→=i^+3j^+βk^\overrightarrow{a}=\widehat{i}+ 5\widehat{j}+\alpha\widehat{k},\overrightarrow{b}=\widehat{i}+ 3\widehat{j}+\beta\widehat{k} and c→=−i^+2j^−3k^\overrightarrow{c}= -\widehat{i}+ 2\widehat{j}- 3\widehat{k} be three vectors such that, ∣b→×c→∣=53|\overrightarrow{b}\times\overrightarrow{c}| = 5\sqrt{3} and a→\overrightarrow{a} is perpendicular to b→\overrightarrow{b}. Then the greatest amongst the values of ∣a→∣2|\overrightarrow{a}|^{2} is