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Day 237: JEE Mains Maths

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

  1. Question 1

    Vector Algebra. Asked once: 4 Apr 2024 (same type asked 7 times) See all 7 of this type

    89
    Let ABCABC be a triangle of area 15215\sqrt{2} and the vectors AB→=i^+2j^−7k^, BC→=ai^+bj^+ck^\overrightarrow{AB}=\widehat{i}+ 2\widehat{j}- 7\widehat{k},\ \overrightarrow{BC}= a\widehat{i}+b\widehat{j}+c\widehat{k} and AC→=6i^+dj^−2k^,d>0\overrightarrow{AC}= 6\widehat{i}+ d\widehat{j}- 2\widehat{k},d> 0. Then the square of the length of the largest side of the triangle ABCABC is

  2. Question 2

    Conic Sections. Asked once: 1 Feb 2024 (same type asked 7 times) See all 7 of this type

    78
    Let C:x2+y2=4C:x^{2}+y^{2}= 4 and C′:x2+y2−4λx+9=0C^{'}:x^{2}+y^{2}- 4\lambda x + 9 = 0 be two circles. If the set of all values of λ\lambda so that the circles CC and C′C^{'} intersect at two distinct points, is R−[a,b]R - \lbrack a,b\rbrack, then the point (8a+12,16b−20)(8a + 12,16b - 20) lies on the curve:

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  3. Question 3

    Binomial Theorem. Asked once: 31 Jan 2024 (same type asked 7 times) See all 7 of this type

    85
    In the expansion of (1+x)(1−x2)(1+3x+3x2+1x3)5,x≠0(1 +x)\left( 1 -x^{2} \right)\left( 1 +\frac{3}{x}+\frac{3}{x^{2}}+\frac{1}{x^{3}} \right)^{5},x\neq 0, the sum of the coefficient of x3x^{3} and x−13x^{- 13} is equal to

  4. Question 4

    Definite Integration. Asked once: 23 Jan 2025 (same type asked 7 times) See all 7 of this type

    144
    If I=∫0π2sin⁡32xsin⁡32x+cos⁡32xdxI =\int_{0}^{\frac{\pi}{2}} \frac{\sin^{\frac{3}{2}}x}{\sin^{\frac{3}{2}}x +\cos^{\frac{3}{2}}x}dx, then ∫02Ixsin⁡xcos⁡xsin⁡4x+cos⁡4xdx\int_{0}^{2I} \frac{x\sin x\cos x}{\sin^{4}x +\cos^{4}x}dx equals:

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  5. Question 5

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

    161
    Let the slope of the tangent to a curve y=f(x)y = f(x) at (x,y)(x,y) be given by 2tan⁡x(cos⁡x−y)2\tan x(\cos x - y). if the curve passes through the point (π/4,0)(\pi/4,0), then the value of ∫0π/2ydx\int_{0}^{\pi/2} ydx is equal to

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