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Day 138: JEE Mains Maths

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

  1. Question 1

    Permutations and Combinations. Asked once: 25 Jun 2022 (same type asked 7 times) See all 7 of this type

    89
    Let AA be a 3×33 \times 3 matrix having entries from. the set {−1,0,1}\mathbf{\{ - 1,0,1\}}. The number of all such matrices A having sum of all the entries equal to 5, is

  2. Question 2

    Trigonometric Equations. Asked once: 3 Apr 2025 (same type asked 7 times) See all 7 of this type

    141
    The number of solutions of equation (4−3)sin⁡x\left( 4 -\sqrt{3} \right)\sin x −23cos⁡2x=−41+3,x∈- 2\sqrt{3}\cos^{2}x= -\frac{4}{1 +\sqrt{3}},x\in [−2π,5π2]\left\lbrack - 2\pi,\frac{5\pi}{2} \right\rbrack is.

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  3. Question 3

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

    75
    Let α\alpha and β\beta be the sum and the product of all the non-zero solutions of the equation (zˉ)2+∣z∣=0,z∈C(\bar{z})^{2}+ |z| = 0,z\in C. Then 4(α2+β2)4\left( \alpha^{2}+\beta^{2} \right) is equal to:

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  4. Question 4

    Vector Algebra. Asked once: 9 Apr 2024 (same type asked 7 times) See all 7 of this type

    78
    Let three vectors a→=αi^+4j^+2k^\overrightarrow{a}= \alpha\widehat{i}+ 4\widehat{j}+ 2\widehat{k}, b→=5i^+3j^+4k^,c→=xi^+yj^+zk^\overrightarrow{b}= 5\widehat{i}+ 3\widehat{j}+ 4\widehat{k},\overrightarrow{c}= x\widehat{i}+ y\widehat{j}+ z\widehat{k} from a triangle such that c→=a→−b→\overrightarrow{c}=\overrightarrow{a}-\overrightarrow{b} and the area of the triangle is 565\sqrt{6}. if α\alpha is a positive real number, then ∣c→∣2|\overrightarrow{c}|^{2} is:

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  5. Question 5

    Conic Sections. Asked once: 22 Jan 2025 (same type asked 7 times) See all 7 of this type

    64
    A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a circle that has centre at the point (2,5)(2,5) and intersects the circle C at exactly two points. If the set of all possible values of rr is the interval (α,β)(\alpha,\beta), then 3β−2α3\beta - 2\alpha is equal to :

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