PYQ Vault
EbooksTutor

Day 511: JEE Mains Maths

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

  1. Question 1

    Matrices. Asked once: 1 Feb 2024

    63
    If A=[21−12],B=[1011],C=ABATA =\begin{bmatrix} \sqrt{2} & 1 \\ - 1 & \sqrt{2} \end{bmatrix},B =\begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix},C =ABA^{T} and XX =ATC2 A=A^{T}C^{2}\text{ }A, then detXdetX is equal to:

    Tap an option to check your answer.

  2. Question 2

    Permutations and Combinations. Asked once: 29 Jan 2024

    179
    Let the set C={(x,y)∣x2−2y=2023,x,y∈N}C=\left\{ (x,y) \mid x^{2}-2^{y}= 2023,x,y\in\mathbb{N} \right\}. Then ∑(x,y)∈C(x+y)\sum_{(x,y) \in C} (x+y) is equal to

  3. Question 3

    Probability. Asked once: 27 Jan 2024

    163
    An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that the first draw gives all white balls and the second draw gives all black balls, is:

    Tap an option to check your answer.

  4. Question 4

    Quadratic Equations. Asked once: 4 Apr 2024

    171
    Let S={sin⁡22θ:(sin⁡4θ+cos⁡4θ)x2+(sin⁡2θ)x+S =\left\{ \sin^{2}2\theta:\left( \sin^{4}\theta +\cos^{4}\theta \right)x^{2}+ (\sin2\theta)x + \right. (sin⁡6θ+cos⁡6θ)=0\left( \sin^{6}\theta +\cos^{6}\theta \right)= 0 has real roots }\}. If α\alpha and β\beta be the smallest and largest elements of the set SS, respectively, then 3((α−2)2+(β−1)2)3\left( (\alpha - 2)^{2}+ (\beta - 1)^{2} \right) equals .........

  5. Question 5

    Relations and Functions. Asked once: 6 Apr 2024

    66
    Let A={n∈[100,700]∩N:n\mathbf{A = \{ n \in \lbrack 100,700\rbrack \cap N:n} is neither a multiple of 3 nor a multiple of 4}\}. Then the number of elements in AA is

    Tap an option to check your answer.