PYQ Vault
EbooksTutor

Day 176: JEE Mains Maths

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

  1. Question 1

    Conic Sections. Asked once: 28 Jan 2025 (same type asked 3 times) See all 3 of this type

    58
    Let the equation of the circle, which touches xx-axis at the point (a,0),a>0(a,0),a > 0 and cuts off an intercept of length bb on yy-axis be x2+y2−αx+βy+γ=0x^{2}+y^{2}- \alpha x + \beta y + \gamma = 0. If the circle lies below x-axis, then the ordered pair (2a,b2)\left( 2a,b^{2} \right) is equal to :

    Tap an option to check your answer.

  2. Question 2

    Quadratic Equations. Asked once: 21 Jan 2026 S2 (same type asked 3 times) See all 3 of this type

    59
    Let α\alpha and β\beta be the roots of equation x2+2ax+(3a+10)=0x^{2}+ 2ax + (3a + 10) = 0 such that α<1<β\alpha < 1 < \beta. Then the set of all possible values of aa is :

    Tap an option to check your answer.

  3. Question 3

    Trigonometric Equations. Asked once: 5 Apr 2024 (same type asked 3 times) See all 3 of this type

    75
    Suppose θ∈[0,π4]\theta\in\left\lbrack 0,\frac{\pi}{4} \right\rbrack is a solution of 4cos⁡θ−3sin⁡θ=14\cos\theta- 3\sin\theta= 1. Then cos⁡θ\cos\theta is equal to :

    Tap an option to check your answer.

  4. Question 4

    Complex Numbers. Asked once: 3 Apr 2025 (same type asked 3 times) See all 3 of this type

    64
    Let z∈Cz\in C be such that z2+3iz−2+i=2+3i\frac{z^{2}+ 3i}{z- 2 +i}= 2 + 3i. Then the sum of all possible values of z2z^{2} is.

    Tap an option to check your answer.

  5. Question 5

    Determinants. Asked once: 6 Apr 2024 (same type asked 3 times) See all 3 of this type

    68
    For α,β∈R\alpha,\beta \in R and a natural number nn, let
    Ar=∣r1n22+α2r2n2−β3r−23n(3n−1)2∣. Then 2A10−A8 is A_{r}=\left| \begin{matrix} r & 1 & \frac{n^{2}}{2}+ \alpha \\ 2r & 2 & n^{2}- \beta \\ 3r - 2 & 3 & \frac{n(3n - 1)}{2} \end{matrix} \right|.\text{~Then~}2A_{10}-A_{8}\text{~is~}

    Tap an option to check your answer.