PYQ Vault
EbooksTutor

Day 402: JEE Mains Maths

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

  1. Question 1

    Quadratic Equations. Asked once: 2021 Paper 4 (same type asked 8 times) See all 8 of this type

    75
    Let α\alpha and β\beta be the roots of x2−6x−2=0x^{2}- 6x- 2 = 0. If an=αn−βna_{n}=\alpha^{n}-\beta^{n} for n≥1n\geq 1, then the value of a10−2a83a9\frac{a_{10}- 2a_{8}}{3a_{9}} is:

    Tap an option to check your answer.

  2. Question 2

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

    86
    If 3(cos⁡2x)=(3−1)cos⁡x+1\sqrt{3}\left( \cos^{2}x \right)= (\sqrt{3}- 1)\cos x+ 1, the number of solutions of the given equation when x∈[0,π2]x\in\left\lbrack 0,\frac{\pi}{2} \right\rbrack is

  3. Question 3

    Differential Equations. Asked once: 29 Jan 2025 (same type asked 41 times) See all 41 of this type

    145
    If for the solution curve y=f(x)y = f(x) of the differential equation dydx+(tan⁡x)y=2+secx(1+2secx)2\frac{dy}{dx}+ (\tan x)y =\frac{2 + secx}{(1 + 2secx)^{2}}, x∈(−π2,π2),f(π3)=310x \in\left( \frac{- \pi}{2},\frac{\pi}{2} \right),f\left( \frac{\pi}{3} \right)=\frac{\sqrt{3}}{10}, then f(π4)f\left( \frac{\pi}{4} \right) is equal to:

    Tap an option to check your answer.

  4. Question 4

    Three Dimensional Geometry. Asked once: 9 Apr 2024 (same type asked 33 times) See all 33 of this type

    75
    The shortest distance between the line x−34=y+7−11=z−15\frac{x- 3}{4}=\frac{y+ 7}{- 11}=\frac{z- 1}{5} and x−53=y−9−6=z+21\frac{x- 5}{3}=\frac{y- 9}{- 6}=\frac{z+ 2}{1} is :

    Tap an option to check your answer.

  5. Question 5

    Determinants. Asked once: 24 Jan 2025 (same type asked 26 times) See all 26 of this type

    136
    If the system of equations
    x+2y−3z=22x+λy+5z=514x+3y+μz=33\begin{matrix} & x+ 2y- 3z= 2 \\ & 2x+\lambda y+ 5z= 5 \\ & 14x+ 3y+\mu z= 33 \end{matrix}
    has infinitely many solutions, then λ+μ\lambda+\mu is equal to:

    Tap an option to check your answer.