JEE Maths PYQ Practice, chapter-wise

JEE Main 2021 (Online) 1st September Evening ShiftQuestion 5506

The range of the function $f(x)=\log_{\sqrt5}\left(3+\cos\left(\frac{3\pi}4+x\right)+\cos\left(\frac\pi4+x\right)+\cos\left(\frac\pi4-x\right)-\cos\left(\frac{3\pi}4-x\right)\right)$ is :

Functions

$\left[\frac1{\sqrt5},\sqrt5\right]$$[0,2]$$\left(0,\sqrt5\right)$$[-2,2]$

JEE Main 2023 (Online) 31st January Morning ShiftQuestion 5507

Let a circle $C_1$ be obtained on rolling the circle $x^2+y^2-4x-6y+11=0$ upwards $4$ units on the tangent $T$ to it at the point $(3,2)$. Let $C_2$ be the image of $C_1$ in $T$. Let $A$ and $B$ be the centers of circles $C_1$ and $C_2$ respectively, and $M$ and $N$ be respectively the feet of perpendiculars drawn from $A$ and $B$ on the $x$-axis. Then the area of the trapezium $AMNB$ is:

Circle

$2\left(2+\sqrt2\right)$$4\left(1+\sqrt2\right)$$3+2\sqrt2$$2\left(1+\sqrt2\right)$

JEE Main 2019 (Online) 11th January Morning ShiftQuestion 5508

Equation of a common tangent to the parabola $y^2=4x$ and the hyperbola $xy=2$ is :

Parabola

$x+y+1=0$$x-2y+4=0$$x+2y+4=0$$4x+2y+1=0$

JEE Main 2023 (Online) 30th January Morning ShiftQuestion 5509

Let $A=\begin{bmatrix}m&n\\p&q\end{bmatrix}$, $d=|A|\ne0$ and $|A-d(\operatorname{Adj}A)|=0$. Then

Matrices

$(1+d)^2=(m+q)^2$$1+d^2=(m+q)^2$$(1+d)^2=m^2+q^2$$1+d^2=m^2+q^2$

JEE Main 2019 (Online) 8th April Evening ShiftQuestion 5510

Let $f(x)=\int_0^x g(t)\,dt$, where $g$ is a non-zero even function. If $f(x+5)=g(x)$, then $\int_0^x f(t)\,dt$ equals

Definite Integration

$\int_5^{x+5}g(t)\,dt$$\int_{x+5}^{5}g(t)\,dt$$5\int_{x+5}^{5}g(t)\,dt$$2\int_5^{x+5}g(t)\,dt$

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