JEE Maths PYQ Practice, chapter-wise

JEE Main 2016 (Offline)Question 5496

A wire of length $2$ units is cut into two parts which are bent respectively to form a square of side $=x$ units and a circle of radius $=r$ units. If the sum of the areas of the square and the circle so formed is minimum, then

Differentiation and its Application

$x=2r$$2x=r$$2x=(\pi+4)r$$(4-\pi)x=\pi r$

JEE Main 2017 (Online) 8th AprilQuestion 5497

Consider an ellipse, whose center is at the origin and its major axis is along the $x$-axis. If its eccentricity is $\frac35$ and the distance between its foci is $6$, then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is:

Ellipse

$32$$80$$40$$8$

JEE Main 2018 (Online) 15th April Morning ShiftQuestion 5498

The mean of a set of $30$ observations is $75$. If each observation is multiplied by a nonzero number $\lambda$ and then each of them is decreased by $25$, their mean remains the same. The $\lambda$ is equal to

Statistics

$\frac{10}{3}$$\frac43$$\frac13$$\frac23$

JEE Main 2023 (Online) 30th January Morning ShiftQuestion 5499

Let $y=x+2$, $4y=3x+6$ and $3y=4x+1$ be three tangent lines to the circle $(x-h)^2+(y-k)^2=r^2$. Then $h+k$ is equal to :

Circle

$5$$5\left(1+\sqrt2\right)$$6$$5\sqrt2$

JEE Main 2019 (Online) 11th January Morning ShiftQuestion 5500

The direction ratios of normal to the plane through the points $(0,-1,0)$ and $(0,0,1)$ and making an angle $\frac\pi4$ with the plane $y-z+5=0$ are: (i) $2,-1,1$ (ii) $2,\sqrt2,-\sqrt2$ (iii) $\sqrt2,1,-1$ (iv) $2\sqrt3,1,-1$

3D Geometry

(i) and (ii)(ii) and (iii)(iii) and (iv)all of (i), (ii), (iii), (iv)

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