If the solution curve of the differential equation (2x $-$ 10y³)dy + ydx = 0, passes through the points (0, 1) and (2, $\beta$), then $\beta$ is a root of the equation :

1

If two tangents drawn from a point P to the parabola y2 = 16(x $-$ 3) are at right angles, then the locus of point P i…

Topic: JEE Main 2021 (27 August Evening Shift)

2

Let M and m respectively be the maximum and minimum values of the function f(x) = tan$-$1 (sin x + cos x) in $\left[ {…

Topic: JEE Main 2021 (27 August Evening Shift)

3

Let $A = \left( {\matrix{ {[x + 1]} & {[x + 2]} & {[x + 3]} \cr {[x]} & {[x + 3]} & {[x + 3]} \c…

Topic: JEE Main 2021 (27 August Evening Shift)

4

The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m $-$ n = 0 and mn + nl …

Topic: JEE Main 2021 (27 August Evening Shift)

1

Let [$\lambda$] be the greatest integer less than or equal to $\lambda$. The set of all values of $\lambda$ for which t…

Topic: JEE Main 2021 (27 August Evening Shift)

2

A box open from top is made from a rectangular sheet of dimension a x b by cutting squares each of side x from eac…

Topic: JEE Main 2021 (27 August Evening Shift)

3

The set of all values of K > $-$1, for which the equation ${(3{x^2} + 4x + 3)^2} - (k + 1)(3{x^2} + 4x + 3)(3{x^2} +…

Topic: JEE Main 2021 (27 August Evening Shift)

4

Let Z be the set of all integers,$A = \{ (x,y) \in Z \times Z:{(x - 2)^2} + {y^2} \le 4\} $, $B = \{ (x,y) \in Z \times…

Topic: JEE Main 2021 (27 August Evening Shift)

5

The area of the region bounded by the parabola (y $-$ 2)2 = (x $-$ 1), the tangent to it at the point whose ordinate is…

Topic: JEE Main 2021 (27 August Evening Shift)

6

If $y(x)=\cot^{-1}\!\left(\dfrac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right),\; x\in\left(…

Topic: JEE Main 2021 (27 August Evening Shift)

7

The value of the integral $\displaystyle \int_{0}^{1} \frac{\sqrt{x}\,dx}{(1+x)(1+3x)(3+x)}$ is:

Topic: JEE Main 2021 (27 August Evening Shift)

8

If $\mathop {\lim }\limits_{x \to \infty } \left( {\sqrt {{x^2} - x + 1} - ax} \right) = b$, then the ordered pair (a,…

Topic: JEE Main 2021 (27 August Evening Shift)