Let x = x(y) be the solution of the differential equation $2y\,{e^{x/{y^2}}}dx + \left( {{y^2} - 4x{e^{x/{y^2}}}} \right)dy = 0$ such that x(1) = 0. Then, x(e) is equal to :

1

The area of the bounded region enclosed by the curve $y = 3 - \left| {x - {1 \over 2}} \right| - |x + 1|$ and the x-axi…

Topic: JEE Main 2022 (28 June Evening Shift)

2

Let f : R $\to$ R be a continuous function satisfying f(x) + f(x + k) = n, for all x $\in$ R where k > 0 and n is a po…

Topic: JEE Main 2022 (28 June Evening Shift)

3

Let f : R $\to$ R be a differentiable function such that $f\left( {{\pi \over 4}} \right) = \sqrt 2 ,\,f\left( {{\pi …

Topic: JEE Main 2022 (28 June Evening Shift)

4

Let f, g : R $\to$ R be functions defined by$f(x) = \left\{ {\matrix{ {[x]} & , & {x < 0} \cr {|1 - x|} & , & {x …

Topic: JEE Main 2022 (28 June Evening Shift)

5

If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 : 7 an…

Topic: JEE Main 2022 (28 June Evening Shift)

6

The term independent of x in the expansion of $(1 - {x^2} + 3{x^3}){\left( {{5 \over 2}{x^3} - {1 \over {5{x^2}}}} \rig…

Topic: JEE Main 2022 (28 June Evening Shift)

7

The number of ways to distribute 30 identical candies among four children C1, C2, C3 and C4 so that C2 receives at leas…

Topic: JEE Main 2022 (28 June Evening Shift)

8

Let f(x) be a quadratic polynomial such that f($-$2) + f(3) = 0. If one of the roots of f(x) = 0 is $-$1, then the sum …

Topic: JEE Main 2022 (28 June Evening Shift)

9

Let R1 = {(a, b) $\in$ N $\times$ N : |a $-$ b| $\le$ 13} andR2 = {(a, b) $\in$ N $\times$ N : |a $-$ b| $\ne$ 13}. The…

Topic: JEE Main 2022 (28 June Evening Shift)

1

Let the slope of the tangent to a curve y = f(x) at (x, y) be given by 2 $\tan x(\cos x - y)$. If the curve passes thro…

Topic: JEE Main 2022 (28 June Evening Shift)

2

Let a triangle be bounded by the lines L1 : 2x + 5y = 10; L2 : $-$4x + 3y = 12 and the line L3, which passes through th…

Topic: JEE Main 2022 (28 June Evening Shift)

3

Let a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola ${{{x^2}…

Topic: JEE Main 2022 (28 June Evening Shift)

4

Let $\overrightarrow a = \alpha \widehat i + 2\widehat j - \widehat k$ and $\overrightarrow b = - 2\widehat i + \alp…

Topic: JEE Main 2022 (28 June Evening Shift)

5

If vertex of a parabola is (2, $-$1) and the equation of its directrix is 4x $-$ 3y = 21, then the length of its latus …

Topic: JEE Main 2022 (28 June Evening Shift)

6

The probability that a randomly chosen one-one function from the set {a, b, c, d} to the set {1, 2, 3, 4, 5} satisfies …

Topic: JEE Main 2022 (28 June Evening Shift)

7

The value of $\mathop {\lim }\limits_{n \to \infty } 6\tan \left\{ {\sum\limits_{r = 1}^n {{{\tan }^{ - 1}}\left( {{1 \…

Topic: JEE Main 2022 (28 June Evening Shift)

8

Let $\overrightarrow a $ be a vector which is perpendicular to the vector $3\widehat i + {1 \over 2}\widehat j + 2\wide…

Topic: JEE Main 2022 (28 June Evening Shift)

9

If cot$\alpha$ = 1 and sec$\beta$ = $ - {5 \over 3}$, where $\pi < \alpha < {{3\pi } \over 2}$ and ${\pi \over 2} < …

Topic: JEE Main 2022 (28 June Evening Shift)