Let E₁ and E₂ be two events such that the conditional probabilities $P({E_1}|{E_2}) = {1 \over 2}$, $P({E_2}|{E_1}) = {3 \over 4}$ and $P({E_1} \cap {E_2}) = {1 \over 8}$. Then :

1

Let f(x) be a polynomial function such that $f(x) + f'(x) + f''(x) = {x^5} + 64$. Then, the value of $\mathop {\lim }\l…

Topic: JEE Main 2022 (25 June Morning Shift)

2

If ${1 \over {2\,.\,{3^{10}}}} + {1 \over {{2^2}\,.\,{3^9}}} + \,\,.....\,\, + \,\,{1 \over {{2^{10}}\,.\,3}} = {K \ove…

Topic: JEE Main 2022 (25 June Morning Shift)

3

Let f : R $\to$ R be defined as $f(x) = {x^3} + x - 5$. If g(x) is a function such that $f(g(x)) = x,\forall 'x' \in R$…

Topic: JEE Main 2022 (25 June Morning Shift)

4

Let $A$ be a $3 \times 3$ real matrix such that $A\begin{pmatrix}1 \\ 1 \\ 0\end{pmatrix} = \begin{pmatrix}1 \\ 1 \\ …

Topic: JEE Main 2022 (25 June Morning Shift)

5

Let f : N $\to$ R be a function such that $f(x + y) = 2f(x)f(y)$ for natural numbers x and y. If f(1) = 2, then the val…

Topic: JEE Main 2022 (25 June Morning Shift)

6

The value of $\int\limits_0^\pi {{{{e^{\cos x}}\sin x} \over {(1 + {{\cos }^2}x)({e^{\cos x}} + {e^{ - \cos x}})}}dx} …

Topic: JEE Main 2022 (25 June Morning Shift)

1

Let $A = \left[ {\matrix{ 0 & { - 2} \cr 2 & 0 \cr } } \right]$. If M and N are two matrices given by $M = \sum…

Topic: JEE Main 2022 (25 June Morning Shift)

2

Let $g:(0,\infty ) \to R$ be a differentiable function such that $\int {\left( {{{x(\cos x - \sin x)} \over {{e^x} + 1}…

Topic: JEE Main 2022 (25 June Morning Shift)

3

Let $f:R \to R$ and $g:R \to R$ be two functions defined by $f(x) = {\log _e}({x^2} + 1) - {e^{ - x}} + 1$ and $g(x) = …

Topic: JEE Main 2022 (25 June Morning Shift)

4

Let $\overrightarrow a = {a_1}\widehat i + {a_2}\widehat j + {a_3}\widehat k$ ${a_i} > 0$, $i = 1,2,3$ be a vector whi…

Topic: JEE Main 2022 (25 June Morning Shift)

5

Let $y = y(x)$ be the solution of the differential equation $(x + 1)y' - y = {e^{3x}}{(x + 1)^2}$, with $y(0) = {1 \ove…

Topic: JEE Main 2022 (25 June Morning Shift)

6

If the solution curve $y = y(x)$ of the differential equation ${y^2}dx + ({x^2} - xy + {y^2})dy = 0$, which passes thro…

Topic: JEE Main 2022 (25 June Morning Shift)

7

Let $x = 2t$, $y = {{{t^2}} \over 3}$ be a conic. Let S be the focus and B be the point on the axis of the conic such t…

Topic: JEE Main 2022 (25 June Morning Shift)

8

Let a circle C in complex plane pass through the points ${z_1} = 3 + 4i$, ${z_2} = 4 + 3i$ and ${z_3} = 5i$. If $z( \ne…

Topic: JEE Main 2022 (25 June Morning Shift)