Let $E$ and $F$ be two independent events. The probability that both $E$ and $F$ happen is $\dfrac{1}{12}$ and the probability that neither $E$ nor $F$ happens is $\dfrac{1}{2}$. Then a value of $\dfrac{P(E)}{P(F)}$ is:
Previous 10 Questions — JEE Main 2017 (9 April Morning Shift)
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A value of $x$ satisfying the equation
$\sin!\big(\cot^{-1}(1+x)\big) = \cos!\big(\tan^{-1} x\big)$
is:
Topic: JEE Main 2017 (9 April Morning Shift)
The sum of all real values of $x$ satisfying the equation
$2^{(x-1)(x^{2} + 5x - 50)} = 1$ is:
Topic: JEE Main 2017 (9 April Morning Shift)
The equation
$\operatorname{Im}\left( \dfrac{iz - 2}{z - i} \right) + 1 = 0,; z \in \mathbb{C},; z \neq i$
represents a…
Topic: JEE Main 2017 (9 April Morning Shift)
The two adjacent sides of a cyclic quadrilateral are $2$ and $5$ and the angle between them is $60^\circ$.
If the area …
Topic: JEE Main 2017 (9 April Morning Shift)
The function $f : \mathbb{N} \to \mathbb{N}$ defined by
$f(x) = x - 5\left\lfloor \dfrac{\pi x}{5} \right\rfloor$,
wher…
Topic: JEE Main 2017 (9 April Morning Shift)
For two $3 \times 3$ matrices $A$ and $B$, let
$A + B = 2B^T$ and $3A + 2B = I_3$,
where $B^T$ is the transpose of $B$ …
Topic: JEE Main 2017 (9 April Morning Shift)
The coefficient of $x^{-5}$ in the binomial expansion of
$\left( \dfrac{x+1}{x^{\frac{2}{3}} - x^{\frac{1}{3}} + 1} ;-;…
Topic: JEE Main 2017 (9 April Morning Shift)
The number of ways in which $5$ boys and $3$ girls can be seated on a round table if a particular boy $B_1$ and a parti…
Topic: JEE Main 2017 (9 April Morning Shift)
If three positive numbers $a, b$ and $c$ are in A.P. such that $abc = 8$, then the minimum possible value of $b$ is :
Topic: JEE Main 2017 (9 April Morning Shift)
Next 10 Questions — JEE Main 2017 (9 April Morning Shift)
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The sum of $100$ observations and the sum of their squares are $400$ and $2475$, respectively.
Later on, three observat…
Topic: JEE Main 2017 (9 April Morning Shift)
If the vector $\vec{b} = 3\vec{j} + 4\vec{k}$ is written as the sum of a vector $\vec{b_1}$ parallel to
$\vec{a} = \vec…
Topic: JEE Main 2017 (9 April Morning Shift)
From a group of $10$ men and $5$ women, four-member committees are to be formed, each of which must contain at least on…
Topic: JEE Main 2017 (9 April Morning Shift)
The eccentricity of an ellipse having centre at the origin, axes along the coordinate axes, and passing through the poi…
Topic: JEE Main 2017 (9 April Morning Shift)
If
$\displaystyle \int_{1}^{2} \frac{dx}{(x^{2} - 2x + 4)^{\tfrac{3}{2}}} = \frac{k}{k+5}$,
then $k$ is equal to:
Topic: JEE Main 2017 (9 April Morning Shift)
If $2x = y^{\tfrac{1}{5}} + y^{-\tfrac{1}{5}}$ and
$(x^{2} - 1)\dfrac{d^{2}y}{dx^{2}} + \lambda x\dfrac{dy}{dx} + ky = …
Topic: JEE Main 2017 (9 April Morning Shift)
A line drawn through the point $P(4,7)$ cuts the circle $x^{2} + y^{2} = 9$ at the points $A$ and $B$.
Then $PA \cdot P…
Topic: JEE Main 2017 (9 April Morning Shift)
Let $f$ be a polynomial function such that
$f(3x) = f'(x)\cdot f''(x)$ for all $x \in \mathbb{R}$.
Then:
Topic: JEE Main 2017 (9 April Morning Shift)
A square, of each side $2$, lies above the $x$-axis and has one vertex at the origin.
If one of the sides passing throu…
Topic: JEE Main 2017 (9 April Morning Shift)
If
$\displaystyle f\left(\frac{3x-4}{3x+4}\right) = x + 2,; x \ne -\frac{4}{3}$
and
$\displaystyle \int f(x),dx = A\ln|…
Topic: JEE Main 2017 (9 April Morning Shift)
