A player $X$ has a biased coin whose probability of showing heads is $p$ and a player $Y$ has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If $X$ starts the game, and the probability of winning the game by both the players is equal, then the value of $p$ is :
Previous 10 Questions — JEE Main 2018 (15 April Evening Shift)
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If the mean of the data $7, 8, 9, 7, 8, 7, \lambda, 8$ is $8$, then the variance of this data is :
Topic: JEE Main 2018 (15 April Evening Shift)
If the position vectors of the vertices $A$, $B$ and $C$ of a $\triangle ABC$ are respectively $4\hat{i}+7\hat{j}+8\hat…
Topic: JEE Main 2018 (15 April Evening Shift)
If $f(x)$ is a quadratic expression such that $f(1)+f(2)=0$, and $-1$ is a root of $f(x)=0$, then the other root of $f(…
Topic: JEE Main 2018 (15 April Evening Shift)
Let $f\colon A\to B$ be a function defined as $f(x)=\dfrac{x-1}{x-2}$, where $A=\mathbb{R}-{2}$ and $B=\mathbb{R}-{1}$.…
Topic: JEE Main 2018 (15 April Evening Shift)
Suppose $A$ is any $3\times 3$ non-singular matrix and $(A-3I)(A-5I)=0$ where $I=I_{3}$ and $O=O_{3}$. If $\alpha A+\be…
Topic: JEE Main 2018 (15 April Evening Shift)
The number of four letter words that can be formed using the letters of the word $\text{BARRACK}$ is :
Topic: JEE Main 2018 (15 April Evening Shift)
If $|z - 3 + 2i| \le 4$ then the difference between the greatest value and the least value of $|z|$ is :
Topic: JEE Main 2018 (15 April Evening Shift)
If the system of linear equations$x + ay + z = 3$$x + 2y + 2z = 6$$x + 5y + 3z = b$has no solution, then :
Topic: JEE Main 2018 (15 April Evening Shift)
If $a$, $b$, $c$ are in A.P. and $a^{2}$, $b^{2}$, $c^{2}$ are in G.P. such that $a < b < c$ and $a + b + c = \dfrac{3}…
Topic: JEE Main 2018 (15 April Evening Shift)
Next 10 Questions — JEE Main 2018 (15 April Evening Shift)
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An angle between the lines whose direction cosines are given by the equations
$l + 3m + 5n = 0$ and $5lm - 2mn + 6nl = …
Topic: JEE Main 2018 (15 April Evening Shift)
Tangents drawn from the point $(-8,0)$ to the parabola $y^{2} = 8x$ touch the parabola at $P$ and $Q$. If $F$ is the fo…
Topic: JEE Main 2018 (15 April Evening Shift)
The foot of the perpendicular drawn from the origin, on the line, $3x + y = \lambda\ (\lambda \ne 0)$ is $P$. If the li…
Topic: JEE Main 2018 (15 April Evening Shift)
The sides of a rhombus $ABCD$ are parallel to the lines, $x - y + 2 = 0$ and $7x - y + 3 = 0$. If the diagonals of the …
Topic: JEE Main 2018 (15 April Evening Shift)
The curve satisfying the differential equation $(x^{2}-y^{2}),dx + 2xy,dy = 0$ and passing through the point $(1,1)$ is…
Topic: JEE Main 2018 (15 April Evening Shift)
If $\displaystyle \int \frac{2x+5}{\sqrt{7-6x-x^{2}}},dx = A\sqrt{7-6x-x^{2}} + B\sin^{-1}!\left(\frac{x+3}{4}\right) +…
Topic: JEE Main 2018 (15 April Evening Shift)
If $I_1=\displaystyle\int_{0}^{1} e^{-x}\cos^{2}x,dx$;
$I_2=\displaystyle\int_{0}^{1} e^{-x^{2}}\cos^{2}x,dx$ and
$I_3=…
Topic: JEE Main 2018 (15 April Evening Shift)
The value of the integral $\displaystyle\int_{\pi/4}^{3\pi/4}\frac{x}{1+\sin x},dx$ is :
Topic: JEE Main 2018 (15 April Evening Shift)
Let $f(x)$ be a polynomial of degree $4$ having extreme values at $x=1$ and $x=2$.
If $\lim_{x\to 0}\left(\dfrac{f(x)}{…
Topic: JEE Main 2018 (15 April Evening Shift)
If $f(x)=\sin^{-1}\left(\dfrac{2x^{3}}{1+9x^{2}}\right)$, then $f'!\left(-\dfrac{1}{2}\right)$ equals
Topic: JEE Main 2018 (15 April Evening Shift)
