When a certain biased die is rolled, a particular face occurs with probability ${1 \over 6} - x$ and its opposite face occurs with probability ${1 \over 6} + x$. All other faces occur with probability ${1 \over 6}$. Note that opposite faces sum to 7 in any die. If 0 < x < ${1 \over 6}$, and the probability of obtaining total sum = 7, when such a die is rolled twice, is ${13 \over 96}$, then the value of x is :
Previous 10 Questions — JEE Main 2021 (27 August Morning Shift)
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If $\alpha$, $\beta$ are the distinct roots of x2 + bx + c = 0, then $\mathop {\lim }\limits_{x \to \beta } {{{e^{2({x…
Topic: JEE Main 2021 (27 August Morning Shift)
Let us consider a curve, y = f(x) passing through the point ($-$2, 2) and the slope of the tangent to the curve at any …
Topic: JEE Main 2021 (27 August Morning Shift)
et y = y(x) be the solution of the differential equation ${{dy} \over {dx}} = 2(y + 2\sin x - 5)x - 2\cos x$ such that …
Topic: JEE Main 2021 (27 August Morning Shift)
$S = { z \in \mathbb{C} : \dfrac{z - i}{z + 2i} \in \mathbb R }$, then:
Topic: JEE Main 2021 (27 August Morning Shift)
If the matrix $A = \left( {\matrix{ 0 & 2 \cr K & { - 1} \cr } } \right)$ satisfies $A({A^3} + 3I) = 2I…
Topic: JEE Main 2021 (27 August Morning Shift)
(sin−1x)2−(cos−1x)2=a,0<x<1,a;=0
then the value of
2x2−12x^2 - 12x2−1
is:
Topic: JEE Main 2021 (27 August Morning Shift)
Let A be a fixed point (0, 6) and B be a moving point (2t, 0). Let M be the mid-point of AB and the perpendicular bisec…
Topic: JEE Main 2021 (27 August Morning Shift)
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If x2 + 9y2 $-$ 4x + 3 = 0, x, y $\in$ R, then x and y respectively lie in the intervals :
Topic: JEE Main 2021 (27 August Morning Shift)
$\int\limits_6^{16} {{{{{\log }_e}{x^2}} \over {{{\log }_e}{x^2} + {{\log }_e}({x^2} - 44x + 484)}}dx} $$ is equal to :
Topic: JEE Main 2021 (27 August Morning Shift)
A wire of length 20 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a …
Topic: JEE Main 2021 (27 August Morning Shift)
