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JEE Advanced

Benzene and naphthalene form an ideal solution at room temperature. For this process, the true statement(s) is (are)

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Let $X=(_{10}C_{1})_{2}+2(_{10}C_{2})_{2}+3(_{10}C_{3})_{2}+¨+10(_{10}C_{10})_{2}$, where $_{10}C_{r}$, $r∈{1,2,,¨ 10}$denote binomial coefficients. Then, the value of $14301 X$is _________.

In R', consider the planes $P_{1},y=0$ and $P_{2}:x+z=1$. Let $P_{3}$, be a plane, different from $P_{1}$, and $P_{2}$, which passes through the intersection of $P_{1}$, and $P_{2}$. If the distance of the point $(0,1,0)$ from $P_{3}$, is $1$ and the distance of a point $(α,β,γ)$ from $P_{3}$ is $2$, then which of the following relation is (are) true ?

Let PQ be a focal chord of the parabola $y_{2}=4ax$ The tangents to the parabola at P and Q meet at a point lying on the line $y=2x+a,a>0$. Length of chord PQ is

Let $S={xϵ(−π,π):x=0,+2π }$The sum of all distinct solutions of the equation $3 secx+cosecx+2(tanx−cotx)=0$ in the set S is equal to

For each positive integer $n$, let $y_{n}=n1 ((n+1)(n+2)n+n˙ )_{n1}$For $x∈R$let $[x]$be the greatest integer less than or equal to $x$. If $(lim)_{n→∞}y_{n}=L$, then the value of $[L]$is ______.

Let x, y and z be three vectors each of magnitude V2 tion on and the angle between each pair of them is E. If a is a let non-zero vector perpendicular to x and yx z and b is a non-zero tor perpendicular to y and z x x, then 1.

Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 1, 2, 3,4, 5; and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let $x_{i}$ be the number on the card drawn from the ith box, i = 1, 2, 3.The probability that $x_{1}+x_{2}+x_{3}$ is odd isThe probability that $x_{1},x_{2},x_{3}$ are in an aritmetic progression is

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is