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JEE Advanced

The number of neutrons emitted when $._{92}U$ undergoes controlled nuclear fission to $._{54}Xe$ and $._{38}Sr$

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A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation $3 x+y−6=0$ and the point D is (3 sqrt3/2, 3/2). Further, it is given that the origin and the centre of C are on the same side of the line PQ. (1)The equation of circle C is (2)Points E and F are given by (3)Equation of the sides QR, RP are

Let $M$be a $2×2$symmetric matrix with integer entries. Then $M$is invertible ifThe first column of $M$is the transpose of the second row of $M$The second row of $M$is the transpose of the first column of $M$$M$is a diagonal matrix with non-zero entries in the main diagonalThe product of entries in the main diagonal of $M$is not the square of an integer

Football teams T1 and T2 have to play two games against each other. It is assumed that theoutcomes of the two games are independent. The probabilities of T1 winning, drawing andlosing a game against T2 are1/ 2,and1/6,1/3respectively. Each team gets 3 points for a win,1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total pointsscored by teams T1 and T2, respectively, after two gamesP $(X=Y)$ is

Let $g:R→R$ be a differentiable function with $g(0)=0,g_{′}(1)=0,g_{′}(1)=0$.Let $f(x)={∣x∣x g(x),0=0and0,x=0$ and $h(x)=e_{∣x∣}$ for all $x∈R$. Let $(foh)(x)$ denote $f(h(x))and(hof)(x)$ denote $h(f(x))$. Then which of thx!=0 and e following is (are) true?

For how many values, of p, the circle $x_{2}+y_{2}+2x+4y−p=0$and the coordinate axes have exactly three common points?

Let $P$be a matrix of order $3×3$such that all the entries in $P$are from the set ${−1,0,1}$. Then, the maximum possible value of the determinant of $P$is ______.

The value of $∫_{0}4x_{3}{dx_{2}d_{2} (1−x_{2})_{5}}dxis$

Let $S={1,2,3,¨ 9}F˙ork=1,2,5,letN_{k}$be the number of subsets of S, each containing five elements out of which exactly $k$are odd. Then $N_{1}+N_{2}+N_{3}+N_{4}+N_{5}=?$210 (b) 252 (c) 125 (d) 126