class 12

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JEE Advanced

In the options given below, let E denote the rest mass energy of a nucleus and n a neutron. The correct option is

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The value of $(((g)_{2}9)_{2})_{(log)((log)9)1}×(7 )_{(log)71}$is ________.

The circle $C_{1}:x_{2}+y_{2}=3,$ with centre at O, intersects the parabola $x_{2}=2y$ at the point P in the first quadrant. Let the tangent to the circle $C_{1}$ at P touches other two circles $C_{2}andC_{3}atR_{2}andR_{3},$ respectively. Suppose $C_{2}andC_{3}$ have equal radii $23 $ and centres at $Q_{2}$ and $Q_{3}$ respectively. If $Q_{2}$ and $Q_{3}$ lie on the y-axis, then (a)$Q2Q3=12$(b)$R2R3=46 $(c)area of triangle $OR2R3$ is $62 $(d)area of triangle $PQ2Q3is=42 $

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.

Let $f:R→R$be a differentiable function with $f(0)=1$and satisfying the equation $f(x+y)=f(x)f_{prime}(y)+f_{prime}(x)f(y)$for all $x,y∈R$. Then, the value of $(g)_{e}(f(4))$is _______

Let $b_{1}>1$ for $i=1,2,……,101.$ Suppose $g_{e}b_{1},g_{e}b_{10}$ are in Arithmetic progression $(A.P.)$ with the common difference $g_{e}2.$ suppose $a_{1},a_{2}……….a_{101}$ are in A.P. such $a_{1}=b_{1}anda_{51}=b_{51}.$ If $t=b_{1}+b_{2}+……+b_{51}ands=a_{1}+a_{2}+……+a_{51}$ then

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

Let $f:R→Randg:R→R$ be respectively given by $f(x)=∣x∣+1andg(x)=x_{2}+1$. Define $h:R→R$ by $h(x)={max{f(x),g(x)},ifx≤0andmin{f(x),g(x)},ifx>0$.The number of points at which $h(x)$ is not differentiable is

$L_{1}=x+3y−5=0,L_{2}=3x−ky−1=0,L_{3}=5x+2y−12=0$ are concurrent if k=