class 12

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JEE Advanced

Total number of geometrical isomers for the complex $[RhCl(CO)(PPh_{3})(NH_{3})]$ is

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Q. The value of is equal $k=1∑13 (sin(4π +(k−1)6π )sin(4π +k6π )1 $ is equal

For $a>b>c>0$, if the distance between $(1,1)$ and the point of intersection of the line $ax+by−c=0$ is less than $22 $ then,

The function $y=f(x)$ is the solution of the differential equation $dxdy +x_{2}−1xy =1−x_{2} x_{4}+2x $ in $(−1,1)$ satisfying $f(0)=0.$ Then $∫_{23}f(x)dx$ is

Let $f:(0,∞)R$ be given by $f(x)=∫_{x1}te_{−(t+t1)}dt ,$ then (a)$f(x)$ is monotonically increasing on $[1,∞)$(b)$f(x)$ is monotonically decreasing on $(0,1)$(c)$f(2_{x})$ is an odd function of $x$ on $R$

Let $△PQR$ be a triangle. Let $a=Q R,b=RP$ and $c=PQ$. If $∣a∣=12,∣∣ b∣∣ =43 $ and $b.c=24$, then which of the following is (are) true ?

let L be a straight line passing through the origin. Suppose that all the points on L are at a constant distance from the two planes $P_{1}:x+2y−z+1=0$ and $P_{2}:2x−y+z−1=0$, Let M be the locus of the feet of the perpendiculars drawn from the points on L to the plane $P_{1}$. Which of the following points lie(s) on M?

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

Let $f:R→R$and $g:R→R$be two non-constant differentiable functions. If $f_{prime}(x)=(e_{(f(x)−g(x))})g_{prime}(x)$for all $x∈R$, and $f(1)=g(2)=1$, then which of the following statement(s) is (are) TRUE?$f(2)<1−(g)_{e}2$(b) $f(2)>1−(g)_{e}2$(c) $g(1)>1−(g)_{e}2$(d) $g(1)<1−(g)_{e}2$