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The correct option(s) regarding the complex $[Co(en)(NH_{3})_{3}(H_{2}O)]_{3}+en=H_{2}NCH_{2}CH_{2}NH_{2}$ is (are)

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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 ?

The number of points in $(−∞,∞),$for which $x_{2}−xsinx−cosx=0,$is6 (b) 4 (c) 2 (d) 0

Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of m/n is

Let $s,t,r$be non-zero complex numbers and $L$be the set of solutions $z=x+iy(x,y∈R,i=−1 )$of the equation $sz+tz+r=0$, where $z=x−iy$. Then, which of the following statement(s) is (are) TRUE?If $L$has exactly one element, then $∣s∣=∣t∣$(b) If $∣s∣=∣t∣$, then $L$has infinitely many elements(c) The number of elements in \displaystyle{\Ln{{n}}}{\left\lbrace{z}\right|}{z}-{1}+{i}{\mid}={5}{\rbrace}is at most 2(d) If $L$has more than one element, then $L$has infinitely many elements

The slope of the tangent to the curve $(y−x_{5})_{2}=x(1+x_{2})_{2}$at the point $(1,3)$is.

Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length $27 $ on y-axis is (are)

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

Let $PR=3i^+j^ −2k^andSQ=i^−3j^ −4k^$determine diagonals of a parallelogram $PQRS,andPT=i^+2j^ +3k^$be another vector. Then the volume of the parallelepiped determine by the vectors $PT$, $PQ$and $PS$is$5$b. $20$c. $10$d. $30$