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$XeF_{4}+O_{2}F_{2}→$ product. The total number of lone pairs on the xenon containing product is : (I)

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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

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

Let $f:R→R,g:R→Randh:R→R$ be the differential functions such that $f(x)=x_{3}+3x+2,g(f(x))=xandh(g(g(x)))=x,forallx∈R.Then$ (a)g'(2)=$151 $ (b)h'(1)=666 (c)h(0)=16 (d)h(g(3))=36

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. $30$

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 $MandN$ be two $3×3$ matrices such that $MN=NM˙$ Further, if $M=N_{2}andM_{2}=N_{4},$ then Determinant of $(M_{2}+MN_{2})$ is 0 There is a $3×3$ non-zeero matrix $U$ such tht $(M_{2}+MN_{2})U$ is the zero matrix Determinant of $(M_{2}+MN_{2})≥1$For a $3×3$ matrix $U,if(M_{2}+MN_{2})U$ equal the zero mattix then $U$ is the zero matrix

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.

For $a∈R$ (the set of all real numbers), $a=−1),$$(lim)_{n→∞}((n+1)_{a−1}[(na+1)+(na+2)+……(na+n)]1_{a}+2_{a}++n_{a} =60.1 $Then $a=$(a)$5$ (b) 7 (c) $2−15 $ (d) $2−17 $