class 12

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JEE Advanced

The product formed in the reaction of $SOCl_{2}$ with white phosphorous is

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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 $f:R→(0,∞)$ and $g:R→R$ be twice differentiable functions such that f" and g" are continuous functions on R. suppose $f_{prime}(2)=g(2)=0,f(2)=0$ and $g_{′}(2)=0$, If $x→2lim f_{′}(x)g_{′}(x)f(x)g(x) =1$ then

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

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

A vertical line passing through the point $(h,0)$ intersects the ellipse $4x_{2} +3y_{2} =1$ at the points $P$ and $Q$.Let the tangents to the ellipse at P and Q meet at $R$. If $δ(h)$ Area of triangle $δPQR$, and $δ_{1}21 ≤h≤1max δ(h)$ A further $δ_{2}21 ≤h≤1min δ(h)$ Then $5 8 δ_{1}−8δ_{2}$

Late $a∈R$and let $f:R$be given by $f(x)=x_{5}−5x+a,$then$f(x)$has three real roots if $a>4$$f(x)$has only one real roots if $a>4$$f(x)$has three real roots if $a<−4$$f(x)$has three real roots if $−4<a<4$

For each positive integer $n$, let $y_{n}=n1 ((n+1)(n+2)n+n˙ )_{n1}$For $x∈R$let $[x]$be the greatest integer less than or equal to $x$. If $(lim)_{n→∞}y_{n}=L$, then the value of $[L]$is ______.

Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover cards numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done isa.$264$ b. $265$ c. $53$ d. $67$