class 12

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JEE Advanced

Which of the following reaction produce propane as major product?

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Which of the following values of $α$satisfying the equation $∣∣ (1+α)_{2}(1+2α)_{2}(1+3α)_{2}(2+α)_{2}(2+2α)_{2}(2+3α)_{2}(3+α)_{2}(3+2α)_{2}(3+3α)_{2}∣∣ =−648α?$$−4$b. $9$c. $−9$d. $4$

Consider the set of eight vector $V={ai^+bj^ +ck^;a,bc∈{−1,1}}˙$Three non-coplanar vectors can be chosen from $V$is $2_{p}$ways. Then $p$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

A circle S passes through the point (0, 1) and is orthogonal to the circles $(x−1)_{2}+y_{2}=16$ and $x_{2}+y_{2}=1$. Then (A) radius of S is 8 (B) radius of S is 7 (C) center of S is (-7,1) (D) center of S is (-8,1)

For $3×3$matrices $MandN,$which of the following statement (s) is (are) NOT correct ?$N_{T}MN$is symmetricor skew-symmetric, according as $m$is symmetric or skew-symmetric.$MN−NM$is skew-symmetric for all symmetric matrices $MandN˙$$MN$is symmetric for all symmetric matrices $MandN$$(adjM)(adjN)=adj(MN)$for all invertible matrices $MandN˙$

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 number of 5 digit numbers which are divisible by 4, with digits from the set ${1,2,3,4,5}$and the repetition of digits is allowed, is ________.

A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation $3 x+y−6=0$ and the point D is (3 sqrt3/2, 3/2). Further, it is given that the origin and the centre of C are on the same side of the line PQ. (1)The equation of circle C is (2)Points E and F are given by (3)Equation of the sides QR, RP are