class 12

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JEE Advanced

STATEMENT - 1 : Band gap in germanium is small. because STATEMENT - 2 : The energy spread of each germanium atomic energy level is infinitesimally small.

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Let $S={1,2,3,¨ 9}F˙ork=1,2,5,letN_{k}$be the number of subsets of S, each containing five elements out of which exactly $k$are odd. Then $N_{1}+N_{2}+N_{3}+N_{4}+N_{5}=?$210 (b) 252 (c) 125 (d) 126

Let $P$be a matrix of order $3×3$such that all the entries in $P$are from the set ${−1,0,1}$. Then, the maximum possible value of the determinant of $P$is ______.

The quadratic equation $p(x)=0$ with real coefficients has purely imaginary roots. Then the equation $p(p(x))=0$ has A. only purely imaginary roots B. all real roots C. two real and purely imaginary roots D. neither real nor purely imaginary roots

Let $u^=u_{1}i^+u_{2}j^ +u_{3}k^$ be a unit vector in be a unit vector in $R_{3}andw^=6 1 (i^+j^ +2k^)$.Given that there exists vector $v^$ in $R_{3}$ such that $∣u^×v∣=1andw^.(u^×v)=1$. Which of the following statement(s) is(are) correct?

Let $n≥2$be integer. Take $n$distinct points on a circle and join each pair of points by a line segment. Color the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of $n$is

Let P and Q be distinct points on the parabola $y_{2}=2x$ such that a circle with PQ as diameter passes through the vertex O of the parabola. If P lies in the first quadrant and the area of the triangle $ΔOPQ$ is $32$ , then which of the following is (are) the coordinates of $P?$

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,

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