class 11

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JEE Advanced

V-T diagram for n mol monoatomic gas is given below Choose the correct statement"

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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_______.

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 $MandN$ 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 $F_{1}(x_{1},0)$ and $F_{2}(x_{2},0)$, for $x_{1}<0$ and $x_{2}>0$, be the foci of the ellipse $9x_{2} +8y_{2} =1$ Suppose a parabola having vertex at the origin and focus at $F_{2}$ intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant. If the tangents to the ellipse at M and N meet at R and the normal to the parabola at M meets the x-axis at Q, then the ratio of area of the triangle MQR to area of the quadrilateral $MF_{1}NF_{2}$ is

Let $f(x)=7tan_{8}x+7tan_{6}x−3tan_{4}x−3tan_{2}x$for all $x∈(−2π ,2π )$ . Then the correct expression (s) is (are) (a) $∫_{0}xf(x)dx=121 $ (b)$∫_{0}f(x)dx=0$(c)$∫_{0}xf(x)=61 $ (d) $∫_{0}f(x)dx=121 $

Let $n_{1},andn_{2}$, be the number of red and black balls, respectively, in box I. Let $n_{3}andn_{4}$,be the number one red and b of red and black balls, respectively, in box II. A ball is drawn at random from box 1 and transferred to box II. If the probability of drawing a red ball from box I, after this transfer, is $31 $ then the correct option(s) with the possible values of $n_{1}andn_{2}$ , is(are)

The function $f(x)=2∣x∣+∣x+2∣=∣∣x∣2∣−2∣x∣∣$has a local minimum or a local maximum at $x=$$−2$ (b) $−32 $ (c) 2 (d) $32 $

Coefficient of $x_{11}$ in the expansion of $(1+x_{2})_{4}(1+x_{3})_{7}(1+x_{4})_{12}$ is 1051 b. 1106 c. 1113 d. 1120