class 12

Missing

JEE Advanced

A set S is given by {1,2,3,4,5,6}. |X| is number of elements in set X. Subsets A and B set S are chosen such that each elements of S is equally likely and $1≤∣B∣≤∣A∣$ then the number of ordered pairs of (A,B) are

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Three randomly chosen nonnegative integers $x,yandz$are found to satisfy the equation $x+y+z=10.$Then the probability that $z$is even, is:$125 $ (b) $21 $ (c) $116 $ (d) $5536 $

The coefficients of three consecutive terms of $(1+x)_{n+5}$are in the ratio 5:10:14. Then $n=$___________.

A box $B_{1}$, contains 1 white ball, 3 red balls and 2 black balls. Another box $B_{2}$, contains 2 white balls, 3 red balls and 4 black balls. A third box $B_{3}$, contains 3 white balls, 4 red balls and 5 black balls.

Let $X$be the set consisting of the first 2018 terms of the arithmetic progression $1,6,11,,¨ $and $Y$be the set consisting of the first 2018 terms of the arithmetic progression $9,16,23,¨$. Then, the number of elements in the set $X∪Y$is _____.

A line $l$ passing through the origin is perpendicular to the lines $l_{1}:(3+t)i^+(−1+2t)j^ +(4+2t)k^,∞<t<∞,l_{2}:(3+s)i^+(3+2s)j^ +(2+s)k^,∞<t<∞$ then the coordinates of the point on $l_{2}$ at a distance of $17 $ from the point of intersection of \displaystyle{l}&{l}_{{1}} is/are:

Let $P$be a point in the first octant, whose image $Q$in the plane $x+y=3$(that is, the line segment $PQ$is perpendicular to the plane $x+y=3$and the mid-point of $PQ$lies in the plane $x+y=3)$lies on the z-axis. Let the distance of $P$from the x-axis be 5. If $R$is the image of $P$in the xy-plane, then the length of $PR$is _______.

Â·If the normals of the parabola $y_{2}=4x$ drawn at the end points of its latus rectum are tangents to the circle $(x−3)_{2}(y+2)_{2}=r_{2}$ , then the value of $r_{2}$ is

A cylindrica container is to be made from certain solid material with the following constraints: It has a fixed inner volume of $Vm_{3}$, has a 2 mm thick solid wall and is open at the top. The bottom of the container is a solid circular disc of thickness 2mm and is of radius equal to the outer radius of the container. If the volume the material used to make the container is minimum when the inner radius of the container is $10mm$. then the value of $250πV $ is