class 12

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JEE Advanced

The carbon-based reduction method is NOT used for the extraction of

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let L be a straight line passing through the origin. Suppose that all the points on L are at a constant distance from the two planes $P_{1}:x+2y−z+1=0$ and $P_{2}:2x−y+z−1=0$, Let M be the locus of the feet of the perpendiculars drawn from the points on L to the plane $P_{1}$. Which of the following points lie(s) on M?

For every pair of continuous functions $f,g:[0,1]→R$ such that $max{f(x):x∈[0,1]}=max{g(x):x∈[0,1]}$ then which are the correct statements

How many $3×3$ matrices $M$ with entries from ${0,1,2}$ are there, for which the sum of the diagonal entries of $M_{T}M$ is 5? (A) 126 (B)198 (C) 162 (D) 135

Let $PR=3i^+j^ −2k^andSQ=i^−3j^ −4k^$determine diagonals of a parallelogram $PQRS,andPT=i^+2j^ +3k^$be another vector. Then the volume of the parallelepiped determine by the vectors $PT$, $PQ$and $PS$is$5$b. $20$c. $10$d. $30$

Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 1, 2, 3,4, 5; and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let $x_{i}$ be the number on the card drawn from the ith box, i = 1, 2, 3.The probability that $x_{1}+x_{2}+x_{3}$ is odd isThe probability that $x_{1},x_{2},x_{3}$ are in an aritmetic progression is

Let $a,b,c$be three non-zero real numbers such that the equation $3 acosx+2bsinx=c,x∈[−2π ,2π ]$, has two distinct real roots $α$and $β$with $α+β=3π $. Then, the value of $ab $is _______.

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 _____.

Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length $27 $ on y-axis is (are)