class 12

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JEE Advanced

Match the reactions in column I with appropriate options in column II.

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The area enclosed by the curves$y=sinx+cosxandy=∣cosx−sinx∣$ over the interval $[0,2π ]$

Let $P_{1}:2x+y−z=3$and $P_{2}:x+2y+z=2$be two planes. Then, which of the following statement(s) is (are) TRUE?The line of intersection of $P_{1}$and $P_{2}$has direction ratios $1,2,−1$(b) The line $93x−4 =91−3y =3z $is perpendicular to the line of intersection of $P_{1}$and $P_{2}$(c) The acute angle between $P_{1}$and $P_{2}$is $60o$(d) If $P_{3}$is the plane passing through the point $(4,2,−2)$and perpendicular to the line of intersection of $P_{1}$and $P_{2}$, then the distance of the point $(2,1,1)$from the plane $P_{3}$is $3 2 $

Let $f_{prime}(x)=2+sin_{4}πx192x_{3} forallx∈Rwithf(21 )=0.Ifm≤∫_{21}f(x)dx≤M,$ then the possible values of $mandM$ are (a)$m=13,M=24$ (b) $m=41 ,M=21 $(c)$m=−11,M=0$ (d) $m=1,M=12$

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)

Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of m/n is

A farmer $F_{1}$has a land in the shape of a triangle with vertices at $P(0,0),Q(1,1)$and $R(2,0)$. From this land, a neighbouring farmer $F_{2}$takes away the region which lies between the side $PQ$and a curve of the form $y=x_{n}(n>1)$. If the area of the region taken away by the farmer $F_{2}$is exactly 30% of the area of $PQR$, then the value of $n$is _______.

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.