class 12

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JEE Advanced

In the nuclear transmutation $_{4}Be+X→_{4}Be+Y$ (X,Y) is (are)

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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 _____.

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 ______.

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

Let $S_{n}=k=1∑4n (−1)2k(k+1) k_{2}˙$Then $S_{n}$can take value (s)$1056$b. $1088$c. $1120$d. $1332$

If a chord, which is not a tangent of the parabola $y_{2}=16x$has the equation $2x+y=p,$and midpoint $(h,k),$then which of the following is(are) possible values (s) of $p,handk?$$p=−1,h=1,k=−3$ $p=2,h=3,k=−4$ $p=−2,h=2,k=−4$ $p=5,h=4,k=−3$

Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover cards numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done isa.$264$ b. $265$ c. $53$ d. $67$

PARAGRAPH $X$Let $S$be the circle in the $xy$-plane defined by the equation $x_{2}+y_{2}=4.$(For Ques. No 15 and 16)Let $E_{1}E_{2}$and $F_{1}F_{2}$be the chords of $S$passing through the point $P_{0}(1,1)$and parallel to the x-axis and the y-axis, respectively. Let $G_{1}G_{2}$be the chord of $S$passing through $P_{0}$and having slope $−1$. Let the tangents to $S$at $E_{1}$and $E_{2}$meet at $E_{3}$, the tangents to $S$at $F_{1}$and $F_{2}$meet at $F_{3}$, and the tangents to $S$at $G_{1}$and $G_{2}$meet at $G_{3}$. Then, the points $E_{3},F_{3}$and $G_{3}$lie on the curve$x+y=4$(b) $(x−4)_{2}+(y−4)_{2}=16$(c) $(x−4)(y−4)=4$(d) $xy=4$

Consider the circle $x_{2}+y_{2}=9$ and the parabola $y_{2}=8x$. They intersect at P and Q in first and 4th quadrant,respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents at the parabola at P and Q intersect the x-axis at S.