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JEE Advanced

Reaction of $Br_{2}$ with $Na_{2}CO_{3}$ in aqueous solution gives sodium bromide and sodium bromate with evolution of $CO_{2}$ gas. The number of sodium bromide molecules involved in the balanced chemical equation is

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Let $S$be the set of all non-zero real numbers such that the quadratic equation $αx_{2}−x+α=0$has two distinct real roots $x_{1}andx_{2}$satisfying the inequality $∣x_{1}−x_{2}∣<1.$Which of the following intervals is (are) a subset (s) of $S?$$(21 ,5 1 )$b. $(5 1 ,0)$c. $(0,5 1 )$d. $(5 1 ,21 )$

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 complex numbers $αandα1 $ lies on circle $(x−x_{0})_{2}(y−y_{0})_{2}=r_{2}and(x−x_{0})_{2}+(y−y_{0})_{2}=4r_{2}$ respectively. If $z_{0}=x_{0}+iy_{0}$ satisfies the equation $2∣z_{0}∣_{2}=r_{2}+2$ then $∣α∣$ is equal to (a) $2 1 $ (b) $21 $ (c) $7 1 $ (d) $31 $

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. $67$

Let $XandY$be two arbitrary, $3×3$, non-zero, skew-symmetric matrices and $Z$be an arbitrary $3×3$, non-zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?a.$Y_{3}Z_{4}Z_{4}Y_{3}$b. $x_{44}+Y_{44}$c. $X_{4}Z_{3}−Z_{3}X_{4}$d. $X_{23}+Y_{23}$

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.

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 x, y and z be three vectors each of magnitude V2 tion on and the angle between each pair of them is E. If a is a let non-zero vector perpendicular to x and yx z and b is a non-zero tor perpendicular to y and z x x, then 1.