Reaction of Br2 with Na2CO3 in aqueous solution gives sodium bromide and sodium bromate with evolution of CO2 gas. The number of sodium bromide molecules involved in the balanced chemical equation is
Let Sbe the set of all non-zero real numbers such that the quadratic equation αx2−x+α=0has two distinct real roots x1andx2satisfying the inequality ∣x1−x2∣<1.Which of the following intervals is (are) a subset (s) of S?(21,51)b. (51,0)c. (0,51)d. (51,21)
Let F1(x1,0) and F2(x2,0), for x1<0 and x2>0, be the foci of the ellipse 9x2+8y2=1 Suppose a parabola having vertex at the origin and focus at F2 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 MF1NF2 is
Let complex numbers αandα1 lies on circle (x−x0)2(y−y0)2=r2and(x−x0)2+(y−y0)2=4r2 respectively. If z0=x0+iy0 satisfies the equation 2∣z0∣2=r2+2 then ∣α∣ is equal to (a) 21 (b) 21 (c) 71 (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 XandYbe two arbitrary, 3×3, non-zero, skew-symmetric matrices and Zbe an arbitrary 3×3, non-zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?a.Y3Z4Z4Y3b. x44+Y44c. X4Z3−Z3X4d. X23+Y23
Consider the circle x2+y2=9 and the parabola y2=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=N2andM2=N4, then Determinant of (M2+MN2) is 0 There is a 3×3 non-zeero matrix U such tht (M2+MN2)U is the zero matrix Determinant of (M2+MN2)≥1For a 3×3 matrix U,if(M2+MN2)U equal the zero mattix then U is the zero matrix