STATEMENT - 1 : Molecules that are not superimposable on their mirror images are chiral.
STATEMENT - 2 : All chiral molecules have chiral centres.
Let Obe the origin, and OXxOY,OZbe three unit vectors in the direction of the sides QR, RP, PQ, respectively of a triangle PQR.If the triangle PQR varies, then the minimum value of cos(P+Q)+cos(Q+R)+cos(R+P)is:−23 (b) 35 (c) 23 (d) −35
Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length 27 on y-axis is (are)
For a>b>c>0, if the distance between (1,1) and the point of intersection of the line ax+by−c=0 is less than 22 then,
Three randomly chosen nonnegative integers x,yandzare found to satisfy the equation x+y+z=10.Then the probability that zis even, is:125 (b) 21 (c) 116 (d) 5536
A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8:15is converted into anopen rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. Then the length of the sides of the rectangular sheet are24 (b) 32 (c) 45 (d) 60
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
In a triangle the sum of two sides is x and the product of the same is y. If x2−c2=y where c is the third side. Determine the ration of the in-radius and circum-radius