Consider a `6xx6` chessboard. Then match the following columns. Column I, Column II Number of rectangles, p. `^10 C_5` Number of squares, q. 441 Number of ways three squares can be selected if they are not in same row or column, r. 91 In how many ways eleven + sign can be arranged in the squares if no row remains empty, s. 2400

Find the number of ways in which two small squares can be selected on the normal chessboard if they are not in same row or same column.

Consider the convex polygon, which has 35 diagonals. Then match the following column. Column I, Column II Number of triangles joining the vertices of the polygon, p. 210 Number of points intersections of diagonal which lies inside the polygon, q. 120 Number of triangles in which exactly one side is common with that of polygon, r. 10 Number of triangles in which exactly two sides are common with that of polygon, s. 60

Find the number of ways in which 5A^(prime)s and 6B ' s can be arranged in a row which reads the same backwards and forwards.

Match the following for the equation x^2+a|x|+1=0,w h e r ea is a parameter. Column I, Column II No real roots, p. a<-2 Two real roots, q. varphi Three real roots, r. a=-2 Four distinct real roots, s. ageq0

The number of ways in which the letters of the word PERSON can placed in the squares of the given figure so that no row remains empty is a. 24xx6! b. 26xx6! c. 26xx7! d. 27xx6!

Consider the parabola y^2=12 x Column I, Column II Equation of tangent can be, p. 2x+y-6=0 Equation of normal can be, q. 3x-y+1=0 Equation of chord of contact w.r.t. any point on the directrix can be, r. x-2y-12=0 Equation of chord which subtends right angle at the vertex can be, s. 2x-y-36=0

Consider three lines as follows. L_1:5x-y+4=0 L_2:3x-y+5=0 L_3: x+y+8=0 If these lines enclose a triangle A B C and the sum of the squares of the tangent to the interior angles can be expressed in the form p/q , where p and q are relatively prime numbers, then the value of p+q is

Column I, Column II The number of five-digit numbers having the product o digit 20 is, p. > 70 A closest has five pairs of shoes. The number of ways in which four shoes can be drawn from it such that there will be no complete pair is, q. <60 Three ladies have each brought their one child for admission to a school. The principal wants to interview the six persons one by one subject to the condition that no mother is interviewed before her child. The number of ways in which interview can be arranged is, r. in (50 ,110) The figures 4, 5, 6, 7, 8 are written in every possible order. The number of numbers greater than 56000 is, s. in (40 ,70)

Four letters, two 'a' and two 'b' are filled into 16 cells of a matrix as given. It is required that each cell contains atmost one letter and each row or column cannot contain same letters. Then the number of ways the matrix can be filled is (A) 3600 (B) 5200 (C) 3960 (D) 4120

In how many ways can a party of 6 men be selected out of 10 Hindus, 8 Muslims, and 6 Christians, if the party consists of atleast one person of each religion? Find the number of ways of selection. (Consider only the religion of the person).