Practice Questions

Q71.The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word EXAMINATION is

Q71.Let (2x2 + 3x + 4) 10 = ∑20r=0 arxr. Then a13a7

Q71.For a positive integer n, (1 + x ) is expanded in increasing powers of x . If three consecutive coefficients in this expansion are in the ratio, 2 : 5 : 12, then n is equal to

Q71.The total number of 3−digit numbers whose sum of digits is 10, is ..........

Q71.The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 45°. After walking a distance of 80 meters towards the top, up a slope inclined at angle of 30° to the horizontal plane the angle of elevation of the top of the hill becomes 75°. Then the height of the hill (in meters) is _____.

Q71.The coefficient of x4 in the expansion of (1 + x + x2 + x3)6 in powers of x, is … . .

Q71.If the sum of the coefficients of all even powers of x in the product (1 + x + x2 + … + x2n)(1 −x + x2 −x3 + … + x2n) is 61, then n is equal to

Q71.The least positive value of ‘ a ’ for which the equation, 2x2 + (a −10)x + 332 = 2a has real roots is ___________.

Q71.A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is ___________

Q71.The number of words (with or without meaning) that can be formed from all the letters of the word ′′LETTER′′ in which vowels never come together is.....

Q72.If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that 4th A.M. is equal to 2nd G.M., then m is equal to:

Q72.Let X = {n ∈N : 1 ≤n ≤50}. If A = {n ∈X : n is a multiple of 2} and B = {n ∈X : n is a multiple of 7}, then the number of elements in the smallest subset of X , containing both A and B , is.

Q72.The coefficient of x4 in the expansion of (1 + x + x2) 10 is ________

Q72.Let PQ be a diameter of the circle x2 + y2 = 9. If α and β are the lengths of the perpendiculars from P and Q on the straight line, x + y = 2 respectively, then the maximum value of αβ is _______

Q72.The sum, ∑7n=1 n(n+1)(2n+1)4 , is equal to √2sinα

Q72.Consider the data on x taking the values 0, 2, 4, 8, . . . . . , 2n with frequencies nC0, nC1, nC2, . . . . , nCn respectively. If the mean of this data is 728 , then n is equal to ....... . 2n

Q72.If Cr ≡25Cr and C0 + 5 ∙C1 + 9 ∙C2 + … + (101) ∙C25 = 225 ∙k, then k is equal to ____________.

Q72.Let A(1, 0), B(6, 2) and C( 32 , 6) be the vertices of a triangle ABC. If P is a point inside the triangle ABC such that the triangles APC, APB and BPC have equal areas, then the length of the line segment PQ, where Q is the point (−76 , −13 ), is

Q72.An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then, the number of ways in which 4 marbles can be drawn so that at the most three of them are red is ___________.

Q72.The numbers of integral values of k for which the line, 3x + 4y = k intersects the circle, x2 + y2 −2x −4y + 4 = 0 at two distinct points is.... x+x2+x3+...+xn−n

Q72.The value of 0. 16 log2.5( 1

Q72.If the variance of the terms in an increasing A. P. b1b2, b3, … … . . , b11 is 90 then the common difference of this A. P. is

Q72.If the system of equations x −2 y + 3z = 9 2x + y + z = b x −7y + az = 24, has infinitely many solutions, then a −b is equal to ______

Q72.The natural number m, for which the coefficient of x in the binomial expansion of (xm + x21 ) 22 is 1540, is

Q72.Let A = {a, b, c} and B = {1, 2, 3, 4}. Then the number of elements in the set C = {f : A →B ∣2 ∈f(A) and f is not one-one } is …