Q1.The focal distance of a point on a parabola y
2 = 8x is 4, its coordinates are
| (a) |
(2, 4) |
(b) |
(– 2, 4) |
(c) |
(– 2, – 4) |
(d) |
none of these |
Q2.The equation of the parabola whose focus is (3, – 4) and directrix is the line x + y – 2 = 0, is
| (a) |
x2 + 2xy + y2 – 8x + 20y + 46 = 0 |
(b) |
x2 – 2xy + y2 – 8x + 20y + 46 = 0 |
| (c) |
x2 – 2xy + y2 + 8x – 20y + 46 = 0 |
(d) |
None of these |
Q3.The equation of the tangent to the parabola y
2 = 6x at the point whose ordinate is 6, is
| (a) |
x + 2y + 6 = 0 |
(b) |
2x – y + 6 = 0 |
(c) |
x – 2y + 6 = 0 |
(d) |
None of these |
Q4.The normal to the parabola y
2 = 8x at (2, 4) meets the parabola again at
| (a) |
(18, 12) |
(b) |
(18, – 12) |
(c) |
(– 18, 12) |
(d) |
None of these |
Q5.The equation of the tangent to the parabola y
2 = 16x inclined at an angle of 60° to x – axis, is
| (a) |
 |
(b) |
 |
(c) |
 |
(d) |
None of these |
Q6.The point of intersection of two perpendicular tangents to a parabola lies on the
| (a) |
axis |
(b) |
tangent at the vertex |
(c) |
directrix |
(d) |
None of these |
Q7.The pole of the line 2x = y with respect to the parabola y
2 = 2x is
| (a) |
 |
(b) |
 |
(c) |
 |
(d) |
None of these |
Q8.The locus of the poles of tangents to the parabola y
2 = 4ax w.r.t. the parabola y
2 = 4bx is the parabola
Q9.The length of latus rectum of the parabola 4y
2 + 2x – 20y + 17 = 0 is
| (a) |
3 |
(b) |
6 |
(c) |
1/2 |
(d) |
9 |
Q10.If the focal distance of a point on the parabola y
2 = 4x is 6, then the coordinates of the point are
| (a) |
 |
(b) |
 |
(c) |
 |
(d) |
None of these |
Q11.The equation of the ellipse referred to its axes as the axes of coordinates with length of major axis 8 and eccentricity
, is
| (a) |
4x2 + 3y2 = 48 |
(b) |
3x2 + 4y2 = 48 |
(c) |
4x2 + 3y2 = 24 |
(d) |
None of these |
Q12.The equation of the ellipse with focus (– 1, 1), directrix x – y + 3 = 0 and eccentricity
, is
| (a) |
7x2 + 2xy + 7y2 + 10x + 10y + 7 = 0 |
(b) |
7x2 + 2xy + 7y2 + 10x – 10y + 7 = 0 |
| (c) |
7x2 + 2xy + 7y2 + 10x – 10y – 7 = 0 |
(d) |
None of these |
Q13.The equation of the normal to the ellipse
at the end of the latus rectum in the first quadrant, is
| (a) |
x + ey – ae3 = 0 |
(b) |
x – ey + ae3 = 0 |
(c) |
x – ey – ae3 = 0 |
(d) |
None of these |
Q14.The condition that the line x cos
a + y sin
a = p may be a tangent to the ellipse
is
| (a) |
a2 cos2 a + b2 sin2 a = p2 |
(b) |
a2 cos2 a + b2 sin2 a = 2p2 |
| (c) |
a2 sin2 a + b2 cos2 a = p2 |
(d) |
None of these |
Q15.If the normal at the end of a latus rectum of an ellipse passes through one extremity of the minor axis, then
| (a) |
e4 + e2 – 1 = 0 |
(b) |
e4 – e2 + 1 = 0 |
(c) |
e4 – e2 – 1 = 0 |
(d) |
None of these |
Q16.In how many ways can 5 beads out 7 different beads be strung into a string?
| (a) |
504 |
(b) |
2520 |
(c) |
252 |
(d) |
none of these |
Q17.A person has 12 friends, out of them 8 are his relatives. In how many ways can he invite his 7 friends so as to include his 5 relatives?
| (a) |
8C3 x 4C2 |
(b) |
12C7 |
(c) |
12C5 x 4C3 |
(d) |
none of these |
Q18.It is essential for a student to pass in 5 different subjects of an examination then the no. of method so that he may failure
| (a) |
31 |
(b) |
32 |
(c) |
10 |
(d) |
15 |
Q19.The number of ways of dividing 20 persons into 10 couples is
| (a) |
 |
(b) |
20C10 |
(c) |
 |
(d) |
none of these |
Q20.The number of words by taking 4 letters out of the letters of the word ‘COURTESY’, when T and S are always included are
| (a) |
120 |
(b) |
720 |
(c) |
360 |
(d) |
none of these |
Q21.The number of ways to put five letters in five envelopes when one letter is kept in right envelope and four letters in wrong envelopes are–
| (a) |
40 |
(b) |
45 |
(c) |
30 |
(d) |
70 |
Q22.
is equal to
| (a) |
51C4 |
(b) |
52C4 |
(c) |
53C4 |
(d) |
none of these |
Q23.A candidate is required to answer 6 out of 10 questions which are divided into two groups each containing 5 questions and he is not permitted to attempt more than 4 from each group. The number of ways in which he can make up his choice is
| (a) |
100 |
(b) |
200 |
(c) |
300 |
(d) |
400 |
Q24.Out of 10 white, 9 black and 7 red balls, the number of ways in which selection of one or more balls can be made, is
| (a) |
881 |
(b) |
891 |
(c) |
879 |
(d) |
892 |
Q25.The number of diagonals in an octagon are
| (a) |
28 |
(b) |
48 |
(c) |
20 |
(d) |
none of these |
Q26.Out of 10 given points 6 are in a straight line. The number of the triangles formed by joining any three of them is
| (a) |
100 |
(b) |
150 |
(c) |
120 |
(d) |
none of these |
Q27.In how many ways the letters AAAAA, BBB, CCC, D, EE, F can be arranged in a row when the letter C occur at different places?
| (a) |
 |
(b) |
 |
(c) |
 |
(d) |
none of these |
Q28.A is a set containing n elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P. A subset Q of A is again chosen. The number of ways of chosen P and Q so that P
Ç Q =
f is
| (a) |
22n – 2nCn |
(b) |
2n |
(c) |
2n – 1 |
(d) |
3n |
Q29.A parallelogram is cut by two sets of m lines parallel to the sides, the number of parallelograms thus formed is
Q30.Along a railway line there are 20 stations. The number of different tickets required in order so that it may be possible to travel from every station to every station is
| (a) |
380 |
(b) |
225 |
(c) |
196 |
(d) |
105 |
Q31.The number of ordered triplets of positive integers which are solutions of the equation x + y + z = 100 is
| (a) |
5081 |
(b) |
6005 |
(c) |
4851 |
(d) |
none of these |
Q32.The number of numbers less than 1000 that can be formed out of the digits 0, 1, 2, 3, 4 and 5, no digit being repeated, is
| (a) |
130 |
(b) |
131 |
(c) |
156 |
(d) |
none of these |
Q33.A variable name in certain computer language must be either a alphabet or alphabet followed by a decimal digit. Total number of different variable names that can exist in that language is equal to
| (a) |
280 |
(b) |
290 |
(c) |
286 |
(d) |
296 |
Q34.The total number of ways of selecting 10 balls out of an unlimited number of identical white, red and blue balls is equal to
| (a) |
12C2 |
(b) |
12C3 |
(c) |
10C2 |
(d) |
10C3 |
Q35.Total number of ways in which 15 identical blankets can be distributed among 4 persons so that each of them get atleast two blankets equal to
| (a) |
10C3 |
(b) |
9C3 |
(c) |
11C3 |
(d) |
none of these |
Q36.The number of ways in which three distinct numbers in AP can be selected from the set {1, 2, 3, …, 24}, is equal to
| (a) |
66 |
(b) |
132 |
(c) |
198 |
(d) |
none of these |
Q37.The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is:
| (a) |
5 |
(b) |
21 |
(c) |
38 |
(d) |
8C3 |
Q38.The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by:
| (a) |
6! x 5! |
(b) |
30 |
(c) |
5! x 4! |
(d) |
7! x 5! |
Q39.If
nC
r denotes the number of combinations of n things taken r at a time, then the expression
nC
r + 1 +
nC
r – 1 + 2 x
nC
r equals:
| (a) |
n + 2Cr |
(b) |
n + 2Cr + 1 |
(c) |
n + 1Cr |
(d) |
n + 1Cr + 1 |
Q40.If the letters of the word SACHIN are arranged in all possible ways and these are written out as in dictionary, then the word SACHIN appears at serial number
| (a) |
600 |
(b) |
601 |
(c) |
602 |
(d) |
603 |
