Straight Objective Type
1. If nPa = nPb where a < b ≤ n (all are positive integers) and a + b = Fn + G then |F| + |G| = ........
1) 1 2) 2 3) 3 4) 4
2. If n is an integer between 0 and 21 then the minimum value of ∠n ∠(21 - n) =
1) ∠9 ∠12 2) ∠10 ∠11 3) ∠20 4) ∠21
3. An n digit number is positive number with exactly ‘n’ digit. Nine hundred distinct n - digit numbers are to be formed using three digit 2, 5 and 7. The smallest value of ‘n’ for which this is possible is
1) 3 2) 5 3) 7 4) 9
4. The highest exponent of 7 in ∠100 is
1) 10 2) 12 3) 14 4) 16
5. The range of the function f(x) = (7 - x)P(x - 3) is
1) {1, 2, 3} 2) {2, 3, 4} 3) { 1, 3, 4} 4) {1, 2, 4}
6. The number of distinct rational numbers x such that 0 < x < 1 and x = p/q where p, q ∈ {1, 2, 3, 4, 5, 6} is
1) 11 2) 12 3) 10 4) 15
7. Two numbers are chosen at random from {1, 2, 3, 4, 5, 6} at a time. The probability that the smaller of the two is < 4 is
1) 1/5 2) 12/5 3) 3/5 4) 4/5
8. A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually six is
1) 1/8 2) 3/8 3) 5/8 4) 7/8
9. A critical point x1 of the function f(x) = x3 is selected at random. The probability that f has extremum at x1 is
1) 1/3 2) 2/3 3) 1/4 4) 0
10. In a Binomial distribution n = 400, P = 1/5 then standard deviation is
1) 10 2) 8 3) 10√2 4) 2√2
11. The probability of a coin showing head is P. Now 100 coins are tossed. If the probability of 50 coins showing heads is same as the probability of 51 coins showing heads then the value of P =
1) 1/2 2) 49/100 3) 51/101 4) 1/3
12. If the range of 6 observation is 14. If the least observation is 4. Then the greatest observation is
1) 18 2) 16 3) 14 4) 12
13. If the coefficient of variation and standard deviation of a distribution are 2 and 0.4 respectively then its mean =
1) 10 2) 20 3) 30 4) 40
14. The standard deviation of 4, 7, 10, 13, 16, 19, 22 is =
1) 2 2) 6 3) 8 4) 4
15. The number of skew symmetric matrices of order 3 × 3 by using the elements of the set A = {−3, −2, −1, 0, 1, 2, 3}
1) 76 2) 77 3) 1 4) 73
16. The number of ways in which TRUE or FALSE examination of 20 statements can be answered on the assumption that no two consecutive questions are answered the same way
1) 20 2) 21 3) 2 4) 1
17. The number of ways in which four letters can be selected from the letters of the word ‘MATHEMATICS’ is ...... ∠11
1) ∠11/(∠2)3 2) 136 3) 133 4) 146
18. The probability that a teacher will give a surprise test during any class meeting is 3/5. If a student is absent on two days. Then the probability that be will miss atleast one test is
1) 9/25 2) 4/25 3) 21/25 4) 13/25
19. If two different numbers are taken from the set {0, 1, 2, 3, .... 10}, then the probability that their sum as well as absolute difference are both multiple of 4 is
1) 6/55 2) 7/55 3) 12/15 4) 14/55
20. The least number of times a fair coin must be tossed. So that the probability of getting atleast one head is atleast 0.8 is
1) 1 2) 2 3) 3 4) 4
21. If in a frequency distribution, the mean and median are 21 and 22 respectively then its mode is
1) 20.5 2) 22 3) 23 4) 24
Numerical Value Type
22. A JEE Main Problem in Mathematics is given to three students whose chances of 1/2, 1/3 and 1/3 respectively. The probability that the problem being solved is
23. A and B are two particular persons who addresses a conference with 8 more speakers. If the addressing is at random, the probability that B speaks after A is
24. Three vertices of a regular hexagon are selected at random. The probability that they form an equilateral triangle is
25. The least positive integer n for which
26. Let n = 2015, the least positive integer K for which Kn2(n2 - 12)(n2 - 22)(n2 - 32)..... (n2 - (n - 1)2) = ∠r for some positive integer r is......
27. The number of integral solutions of x2 + y2 = x2y2 is......
28.
29. In a football championship 36 matches were played. Every team played one match with each other. The number of teams participating in the championship is..
30. If [y] denote the greatest integer ≤ y and
smallest interval [a b) where b = a is equal to
31. Let Tn denote the number of triangles which can be formed by using the vertices of regular polygon of n sides. If Tn+1 - Tn = 21 then n =
32. The number of ways of writing 98 as the product of two positive integers is .....
33. A man alternately tossed a coin and throws die beginning with coin. The probability that be gets head before he gets 5 or 6 on die is.....
Answers 1-3; 2-2; 3-3; 4-4; 5-1; 6-1; 7-4; 8-2; 9-4; 10-2; 11-3; 12-1; 13-2; 14-2; 15-4; 16-3; 17-2; 18-3; 19-1; 20-3; 21-4; 22-0.75; 23-0.5; 24-0.10; 25-1.4; 26-2; 27-1; 28-2; 29-9; 30-8; 31-7; 32-3; 33-0.75.
