Mathematics ECAT Pre Engineering Online Test With Answers

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Mathematics ECAT Pre Engineering Online Test

Sr. # Questions Answers Choice
1 1+3x+6x2 +10x3 +....= (1+x)-3 (1-x)-2 (1-x)-3 (1+x)-2
2 The general term in the expansion of (a+x)n is (r-1)th term (r+1)th term rth term none
3 If the sum of even coefficients in the expansion of (1+x)n is 128 then n=7 n=9 n=8 None
4 The sum of first n even number is n2 n(n+1) n+1 n+2
5 The third term in the expansion of (1+2x) is -2x2 -4x2 2x2 4x2
6 If n∈Z+ then(a+x)n is a/an Finite series Convergent series Infinite series Divergent series
7 The proposition S(k+1) is true when ______ is true∀K∈N S(n) S(k) S(1) S(k-1)
8 If x+y+z+......+2n = 2n+1-1∀n∈W,then cube root of xyz is equal to 1 4 2 8
9 The exponent of x in 10th term in the expansion of (a+x)n 10 12 11 9
10 In the expansion of (x+y)n the coefficient of 5th and 12th terms are equal then n= 12 n=14 17 n=15
11 The last term of (1+2x)-2 (-1)-2 (2x)-2 (-1)-4(-2x)-2 (-1)-3(2x)-3 Does not exist
12 The no of term is the expansion of (a+x)n-1 is n+1 n-1 n n-2
13 There are two middle terms in the expansion of (a+x)n if n is Even +ve integer +ve integer Odd +ve integer All
14 The coefficient of xn in the expansion of (1-x)-1 is (-1)n2n 1 (-1)n(n+1) (n+1)
15 The middle term(s) of (a+x)11 is 6th term 6thor 7th 7th term 6thand7th
16 The proposition S(n) for any n∈ N is only true if k∈ N and S(k +1) is true S(1) is true and S(k+1) is true whenever S (k) is true S(k+1) is true whenever S (k) is true S(k) is true
17 For any positive integer n ABn = Bn A ⇔ AB = BA ABn = Bn A⇔ A,B are square matrices and AB = BA ABn = BnA⇔ A + B ABn = BnA ⇔ A and B are square matries
18 The coefficient of xn in the expansion of (1-2x)-1 is (-1)n2n 2n (-1)(n+1)xr (n+1)2n
19 The proposition S(n) is true∀n∈N,S(k+1) true when ______is true S(1) Both a & c S(k) None
20 There is no integer n for which 3n is Even Prime Odd Real
21 The sum even binomial coefficient of (3+2x)5 is ______term 16 30 8 32
22 Which one is not defined∀n∈Z+ -n! n! (-n)! n!+0!=n!+1
23 Number of combination of zero or more things out of n different things nPn nPr nCr 2n
24 How many comittees of 5 numbers can be chosen from a group of 8 players person when each committee must include 2 particular persons 8! 5!3! 5! 20
25 How many 6-Digit number can be formed without repairing any digit from the digits 0,1,2,3,4,5 720 600 120 6-5!
26 Probability of an impossible event is 0 -1 1 ∞
27 A key ring is an example of Permutation Circular permutation Combination None
28 The factorial of a positive integers is a (an) Rational number Positive integer Real number None
29 How many different 5-digit even numbers are possible form digit 1,2,4,6,8 4 : 4! 4! 5! 4!+4!
30 If for two events A and B , P(A∪B)=1,then events A and B are Certain events Mutually exclusive Complementary events Independent
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