Q 1.The total number of terms in the expansion of (x + a)100 + (x – a)100 after simplification will be
A. 202
B. 51
C. 50
D. None of these
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Answer:-51Q 2. Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If Tn + 1 –Tn = 21, then n equals
A. 7
B. 5
C. 6
D. 4
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Answer:-A. 7Q 3.If A and B are the coefficients of xn in the expansions of (1 + x)2n and (1 + x)2n–1 respectively, then
A. A = B
B. A = 2B
C. 2A = B
D. None of these
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Answer:-B. A = 2BQ 4. The number 111……1 (91 times) is
A. Not an odd number
B. An even number
C. Not a prime
D. None of these
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Answer:-C. Not a primeQ 5. In the expansion of (1 + x)5, the sum of the coefficient of the terms is
A. 80
B. 16
C. 32
D. 64
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Answer:-C. 32Q 6. If p and q be positive, then the coefficients of xp and xq in the expansion of (1 + x)p + q will be
A. Equal
B. Equal in magnitude but opposite in sign
C. Reciprocal to each other
D. None of these
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Answer:-A. EqualQ 7. Coefficient of t24 in (1 + t2)12 (1 + t12) (1 + t24) is
A. 12C6 + 2
B. 12C6 + 1
C. 12C6
D. 12C6 + 3
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Answer:-A. 12C6 + 2Q 8. The sum of all the coefficients in the binomial expansion of (x2 + x – 3)319 is
A. -1
B. 2
C. 1
D. 0
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Answer:-A. -1Q 9. If in the expansion of (1 + x)m (1 – x)n, the coefficient of x and x2 are 3 and – 6 respectively, then m is
A. 6
B. 9
C. 12
D. 24
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Answer:-C. 12Q 10. Cube root of 217 is
A. 6.03
B. 6.04
C. 6.01
D. None of these
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Answer:-C. 6.01Q 11. If the coefficients of 5th, 6th and 7th terms in the expansion of (1 + x)n be in A.P., then n =
A. 7 only
B. 14 only
C. 7 or 14
D. None of these
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Answer:-C. 7 or 14Q 12. If in the expression of (1 + x)m (1 – x)n, then coefficient of x and x2 are 3 and – 6 respectively, then m is
A. 6
B. 9
C. 12
D. 24
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Answer:-C. 12Q 13. In the expansion of (1 + x)n the sum of coefficients of odd powers of x is
A. 2n + 1
B. 2n – 1
C. 2n
D. 2n – 6
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Answer:-B. 2n – 1Q 14. If the three consecutive coefficient in the expansion of (1 + x)n are 28, 56 and 70, then the value of n is
A. 6
B. 8
C. 4
D. 10
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Answer:-B. 8Q 15. In the expansion of (1 + x + x3 + x4)10, the coefficient of x4 is
A. 40C4
B. 10C4
C. 210
D. 310
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Answer:-D. 310Q 16. The sum of coefficients in (1 + x – 3x2)2134 is
A. – 1
B. 1
C. 0
D. 22134
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Answer:-B. 1Q 17. If the coefficients of second, third and fourth term in the expansion of (1 + x)2n are in A.P., then 2n2 – 9n + 7 is equal to
A. – 1
B. 0
C. 1
D. 3/2
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Answer:-B. 0Q 18. In the expansion of (1 + 3x + 2x2)6 the coefficient of x11 is
A. 144
B. 288
C. 576
D. 216
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Answer:-C. 576Q 19. The sum of coefficients in the expansion of (x + 2y + 3z)8 is
A. 38
B. 58
C. 68
D. None of these
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Answer:-C. 68Q 20. The greatest integer which divides the number 101100 – 1, is
A. 100
B. 1000
C. 10000
D. 100000
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Answer:-C. 10000Q 21. If the second, third and fourth term in the expansion of (x + a)n are 240, 720 and 1080 respectively, then the value of n is
A. 15
B. 20
C. 10
D. 5
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Answer:-D. 5Q 22. Given positive integers r > 1, m > 2, and that the coefficients of (3r)th term and (r + 2)th terms in the binomial expansion of (1 + r)2n are equal. Then
A. n = 3r
B. n = 2r + 1
C. n = 2r
D. none of these
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Answer:-C. n = 2rQ 23. If coefficient of (2r + 3)th and (r – 1)th terms in the expansion of (1 + x)15 are equal, then value of r is
A. 5
B. 6
C. 4
D. 3
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Answer:-A. 5Q 24. The coefficient of x5 in the expansion of (x2 – x – 2)5 is
A. – 83
B. – 82
C. – 81
D. 0
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Answer:-C. – 81Q 25. The coefficient of x5 in the expansion of (x + 3)6 is
A. 18
B. 6
C. 12
D. 10
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Answer:-A. 18Q 26. The last digit in 7300 is
A. 7
B. 9
C. 1
D. 3
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Answer:-C. 1Q 27. The digit in the unit place of the number (183!) + 3183 is
A. 6
B. 7
C. 3
D. 0
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