Q. What is the sum of the coefficients in the expansion of (x + 1)^7?
Solution
The sum of the coefficients is found by substituting x = 1, giving (1 + 1)^7 = 2^7 = 128.
Correct Answer: A — 128
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Q. What is the term containing x^2 in the expansion of (3x + 4)^4?
-
A.
144
-
B.
216
-
C.
432
-
D.
576
Solution
The term containing x^2 is given by C(4,2) * (3x)^2 * 4^2 = 6 * 9 * 16 = 864.
Correct Answer: B — 216
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Q. What is the term independent of x in the expansion of (3x - 4)^7?
Solution
The term independent of x occurs when k = 7, C(7, 3) * (3)^3 * (-4)^4 = 35 * 27 * 256 = 84.
Correct Answer: C — 84
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Q. What is the total number of terms in the expansion of (x + 2y)^6?
Solution
The total number of terms is n + 1 = 6 + 1 = 7.
Correct Answer: C — 8
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Q. What is the value of (2 + 3)^3 using the binomial theorem?
-
A.
27
-
B.
125
-
C.
216
-
D.
343
Solution
Using the binomial theorem, (2 + 3)^3 = 5^3 = 125.
Correct Answer: A — 27
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Q. What is the value of the 5th term in the expansion of (x + 2)^6?
-
A.
80
-
B.
120
-
C.
160
-
D.
240
Solution
The 5th term is given by C(6,4) * (x)^4 * (2)^2 = 15 * x^4 * 4 = 240.
Correct Answer: B — 120
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Q. What is the value of the coefficient of x^3 in the expansion of (x - 1)^6?
-
A.
-20
-
B.
-30
-
C.
-40
-
D.
-10
Solution
The coefficient of x^3 is C(6,3) * (-1)^3 = 20 * (-1) = -20.
Correct Answer: B — -30
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Q. What is the value of the coefficient of x^5 in the expansion of (x + 3)^7?
-
A.
21
-
B.
63
-
C.
126
-
D.
189
Solution
The coefficient of x^5 is C(7,5) * (3)^2 = 21 * 9 = 189.
Correct Answer: C — 126
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Q. What is the value of the coefficient of x^5 in the expansion of (x + 3)^8?
-
A.
1680
-
B.
168
-
C.
840
-
D.
280
Solution
The coefficient of x^5 is C(8, 5) * (3)^3 = 56 * 27 = 1512.
Correct Answer: A — 1680
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