Q. What is the structural formula of propane?
-
A.
C3H8
-
B.
C2H6
-
C.
C4H10
-
D.
C5H12
Solution
The structural formula of propane is C3H8, indicating three carbon atoms.
Correct Answer:
A
— C3H8
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Q. What is the structure of a nucleotide?
-
A.
Sugar, phosphate, and base
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B.
Amino group, carboxyl group, and side chain
-
C.
Glycerol and fatty acids
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D.
Monosaccharides
Solution
A nucleotide consists of a sugar, a phosphate group, and a nitrogenous base.
Correct Answer:
A
— Sugar, phosphate, and base
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Q. What is the structure of DNA described as? (2022)
-
A.
Single helix
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B.
Double helix
-
C.
Triple helix
-
D.
Linear strand
Solution
DNA is described as a double helix, consisting of two strands that wind around each other.
Correct Answer:
B
— Double helix
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Q. What is the structure of DNA primarily composed of? (2023)
-
A.
Amino acids
-
B.
Nucleotides
-
C.
Fatty acids
-
D.
Monosaccharides
Solution
DNA is composed of nucleotides, which include a sugar, phosphate, and nitrogenous base.
Correct Answer:
B
— Nucleotides
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Q. What is the structure of DNA?
-
A.
Single-stranded
-
B.
Double helix
-
C.
Triple helix
-
D.
Linear
Solution
DNA has a double helix structure, consisting of two strands that coil around each other.
Correct Answer:
B
— Double helix
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Q. What is the sum of all factors of 24?
Solution
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Their sum is 60.
Correct Answer:
A
— 60
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Q. What is the sum of the angles in a triangle? (2017)
-
A.
180 degrees
-
B.
360 degrees
-
C.
90 degrees
-
D.
270 degrees
Solution
The sum of the angles in a triangle is always 180 degrees.
Correct Answer:
A
— 180 degrees
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Q. What is the sum of the coefficients in the expansion of (2 + 3)^4? (2022)
-
A.
81
-
B.
64
-
C.
100
-
D.
125
Solution
The sum of the coefficients is (2 + 3)^4 = 5^4 = 625.
Correct Answer:
A
— 81
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Q. What is the sum of the coefficients in the expansion of (2 + 3x)^4?
-
A.
81
-
B.
64
-
C.
100
-
D.
125
Solution
The sum of the coefficients is found by substituting x = 1: (2 + 3*1)^4 = 5^4 = 625.
Correct Answer:
A
— 81
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Q. What is the sum of the coefficients in the expansion of (2x - 3)^4?
Solution
To find the sum of the coefficients, substitute x = 1: (2*1 - 3)^4 = (-1)^4 = 1. The sum of coefficients is 81.
Correct Answer:
B
— 81
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Q. What is the sum of the coefficients in the expansion of (3x - 2)^4? (2023)
Solution
To find the sum of the coefficients, substitute x = 1. Thus, (3(1) - 2)^4 = (3 - 2)^4 = 1^4 = 1.
Correct Answer:
B
— 81
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Q. What is the sum of the coefficients in the expansion of (x + 1)^4?
Solution
The sum of the coefficients in the expansion of (x + 1)^4 is (1 + 1)^4 = 2^4 = 16.
Correct Answer:
C
— 16
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Q. What is the sum of the coefficients in the expansion of (x + 1)^5?
Solution
The sum of the coefficients is found by substituting x = 1, so (1 + 1)^5 = 2^5 = 32.
Correct Answer:
D
— 32
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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 sum of the coefficients in the expansion of (x + 1)^8?
-
A.
256
-
B.
512
-
C.
128
-
D.
64
Solution
The sum of the coefficients in the expansion of (x + 1)^n is given by (1 + 1)^n = 2^n. Here, n=8, so the sum is 2^8 = 256.
Correct Answer:
B
— 512
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Q. What is the sum of the coefficients in the expansion of (x + 2)^5? (2021)
Solution
The sum of the coefficients is found by substituting x=1. So, (1 + 2)^5 = 3^5 = 243.
Correct Answer:
B
— 64
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Q. What is the sum of the complex numbers 1 + 2i and 3 - 4i? (2023)
-
A.
4 - 2i
-
B.
4 + 2i
-
C.
2 - 2i
-
D.
2 + 2i
Solution
(1 + 2i) + (3 - 4i) = (1 + 3) + (2 - 4)i = 4 - 2i.
Correct Answer:
A
— 4 - 2i
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Q. What is the sum of the complex numbers 2 + 3i and 4 - 5i?
-
A.
6 - 2i
-
B.
6 + 2i
-
C.
2 - 2i
-
D.
2 + 2i
Solution
The sum is (2 + 4) + (3 - 5)i = 6 - 2i.
Correct Answer:
A
— 6 - 2i
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Q. What is the sum of the complex numbers 3 + 2i and 1 - 4i? (2023)
-
A.
4 - 2i
-
B.
2 - 2i
-
C.
4 + 2i
-
D.
2 + 2i
Solution
(3 + 2i) + (1 - 4i) = (3 + 1) + (2 - 4)i = 4 - 2i.
Correct Answer:
A
— 4 - 2i
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Q. What is the sum of the complex numbers z1 = 2 + 2i and z2 = 3 - 4i?
-
A.
5 - 2i
-
B.
5 + 2i
-
C.
1 - 2i
-
D.
1 + 2i
Solution
To find the sum, we add the real parts and the imaginary parts: (2 + 3) + (2 - 4)i = 5 - 2i.
Correct Answer:
A
— 5 - 2i
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Q. What is the sum of the complex numbers z1 = 2 + 3i and z2 = 4 - 2i?
-
A.
6 + i
-
B.
6 + i
-
C.
2 + 5i
-
D.
8 + i
Solution
The sum of two complex numbers z1 + z2 = (2 + 3i) + (4 - 2i) = (2 + 4) + (3 - 2)i = 6 + i.
Correct Answer:
A
— 6 + i
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Q. What is the sum of the decimal equivalents of '101' and '110' in binary?
Solution
'101' is 5 and '110' is 6 in decimal. Their sum is 5 + 6 = 11.
Correct Answer:
C
— 7
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Q. What is the sum of the digits in the number '1011' in binary?
Solution
The sum of the digits in '1011' is 1 + 0 + 1 + 1 = 3.
Correct Answer:
C
— 4
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Q. What is the sum of the digits of the number '123' in base 4?
Solution
The digits are 1, 2, and 3. Their sum is 1 + 2 + 3 = 6.
Correct Answer:
A
— 6
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Q. What is the sum of the first 10 prime numbers?
Solution
The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Their sum is 129.
Correct Answer:
C
— 129
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Q. What is the sum of the first 15 terms of an arithmetic progression where the first term is 2 and the common difference is 4?
-
A.
120
-
B.
130
-
C.
140
-
D.
150
Solution
The sum of the first n terms S_n = n/2 * (2a + (n-1)d). Here, S_15 = 15/2 * (2*2 + 14*4) = 15/2 * (4 + 56) = 15/2 * 60 = 450.
Correct Answer:
A
— 120
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Q. What is the sum of the first 15 terms of an arithmetic progression where the first term is 10 and the common difference is 2?
-
A.
150
-
B.
160
-
C.
170
-
D.
180
Solution
The sum of the first n terms S_n = n/2 * (2a + (n-1)d). Here, S_15 = 15/2 * (2*10 + 14*2) = 15/2 * (20 + 28) = 15/2 * 48 = 360.
Correct Answer:
B
— 160
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Q. What is the sum of the first 5 natural numbers?
Solution
Sum = 1 + 2 + 3 + 4 + 5 = 15.
Correct Answer:
B
— 15
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Q. What is the sum of the first 5 terms of a GP where the first term is 2 and the common ratio is 3?
-
A.
242
-
B.
364
-
C.
486
-
D.
728
Solution
The sum of the first n terms of a GP is given by S_n = a(1 - r^n) / (1 - r). Here, S_5 = 2(1 - 3^5) / (1 - 3) = 2(1 - 243) / (-2) = 242.
Correct Answer:
A
— 242
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Q. What is the sum of the first 5 terms of the series 1, 1/2, 1/4, ...?
Solution
S_5 = 1 + 1/2 + 1/4 + 1/8 + 1/16 = 1.5.
Correct Answer:
A
— 1.5
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