Major Competitive Exams
Q. What is the Stefan-Boltzmann law related to?
A.
Conduction
B.
Convection
C.
Radiation
D.
Thermal expansion
Show solution
Solution
The Stefan-Boltzmann law states that the total energy radiated per unit surface area of a black body is proportional to the fourth power of its absolute temperature.
Correct Answer: C — Radiation
Learn More →
Q. What is the structural formula for 2-methylpropane?
A.
CH3-CH2-CH(CH3)-CH3
B.
CH3-CH(CH3)-CH2-CH3
C.
CH3-CH2-CH2-CH3
D.
CH3-CH2-CH(CH2)-CH3
Show solution
Solution
The structural formula for 2-methylpropane is CH3-CH(CH3)-CH2-CH3.
Correct Answer: B — CH3-CH(CH3)-CH2-CH3
Learn More →
Q. What is the structural formula for hexane?
A.
C6H14
B.
C5H12
C.
C4H10
D.
C3H8
Show solution
Solution
The structural formula for hexane is C6H14.
Correct Answer: A — C6H14
Learn More →
Q. What is the structural formula of 2-methylpropane?
A.
CH3-CH2-CH(CH3)-CH3
B.
CH3-CH(CH3)-CH2-CH3
C.
CH3-CH2-CH2-CH3
D.
CH3-CH2-CH(CH2)-CH3
Show solution
Solution
The structural formula of 2-methylpropane is CH3-CH(CH3)-CH2-CH3.
Correct Answer: B — CH3-CH(CH3)-CH2-CH3
Learn More →
Q. What is the structural formula of propane?
A.
C3H8
B.
C2H6
C.
C4H10
D.
C5H12
Show solution
Solution
The structural formula of propane is C3H8, indicating three carbon atoms.
Correct Answer: A — C3H8
Learn More →
Q. What is the structure of a nucleotide?
A.
Sugar, phosphate, and base
B.
Amino group, carboxyl group, and side chain
C.
Glycerol and fatty acids
D.
Monosaccharides
Show solution
Solution
A nucleotide consists of a sugar, a phosphate group, and a nitrogenous base.
Correct Answer: A — Sugar, phosphate, and base
Learn More →
Q. What is the structure of DNA primarily composed of? (2023)
A.
Amino acids
B.
Nucleotides
C.
Fatty acids
D.
Monosaccharides
Show solution
Solution
DNA is composed of nucleotides, which include a sugar, phosphate, and nitrogenous base.
Correct Answer: B — Nucleotides
Learn More →
Q. What is the structure of DNA?
A.
Single-stranded
B.
Double helix
C.
Triple helix
D.
Linear
Show solution
Solution
DNA has a double helix structure, consisting of two strands that coil around each other.
Correct Answer: B — Double helix
Learn More →
Q. What is the sum of the angles in a triangle? (2017)
A.
180 degrees
B.
360 degrees
C.
90 degrees
D.
270 degrees
Show solution
Solution
The sum of the angles in a triangle is always 180 degrees.
Correct Answer: A — 180 degrees
Learn More →
Q. What is the sum of the coefficients in the expansion of (2 + 3x)^4?
A.
81
B.
64
C.
100
D.
125
Show solution
Solution
The sum of the coefficients is found by substituting x = 1: (2 + 3*1)^4 = 5^4 = 625.
Correct Answer: A — 81
Learn More →
Q. What is the sum of the coefficients in the expansion of (x + 1)^5?
Show solution
Solution
The sum of the coefficients is found by substituting x = 1, so (1 + 1)^5 = 2^5 = 32.
Correct Answer: D — 32
Learn More →
Q. What is the sum of the coefficients in the expansion of (x + 1)^7?
Show solution
Solution
The sum of the coefficients is found by substituting x = 1, giving (1 + 1)^7 = 2^7 = 128.
Correct Answer: A — 128
Learn More →
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
Show solution
Solution
The sum is (2 + 4) + (3 - 5)i = 6 - 2i.
Correct Answer: A — 6 - 2i
Learn More →
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
Show solution
Solution
(3 + 2i) + (1 - 4i) = (3 + 1) + (2 - 4)i = 4 - 2i.
Correct Answer: A — 4 - 2i
Learn More →
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
Show solution
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
Learn More →
Q. What is the sum of the first 5 natural numbers?
Show solution
Solution
Sum = 1 + 2 + 3 + 4 + 5 = 15.
Correct Answer: B — 15
Learn More →
Q. What is the sum of the first 5 terms of the series 1, 1/2, 1/4, ...?
Show solution
Solution
S_5 = 1 + 1/2 + 1/4 + 1/8 + 1/16 = 1.5.
Correct Answer: A — 1.5
Learn More →
Q. What is the sum of the first 6 terms of the arithmetic series 10, 15, 20, ...?
A.
90
B.
100
C.
110
D.
120
Show solution
Solution
The sum S_n = n/2 * (2a + (n-1)d) = 6/2 * (2*10 + 5*5) = 3 * (20 + 25) = 135.
Correct Answer: A — 90
Learn More →
Q. What is the sum of the first n terms of the arithmetic series 2, 5, 8, ...?
A.
n/2 * (2 + (n-1) * 3)
B.
n * (2 + 3n)/2
C.
3n^2/2 + n/2
D.
n * (n + 1)
Show solution
Solution
The first term a = 2, common difference d = 3. The sum of the first n terms S_n = n/2 * (2a + (n-1)d) = n/2 * (2 + (n-1) * 3).
Correct Answer: A — n/2 * (2 + (n-1) * 3)
Learn More →
Q. What is the sum of the infinite geometric series 1 + 1/2 + 1/4 + ...?
Show solution
Solution
The sum S = a/(1 - r) = 1/(1 - 1/2) = 1/(1/2) = 2.
Correct Answer: A — 2
Learn More →
Q. What is the sum of the interior angles of a quadrilateral? (2023)
A.
180 degrees
B.
360 degrees
C.
540 degrees
D.
720 degrees
Show solution
Solution
The sum of the interior angles of any quadrilateral is 360 degrees.
Correct Answer: B — 360 degrees
Learn More →
Q. What is the sum of the roots of the equation 2x^2 - 3x + 1 = 0?
Show solution
Solution
The sum of the roots is given by -b/a = 3/2.
Correct Answer: B — 3/2
Learn More →
Q. What is the sum of the roots of the equation 2x^2 - 4x + 1 = 0?
Show solution
Solution
The sum of the roots is given by -b/a = 4/2 = 2.
Correct Answer: B — 1
Learn More →
Q. What is the sum of the roots of the equation 2x² - 4x + 1 = 0? (2023)
Show solution
Solution
The sum of the roots is given by -b/a = 4/2 = 2.
Correct Answer: A — 2
Learn More →
Q. What is the sum of the roots of the equation 3x^2 - 12x + 9 = 0?
Show solution
Solution
Using Vieta's formulas, the sum of the roots is -(-12)/3 = 4.
Correct Answer: B — 4
Learn More →
Q. What is the sum of the roots of the equation f(x) = x^2 - 5x + 6?
Show solution
Solution
The sum of the roots of ax^2 + bx + c = 0 is -b/a. Here, sum = 5.
Correct Answer: A — 5
Learn More →
Q. What is the sum of the roots of the equation x^2 - 4x + 3 = 0?
Show solution
Solution
The sum of the roots is given by -b/a = 4/1 = 4.
Correct Answer: D — 4
Learn More →
Q. What is the sum of the roots of the quadratic equation 2x^2 - 8x + 6 = 0?
Show solution
Solution
The sum of the roots is given by -b/a = 8/2 = 4.
Correct Answer: B — 4
Learn More →
Q. What is the sum of the roots of the quadratic equation f(x) = x^2 - 5x + 6?
Show solution
Solution
The sum of the roots is given by -b/a = 5/1 = 5.
Correct Answer: A — 5
Learn More →
Q. What is the sum of the roots of the quadratic equation x^2 - 4x + 3 = 0?
Show solution
Solution
The sum of the roots is given by -b/a = 4/1 = 4.
Correct Answer: D — 4
Learn More →
Showing 10261 to 10290 of 13429 (448 Pages)
