Q. Which of the following equations has roots that are both negative? (2022)
A.
x² + 4x + 4 = 0
B.
x² - 4x + 4 = 0
C.
x² + 2x + 1 = 0
D.
x² - 2x + 1 = 0
Show solution
Solution
The equation x² + 4x + 4 = 0 has roots -2 and -2, which are both negative.
Correct Answer:
A
— x² + 4x + 4 = 0
Learn More →
Q. Which of the following equations is true in modular arithmetic?
A.
5 ≡ 10 (mod 5)
B.
6 ≡ 12 (mod 6)
C.
7 ≡ 14 (mod 7)
D.
8 ≡ 15 (mod 8)
Show solution
Solution
8 ≡ 15 (mod 8) is false; the correct answer is 5 ≡ 10 (mod 5) is true.
Correct Answer:
D
— 8 ≡ 15 (mod 8)
Learn More →
Q. Which of the following equations is used to calculate dynamic viscosity?
A.
Bernoulli's equation
B.
Navier-Stokes equation
C.
Poiseuille's law
D.
Archimedes' principle
Show solution
Solution
Dynamic viscosity can be calculated using Poiseuille's law.
Correct Answer:
C
— Poiseuille's law
Learn More →
Q. Which of the following equations relates Gibbs Free Energy to enthalpy and entropy?
A.
ΔG = ΔH - TΔS
B.
ΔG = TΔS - ΔH
C.
ΔG = ΔH + TΔS
D.
ΔG = ΔH / T + ΔS
Show solution
Solution
The correct relation is ΔG = ΔH - TΔS.
Correct Answer:
A
— ΔG = ΔH - TΔS
Learn More →
Q. Which of the following equations represents a circle with a center at (0, 0) and a radius of 5?
A.
x^2 + y^2 = 5
B.
x^2 + y^2 = 25
C.
x^2 - y^2 = 25
D.
x^2 + y^2 = 10
Show solution
Solution
The standard equation of a circle with center (0, 0) and radius r is x^2 + y^2 = r^2. Here, r = 5, so r^2 = 25.
Correct Answer:
B
— x^2 + y^2 = 25
Learn More →
Q. Which of the following equations represents a circle with a center at (3, -2) and a radius of 5?
A.
(x - 3)² + (y + 2)² = 25
B.
(x + 3)² + (y - 2)² = 25
C.
(x - 3)² + (y - 2)² = 25
D.
(x + 3)² + (y + 2)² = 25
Show solution
Solution
The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Correct Answer:
A
— (x - 3)² + (y + 2)² = 25
Learn More →
Q. Which of the following equations represents a line parallel to the line represented by 2x + 3y = 6?
A.
2x + 3y = 12
B.
3x + 2y = 6
C.
x - 2y = 4
D.
4x + 6y = 18
Show solution
Solution
Parallel lines have the same slope. The equation 2x + 3y = 12 has the same slope as 2x + 3y = 6.
Correct Answer:
A
— 2x + 3y = 12
Learn More →
Q. Which of the following equations represents a line parallel to y = -3x + 4?
A.
y = -3x + 1
B.
y = 3x - 4
C.
y = -x + 2
D.
y = 2x + 3
Show solution
Solution
Parallel lines have the same slope. The slope of y = -3x + 4 is -3, so any line with the same slope, like y = -3x + 1, is parallel.
Correct Answer:
A
— y = -3x + 1
Learn More →
Q. Which of the following equations represents a valid modular arithmetic statement?
A.
5x ≡ 10 (mod 5)
B.
6x ≡ 12 (mod 6)
C.
7x ≡ 14 (mod 7)
D.
8x ≡ 16 (mod 8)
Show solution
Solution
All options are valid, but 5x ≡ 10 (mod 5) simplifies to 0 ≡ 0, which is trivially true.
Correct Answer:
A
— 5x ≡ 10 (mod 5)
Learn More →
Q. Which of the following equations represents Bernoulli's principle?
A.
P + 1/2 ρv² + ρgh = constant
B.
P = ρgh
C.
F = ma
D.
V = IR
Show solution
Solution
Bernoulli's principle is represented by the equation P + 1/2 ρv² + ρgh = constant, relating pressure, velocity, and height in a fluid.
Correct Answer:
A
— P + 1/2 ρv² + ρgh = constant
Learn More →
Q. Which of the following equations represents the condition for the first minimum in single-slit diffraction?
A.
a sin(θ) = mλ
B.
a sin(θ) = (m + 0.5)λ
C.
a sin(θ) = (m + 1)λ
D.
a sin(θ) = 0
Show solution
Solution
The condition for the first minimum in single-slit diffraction is given by a sin(θ) = mλ, where m = 1 for the first minimum.
Correct Answer:
A
— a sin(θ) = mλ
Learn More →
Q. Which of the following equations represents the condition for the first minimum in a single-slit diffraction pattern?
A.
a sin(θ) = λ
B.
a sin(θ) = 2λ
C.
a sin(θ) = 3λ
D.
a sin(θ) = 0
Show solution
Solution
The condition for the first minimum in a single-slit diffraction pattern is given by a sin(θ) = λ, where 'a' is the slit width and 'λ' is the wavelength.
Correct Answer:
A
— a sin(θ) = λ
Learn More →
Q. Which of the following equations represents the ideal gas law?
A.
PV = nRT
B.
PV = nR
C.
PV = RT
D.
P = nRT/V
Show solution
Solution
The ideal gas law is represented by the equation PV = nRT.
Correct Answer:
A
— PV = nRT
Learn More →
Q. Which of the following equations represents the relationship between shear stress and shear rate in a Newtonian fluid?
A.
τ = μ(du/dy)
B.
τ = ρg
C.
F = ma
D.
P = F/A
Show solution
Solution
In a Newtonian fluid, shear stress (τ) is directly proportional to the shear rate (du/dy) with the proportionality constant being the dynamic viscosity (μ).
Correct Answer:
A
— τ = μ(du/dy)
Learn More →
Q. Which of the following ethers is commonly used as an anesthetic?
A.
Diethyl ether
B.
Methyl ethyl ether
C.
Phenyl ether
D.
Tert-butyl ether
Show solution
Solution
Diethyl ether is well-known for its use as a general anesthetic in the past.
Correct Answer:
A
— Diethyl ether
Learn More →
Q. Which of the following events directly led to the American Civil War?
A.
The signing of the Declaration of Independence
B.
The Dred Scott decision
C.
The Louisiana Purchase
D.
The Emancipation Proclamation
Show solution
Solution
The Dred Scott decision in 1857 heightened tensions between the North and South over slavery, contributing directly to the outbreak of the American Civil War in 1861.
Correct Answer:
B
— The Dred Scott decision
Learn More →
Q. Which of the following events in the 20th century significantly impacted India's relations with its neighboring countries? (1947)
A.
Partition of India
B.
Independence of India
C.
Non-Aligned Movement
D.
Green Revolution
Show solution
Solution
The Partition of India in 1947 had a profound impact on India's relations with its neighboring countries, particularly Pakistan and Bangladesh, leading to long-standing conflicts and issues.
Correct Answer:
A
— Partition of India
Learn More →
Q. Which of the following events is associated with the year 1919? (1919)
A.
Jallianwala Bagh Massacre
B.
Civil Disobedience Movement
C.
Dandi March
D.
Formation of Indian National Congress
Show solution
Solution
The Jallianwala Bagh Massacre occurred on April 13, 1919.
Correct Answer:
A
— Jallianwala Bagh Massacre
Learn More →
Q. Which of the following events is often cited as a consequence of climate change during the Medieval period?
A.
The fall of the Roman Empire
B.
The Black Death
C.
The Crusades
D.
The Renaissance
Show solution
Solution
The Black Death (1347-1351) is often linked to climate change, as the cooler temperatures and crop failures may have contributed to the spread of the plague.
Correct Answer:
B
— The Black Death
Learn More →
Q. Which of the following events marked a significant shift towards inclusive growth in India during the 1990s? (1991)
A.
Green Revolution
B.
Economic Liberalization
C.
Panchayati Raj
D.
Nationalization of Banks
Show solution
Solution
Economic Liberalization in the 1990s aimed to integrate the Indian economy with the global market, promoting inclusive growth through increased opportunities.
Correct Answer:
B
— Economic Liberalization
Learn More →
Q. Which of the following events marked the beginning of the French Revolution?
A.
The Storming of the Bastille
B.
The Declaration of the Rights of Man
C.
The Reign of Terror
D.
The Execution of Louis XVI
Show solution
Solution
The Storming of the Bastille on July 14, 1789, is widely regarded as the event that marked the beginning of the French Revolution.
Correct Answer:
A
— The Storming of the Bastille
Learn More →
Q. Which of the following events marked the beginning of the Indian National Congress?
A.
First Round Table Conference
B.
Formation of the Indian National Congress
C.
Quit India Movement
D.
Civil Disobedience Movement
Show solution
Solution
The Indian National Congress was formed in 1885, marking the beginning of organized political activity in India.
Correct Answer:
B
— Formation of the Indian National Congress
Learn More →
Q. Which of the following events marked the beginning of the Indian National Movement?
A.
Formation of the Indian National Congress in 1885
B.
The Revolt of 1857
C.
The Partition of Bengal in 1905
D.
The Jallianwala Bagh Massacre in 1919
Show solution
Solution
The formation of the Indian National Congress in 1885 is considered the beginning of the organized Indian National Movement.
Correct Answer:
A
— Formation of the Indian National Congress in 1885
Learn More →
Q. Which of the following events marked the beginning of the modern Indian freedom struggle?
A.
The Sepoy Mutiny of 1857
B.
The formation of the Indian National Congress in 1885
C.
The Jallianwala Bagh massacre in 1919
D.
The Quit India Movement of 1942
Show solution
Solution
The Sepoy Mutiny of 1857 is often considered the first major revolt against British rule, marking the beginning of the modern Indian freedom struggle.
Correct Answer:
A
— The Sepoy Mutiny of 1857
Learn More →
Q. Which of the following events marked the beginning of the Space Age? (1957)
A.
A. Launch of Sputnik 1
B.
B. Apollo 11 Moon landing
C.
C. Launch of Vostok 1
D.
D. First human in space
Show solution
Solution
The launch of Sputnik 1 by the Soviet Union in 1957 is widely regarded as the event that marked the beginning of the Space Age, initiating the exploration of outer space.
Correct Answer:
A
— A. Launch of Sputnik 1
Learn More →
Q. Which of the following events marked the end of the Cold War? (1989)
A.
Fall of the Berlin Wall
B.
Vietnam War
C.
Cuban Missile Crisis
D.
Korean War
Show solution
Solution
The Fall of the Berlin Wall in 1989 is widely regarded as the event that marked the end of the Cold War.
Correct Answer:
A
— Fall of the Berlin Wall
Learn More →
Q. Which of the following events occurred first in the Indian Freedom Movement? (1920)
A.
Jallianwala Bagh Massacre
B.
Civil Disobedience Movement
C.
Non-Cooperation Movement
D.
Quit India Movement
Show solution
Solution
The Non-Cooperation Movement was launched in 1920, while the Jallianwala Bagh Massacre occurred in 1919.
Correct Answer:
C
— Non-Cooperation Movement
Learn More →
Q. Which of the following events occurred in 2001, significantly impacting global politics? (2001)
A.
9/11 Attacks
B.
Iraq War
C.
Global Financial Crisis
D.
Brexit Referendum
Show solution
Solution
The 9/11 attacks occurred on September 11, 2001, leading to major changes in global politics.
Correct Answer:
A
— 9/11 Attacks
Learn More →
Q. Which of the following expressions correctly relates ΔG, ΔH, and ΔS?
A.
ΔG = ΔH + TΔS
B.
ΔG = ΔH - TΔS
C.
ΔG = TΔS - ΔH
D.
ΔG = ΔH + ΔS
Show solution
Solution
The correct relation is ΔG = ΔH - TΔS.
Correct Answer:
B
— ΔG = ΔH - TΔS
Learn More →
Q. Which of the following expressions is equivalent to (2^3)^2?
A.
2^5
B.
2^6
C.
2^9
D.
2^1
Show solution
Solution
Using the power of a power property, (a^m)^n = a^(m*n), we get 2^(3*2) = 2^6.
Correct Answer:
B
— 2^6
Learn More →
Showing 24031 to 24060 of 27860 (929 Pages)