Explanation

• Liaquat Ali Khan was assassinated on 16 October 1951.
• Age: 56 years
• He was Pakistan’s first Prime Minister.
• Birth: 1 October 1895
• Place of assassination: Company Bagh (Liaquat Bagh), Rawalpindi
• Title: Shaheed-e-Millat (Martyr of the Nation)
• His assassin Syed Akbar was immediately killed on the spot by police.

Last verified on 01-05-2026

Explanation

• The phrase “went on ___ one point only” means repeatedly focusing on that point.
• “Stressing” fits because it means emphasizing a single idea continuously.

Last verified on 20-06-2026

Explanation

• In “either…or”, the verb agrees with the nearest subject (here: dog = singular).
• Since “dog” is singular, we use “was.”
• So, the correct subject-verb agreement is singular verb “was” with singular nearest subject.

Last verified on 20-06-2026

Explanation

• Pakistan became an "Islamic Republic" in its 1956 constitution.
• This constitution was the first to declare Pakistan as an Islamic Republic.
• It is reflecting the country's identity as a democratic state founded on the principles of Islam.

Additional information:

• The constitution was adopted on March 23, 1956.
• The 1956 Constitution was abrogated in 1958.
• When President Iskander Mirza imposed martial law and declared himself the Chief Martial Law Administrator.

Last verified on 23-03-2026

Explanation

• The “Quit India” Movement was launched by Mahatma Gandhi against British rule.
• It was announced on 8 August 1942 at the All India Congress Committee session in Bombay.
• The slogan of the movement was “Do or Die”.
• Key leaders arrested: Gandhi, Nehru, Congress leaders
• Mass arrests: 9 August 1942
• Movement type: Mass civil disobedience
• Goal: End British colonial rule

Last verified on 09-06-2026

Explanation

x cot y dy = dx  

cot y dy = dx/x  

∫ cot y dy = ∫ dx/x  

ln|sin y| = ln|x| + C  

siny = Cx

Last verified on 05-06-2026

Explanation

If a real root of f(x) = 0 lies in the interval, then the graph of f(x) must cross the x-axis between a and b.[a][b]

To cross the x-axis:

At one end the function value will be positive, f(a) > 0

At the other end the function value will be negative, f(b) < 0

When signs are opposite, their product is negative.

So f(a) × f(b) < 0

Last verified on 05-06-2026

Explanation

Matrix rows are dependent ⇒ Rank = 2

Determinant of this matrix = 0

So, R − D = 2 − 0 = 2

Last verified on 05-06-2026

Explanation

Equation 3x² + 7xy + 2y² = 0 represents a pair of lines through origin.

Factor it:

3x² + 6xy + xy + 2y² = 0  

3x(x + 2y) + y(x + 2y) = 0  

(3x + y)(x + 2y) = 0

So lines are: y = -3x and y = -x/2  

Slopes: m₁ = -3, m₂ = -1/2

Angle between lines:

tan θ = |(m₁ - m₂)/(1 + m₁m₂)|  

= |(-3 + 1/2) / (1 + 3/2)|  

= |(-5/2) / (5/2)| = | -1 | = 1

tan θ = 1 → θ = 45°

So the acute angle between the two lines is 45°.

Last verified on 05-06-2026

Explanation

∂²u/∂x² + ∂²u/∂y² = f(x,y) is the 2D Poisson equation.  

If f(x,y) = 0, then it becomes Laplace's equation: ∇²u = 0

Last verified on 05-06-2026