SPSC Lecturer Mathematics Past Paper 2000 to till date

Q51: The 2024 Australian Open is won by _____?

سن 2024 آسٹریلیائی اوپن _____ کے ذریعہ جیتا ہے؟

Mike Bryan

Jannik Sinner

Novak Djokovic

None of these

Q52: Choose the sentence with correct subject-verb agreement? Either the cat or the dog were responsible for the mess, Either the cat or the dog was responsible for the mess, Either the cats or the dog were responsible for the mess

صحیح مضمون فعل کے معاہدے کے ساتھ جملے کا انتخاب کریں؟

Either the cat or the dog were responsible for the mess

Either the cat or the dog was responsible for the mess

Either the cats or the dog were responsible for the mess

Either the cats or the dog was responsible for the mess

Q53: If 1 - I, is a root of the equation x² + ax + b = 0, where a, b, ∈ R, then the value of a - b is?

1

2

-4

None of these

Q54: What is the value of the given limit, lim 2/x x→∞?

0

2

1/2

None of these

Q55: Rolle's Theorem is special case of ______?

Taylor Series of a function

Leibniz theorem

Mean value theorem

None of these

Explanation

Rolle's Theorem is a special case of the Mean Value Theorem (MVT) where the function has equal values at two endpoints.

It ensuring the derivative is zero at some point in the interval.

It is derived from MVT by adding the condition $f(a) = f(b)$ .

Q56: Idiom: Out of blue means?

In rage

From nowhere

Campout fast

None of these

Q57: One that lives on another is called?

Parasite

Eligible

Independent

None of these

Q58: The probability distribution whose mean and standard deviation are equal is _____?

Log-normal distribution

Exponential distribution

Normal

None of these

Q59: As u = (2, -2, 3) and v = (1, -3, 4), then ||-2u + 2v|| is ______?

2√3

√2

√3

None of these

Calculation: First, compute -2u + 2v:−2u=(−4,4,−6)−2u=(−4,4,−6)2v=(2,−6,8)2v=(2,−6,8)−2u+2v=(−4+2,4−6,−6+8)=(−2,−2,2)−2u+2v=(−4+2,4−6,−6+8)=(−2,−2,2)

Explanation

Calculation: First, compute -2u + 2v:
- $- 2 u = (- 4, 4, - 6)$
- $2 v = (2, - 6, 8)$
- $- 2 u + 2 v = (- 4 + 2, 4 - 6, - 6 + 8) = (- 2, - 2, 2)$
Norm Calculation: The norm (magnitude) of $- 2 u + 2 v$ is:
$∣ ∣ - 2 u + 2 v ∣ ∣ = \sqrt{(- 2)^{2} + (- 2)^{2} + 2^{2}} = \sqrt{4 + 4 + 4} = \sqrt{12} = 2 \sqrt{3}$

Answer:

Q60: Which of the following expressions represents the distributive law of Boolean algebra?

A(B + C) = AB + AC

A + (BC) = (A + B)(A + C)

AB + BC = A(B + C)

None of these