SPSC 25 years Past Papers 2001 to 2025

Q1961: ∫ lnxdx = - - - - - -?

xlnx – x + c

xlnx + x + c

1/x

None of these

Q1962: Lagrange's mean value theorem is a particular case of _____? Cauchy's mean value theorem,

Cauchy's mean value theorem

Euler's theorem

Leibniz's theorem

None of these

Q1963: The phenomenon of land and sea breeze is a result of _____?

زمین اور سمندری ہوا کا رجحان _____ کا نتیجہ ہے؟

Entropy

Conduction

Convection

None of these

Q1964: The Black Forest is located in which country?

بلیک فاریسٹ کس ملک میں واقع ہے؟

China

Germany

France

Britain

Q1965: Two uniform spheres are pivoted on horizontal axes that are tangent to their surfaces. The one with the longer period of oscillation is the one with _______?

افقی محوروں پر دو یکساں دائرے محو ہیں جو ان کی سطحوں پر ٹینجینٹ ہیں۔ ایک طویل مدت کے ساتھ ایک ہے جس میں _______ ہے؟

The larger radius

The larger rotational inertia

The smaller mass

None of these

Q1966: Lenz' Law can explain _____?

لینز کا قانون _____ کی وضاحت کرسکتا ہے؟

Only two of the three types of magnetism

Ferromagnetism only

Diamagnetism only

None of these

Q1967: The power loss P in a resistor is calculated using the formula P = V²/R. The uncertainty in the potential difference V is e% and the uncertainty in R is 2%. What is the uncertainty in P?

11%

7%

8%

None of these

Explanation

Uncertainty propagation in multiplication/division follows the rule:
$\frac{Δ P}{P} = 2 \times \frac{Δ V}{V} + \frac{Δ R}{R}$

Given uncertainty in V = e% and uncertainty in R = 2%,
$text{Total uncertainty} = 2(e) + 2 = 8%$ (assuming e = 3%)

Q1968: The movie was so boring that I walked _____ before it ended.

Out

Away

Off

None of these

Q1969: Phenols are not having ______?

فینولز ______ نہیں ہیں؟

Hydroxyl group

Benzene ring

Carbonyl group

None of these

Q1970: Arene predominantly undergoes _____?

ارین بنیادی طور پر _____ سے گزرتا ہے؟

Elimination

Addition

Substitution

None of these