SPSC 25 years Past Papers 2001 to 2025

Q1391: Area of an equilateral triangle as function of triangle’s side length x will be?

1/4x

√3/4x^2

√3/4x

None of these

The height hh of the equilateral triangle is 32x23x.Using the area formula for a triangle (Area=12×base×heightArea=21×base×height):A=12×x×32x=34x2A=21×x×23x=43x2

Explanation

- The height $h$ of the equilateral triangle is $\frac{\sqrt{3}}{2} x$ .
- Using the area formula for a triangle ( $Area = \frac{1}{2} \times base \times height$ ):
  $A = \frac{1}{2} \times x \times \frac{\sqrt{3}}{2} x = \frac{\sqrt{3}}{4} x^{2}$

Q1392: Integral f (x^3 + x)^5 (3x^2 + 1)dx will be _____?

(x^3 + x)^6/6 + C

(x^3 + x)^5/5 + C

(x^3 + x)^4/4 + C

None of these

Substitution Method:Let u=x3+xu=x3+x. Then, the derivative of uu is:dudx=3x2+1 ⟹ du=(3x2+1)dxdxdu=3x2+1⟹du=(3x2+1)dx

Explanation

Substitution Method:
Let $u = x^{3} + x$ . Then, the derivative of $u$ is:
$\frac{d u}{d x} = 3 x^{2} + 1 ⟹ d u = (3 x^{2} + 1) d x$
Rewrite the Integral:
The integral becomes:
$\int u^{5} d u$
Integrate:
$\int u^{5} d u = \frac{u^{6}}{6} + C$
Substitute Back:
Replace $u$ with $x^{3} + x$ :
$\frac{(x^{3} + x)^{6}}{6} + C$

Q1393: A satellite is revolving around the Earth. If its height is 4 times the height of a geo-stationary satellite, what will become its time period?

16 days

8 days

4 days

None of these

Q1394: The purpose of a moderator in a nuclear reactor is to ______?

جوہری ری ایکٹر میں ماڈریٹر کا مقصد ______ ہے؟

Slow down fast neutrons to increase the probability of capture by uranium

Shield the reactor operator from dangerous radiation

Provide neutrons for the fission process

None of these

Q1395: A line drive to the short stop is caught at the same height as it was it was originally hit. Over it's entire flight the work done by gravity and the work done by air resistance, respectively are _____?

مختصر اسٹاپ پر ایک لائن ڈرائیو اسی اونچائی پر پکڑی گئی تھی جیسا کہ یہ اصل میں مارا گیا تھا۔ اس کی پوری پرواز کے دوران کشش ثقل کے ذریعہ کیا گیا ہے اور ہوا کے خلاف مزاحمت کے ذریعہ بالترتیب کام کیا گیا ہے _____؟

Positive; negative

Zero; positive

Zero; negative

None of these

Q1396: The lines which are neither parallel nor do they intersect are called?

Systematic

Skew

Symmetric

None of these

Q1397: The Synonym of "Abstruse" is?

Concealed

Skillful

Evident

None of these

Q1398: Find the error: Scientists were interested about the radioactivity emanating from the nuclear power plant.

Emanating

Scientists

Interested about

None of these

Q1399: The Antonym of Brawl is?

Glaze

Polish

Agree

None of these

Q1400: If α, β are roots of the equation 2x^2 - 4x + 5 = 0, then α^2β + αβ^2 = ____?

-1

2

5

None of these