SPSC Lecturer Mathematics Solved Past Paper 2000 to 2025

Testpoint Whatsapp group

Testpoint Whatsapp group

Lecturer Mathematics Past Papers Click here

چار آپشن میں سے کسی ایک پر کلک کرنے سے جواب سرخ ہو جائے گا۔

Let the functions f:R→R and be defined as f(x)=x^2. Then f^−1(−9) = will be?

Ø
-3
3
None of these

(0)

اس سوال کو وضاحت کے ساتھ پڑھیں

lim x → 0 √x^2+100 - 10/x^2 will be?

Does not exist
1/20
∞
None of these

(0)

اس سوال کو وضاحت کے ساتھ پڑھیں

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

(0)

اس سوال کو وضاحت کے ساتھ پڑھیں

Explanation

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

Solution of the separable differential equation (1+ x)dy - ydx = 0 is _____?

y = c(1 - x)
y = c^2 + (1 + x)
y = c(1 + x)
None of these

(0)

اس سوال کو وضاحت کے ساتھ پڑھیں

Y = 5x and dx/dt = 2 the day/dt will be _____?

12
11
10
None of these

(0)

اس سوال کو وضاحت کے ساتھ پڑھیں

Average rate of change of function f(x)=x ^3 +1 over the interval [2,3] will be?

21
20
19
None of these

(0)

اس سوال کو وضاحت کے ساتھ پڑھیں

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

(0)

اس سوال کو وضاحت کے ساتھ پڑھیں

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 $x^{3} + x$ :
$\frac{(x^{3} + x)^{6}}{6} + C$

If is continuous at every point in [a,b], and f is any antiderivative of f on [a,b], then ____?

∫baf(x)dx=F(b)+F(a)
∫baf(x)dx=F(b)−F(a)
∫f(x)dx=F(b)−F(a)
None of these

(0)

اس سوال کو وضاحت کے ساتھ پڑھیں

Explanation

Fundamental Theorem of Calculus:
If $f$ is continuous on $[a, b]$ and $F$ is any antiderivative of $f$ on $[a, b]$ , then:
$\int_{a}^{b} f (x) d x = F (b) - F (a)$

By using finite approximation to estimate the area under the graph of the function using a lower sum with two rectangles of equal width of the function f(x)=x^2 in the interval [0,1] will be?

0.125
0.2187
0.625
None of these

(0)

اس سوال کو وضاحت کے ساتھ پڑھیں

As z1 = 3 - 4i and z2 = -4 + 3i, then the acute angle between the vectors will be?

18°16'
17°16'
16°16'
None of these

(0)

اس سوال کو وضاحت کے ساتھ پڑھیں

‹
1
2
...
18
19
20
21
22
23
›

All Rights Reserved © TestPointpk.com