SPSC Mathematics 25 years Past Papers (2001 to 2026) MCQs Download PDF

Testpoint Whatsapp group

Testpoint Whatsapp group

SPSC 5 years Past Papers Click here

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

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

The probability of getting a total of 7 or 11 when a pair of dice are tossed will be?

4/9
1/9
2/9
None of these

(0)

اس سوال کو وضاحت کے ساتھ پڑھیں

From the data 3.4, 2.5, 4.8, 2.9, 3.6, 2.8, 3.3, 5.6, 3.7, 2.8, 4.4, 4.0, 5.2, 3.0, 4.8, the sample median will be?

2.9
3.7
3.6
None of these

(0)

اس سوال کو وضاحت کے ساتھ پڑھیں

Explanation

Arrange Data in Ascending Order:
$2.5, 2.8, 2.8, 2.9, 3.0, 3.3, 3.4, 3.6, 3.7, 4.0, 4.4, 4.8, 4.8, 5.2, 5.6$
Find Median:
- There are 15 data points (odd number), so the median is the 8th value in the ordered list.
- The 8th value is 3.6.

A consistent system of linear equations has ______?

Maximum two solutions
At least one solution
Minimum two solution
None of these

(0)

اس سوال کو وضاحت کے ساتھ پڑھیں

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

2√3
√2
√3
None of these

(0)

اس سوال کو وضاحت کے ساتھ پڑھیں

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:

‹
1
2
...
17
18
19
20
21
22
›

All Rights Reserved © TestPointpk.com