BISE Multan · Class 12 · Mathematics

BISE Multan · Class 12 · Mathematics · 2025 · Second Annual · Group 2

2025 · Second Annual

Transcribed from the identified examination paper. Check the board, session and course before use. SchoolOrbit is not affiliated with the issuing board.

Objective

Source code: 4192 · Printed marks: 20 · Time: 30 Minutes

MATHEMATICS PAPER-II GROUP-II

OBJECTIVE

Q.No.1

You have four choices for each objective type question as A, B, C and D. The choice which you think is correct, fill that bubble in front of that question number, on bubble sheet. Use marker or pen to fill the bubbles. Cutting or filling two or more bubbles will result in zero mark in that question.

1
If $f (x)$ is continuous at $x = a$ , then $\underset{x \to a}{L i m} f (x) =$
- (A)
  $f (0)$
- (B)
  $f (x)$
- (C)
  $f (a)$
- (D)
  $\infty$
2
The range of the function $f (x) = \sqrt{x^{2} - 4}$ is:
- (A)
  $R - (- 2, 2)$
- (B)
  $(0, \infty)$
- (C)
  $R$
- (D)
  $[- 2, 2]$
3
$\frac{d}{d x} (\frac{1}{\sec x}) =$
- (A)
  $\cos x$
- (B)
  $\tan^{2} x$
- (C)
  $\sin x$
- (D)
  $- \sin x$
4
$\frac{d}{d x} (x^{n}) =$
- (A)
  $n x^{n - 1}$
- (B)
  $n x^{n + 1}$
- (C)
  $n x$
- (D)
  $0$
5
Derivative of $x^{3}$ w.r.t. $x^{3}$ is:
- (A)
  $0$
- (B)
  $1$
- (C)
  $x^{3}$
- (D)
  $3 x^{2}$
6
Derivative of $\sqrt{x}$ at $x = a$ is:
- (A)
  $\frac{- 1}{\sqrt{a}}$
- (B)
  $\frac{- 1}{2 \sqrt{a}}$
- (C)
  $\frac{1}{2 \sqrt{a}}$
- (D)
  $2 \sqrt{a}$
7
$\int \sin 2 x d x =$
- (A)
  $\frac{- \cos 2 x}{2}$
- (B)
  $\frac{\cos 2 x}{2}$
- (C)
  $2 \cos 2 x$
- (D)
  $- \cos 2 x$
8
$\int \ln x d x =$
- (A)
  $x - x \ln x + c$
- (B)
  $x \ln x + x + c$
- (C)
  $1 / x + c$
- (D)
  $x \ln x - x + c$
9
$\int_{0}^{1} \frac{1}{\sqrt{1 - x^{2}}} d x =$
- (A)
  $π / 4$
- (B)
  $π / 3$
- (C)
  $π / 2$
- (D)
  $π$
10
Solution of $\frac{d y}{d x} = \cos x$ is $y =$ ?
- (A)
  $\sin x + c$
- (B)
  $- \sin x + c$
- (C)
  $\cos x + c$
- (D)
  $\ln (\sin x) + c$
11
The point $(3, - 8)$ lies in the quadrant:
- (A)
  I
- (B)
  II
- (C)
  III
- (D)
  IV
12
The inclination of the line $y = x$ is:
- (A)
  $180^{\circ}$
- (B)
  $60^{\circ}$
- (C)
  $45^{\circ}$
- (D)
  $30^{\circ}$
13
The slope of the line parallel to $x$ -axis is:
- (A)
  $0$
- (B)
  $1$
- (C)
  $\sqrt{3}$
- (D)
  Undefined
14
$(0, 0)$ lies in the solution of inequality:
- (A)
  $7 x + 2 y > 3$
- (B)
  $3 x + 5 y > 7$
- (C)
  $3 x + 5 y < 5$
- (D)
  $x + y < 0$
15
The radius of the circle $x^{2} + y^{2} - 6 x + 2 y + 1 = 0$ is:
- (A)
  $3$
- (B)
  $2$
- (C)
  $5$
- (D)
  $4$
16
Centre of circle $(x - 3)^{2} + (y + 2)^{2} = 26$ is:
- (A)
  $(- 3, 2)$
- (B)
  $(3, - 2)$
- (C)
  $(- 3, - 2)$
- (D)
  $(3, 2)$
17
$x^{2} + 3 y^{2} = 9$ is equation of:
- (A)
  Parabola
- (B)
  Circle
- (C)
  Ellipse
- (D)
  Hyperbola
18
An example of vector quantity is:
- (A)
  Magnetic field
- (B)
  Length
- (C)
  Temperature
- (D)
  Work
19
Magnitude of the vector $\underline{u} = [3, - 4]$ is:
- (A)
  $25$
- (B)
  $5$
- (C)
  $- 5$
- (D)
  $\pm 5$
20
The angle between the vectors $2 \hat{i} + 3 \hat{j} + \hat{k}$ and $2 \hat{i} - \hat{j} - \hat{k}$ is:
- (A)
  $π$
- (B)
  $π / 4$
- (C)
  $π / 6$
- (D)
  $π / 2$

Original source references (4)

The original files and numbering are retained. Equivalent files do not repeat the questions above.

Objective · 4192 · Printed marks: 20 · Time: 30 Minutes
Objective · 4194 · Printed marks: 20 · Time: 30 Minutes : same questions, source numbering preserved separately
Objective · 4196 · Printed marks: 20 · Time: 30 Minutes : same questions, source numbering preserved separately
Objective · 4198 · Printed marks: 20 · Time: 30 Minutes : same questions, source numbering preserved separately