BISE Multan · Class 12 · Mathematics

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

2025 · First 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
$\sinh^{2} x - \cosh^{2} x =$
- (A)
  $- 1$
- (B)
  $1$
- (C)
  $0$
- (D)
  $2$
2
If $f (x) = \sqrt{x}$ , then $f^{- 1} (x)$ is:
- (A)
  $x$
- (B)
  $x^{2}$
- (C)
  $- x$
- (D)
  $1 / x$
3
$\frac{d}{d x} (\ln (\frac{1}{x})) =$
- (A)
  $1 / x$
- (B)
  $- 1 / x$
- (C)
  $- 1 / x^{2}$
- (D)
  $x^{2}$
4
$\frac{d}{d x} (\tanh^{- 1} x) =$
- (A)
  $\frac{1}{1 + x^{2}}$
- (B)
  $\frac{- 1}{1 + x^{2}}$
- (C)
  $\frac{- 1}{1 - x^{2}}$
- (D)
  $\frac{1}{1 - x^{2}}$
5
$\frac{d^{3}}{d x^{3}} (x^{2} + 1) =$
- (A)
  $0$
- (B)
  $1$
- (C)
  $3 x^{2}$
- (D)
  $2 x$
6
If $f (x) = 4 - x^{2}$ , then $f (x)$ decreases in interval:
- (A)
  $(- 2, 0)$
- (B)
  $(0, 2)$
- (C)
  $(- 3, - 2)$
- (D)
  $(- 1, 1)$
7
$\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + c$ is not valid for:
- (A)
  $n = 1$
- (B)
  $n = 0$
- (C)
  $n = 2$
- (D)
  $n = - 1$
8
$\int_{1}^{4} 3 \sqrt{x} d x =$
- (A)
  $12$
- (B)
  $13$
- (C)
  $14$
- (D)
  $15$
9
Solution of differential equation $\frac{d y}{d x} = - y$ is:
- (A)
  $y = c e^{x}$
- (B)
  $y = c e^{- x}$
- (C)
  $x y = c$
- (D)
  $y = c x$
10
$\int \sin x \cos x d x =$
- (A)
  $\sin x + c$
- (B)
  $\frac{\cos^{2} x}{2} + c$
- (C)
  $\frac{\sin^{3} x}{3} + c$
- (D)
  $\frac{\sin^{2} x}{2} + c$
11
Inclination of a line $y = x$ is:
- (A)
  $0^{\circ}$
- (B)
  $30^{\circ}$
- (C)
  $45^{\circ}$
- (D)
  $60^{\circ}$
12
Distance of a line $y = 2$ from $(0, 0)$ is:
- (A)
  $0$
- (B)
  $2$
- (C)
  $1$
- (D)
  $1 / 2$
13
Equation $x^{2} - x y = 0$ represents the number of straight lines:
- (A)
  $2$
- (B)
  $1$
- (C)
  $3$
- (D)
  $4$
14
$2 x - y \geq 4$ is satisfied by:
- (A)
  $(2, 1)$
- (B)
  $(1, - 2)$
- (C)
  $(0, 0)$
- (D)
  $(1, 1)$
15
Centre of circle $(x - 2)^{2} + y^{2} = 16$ is:
- (A)
  $(2, - 2)$
- (B)
  $(0, 2)$
- (C)
  $(- 2, 2)$
- (D)
  $(2, 0)$
16
Directrix of parabola $x^{2} = - 16 y$ is:
- (A)
  $y + 4 = 0$
- (B)
  $y - 4 = 0$
- (C)
  $y + 6 = 0$
- (D)
  $y - 16 = 0$
17
Eccentricity of circle is:
- (A)
  $0$
- (B)
  $1$
- (C)
  $1 / 2$
- (D)
  $2$
18
$\vec{a}$ and $\vec{b}$ are perpendicular of:
- (A)
  $\vec{a} \times \vec{b} = 0$
- (B)
  $\vec{a} \cdot \vec{b} = 0$
- (C)
  $\vec{a} \cdot \vec{b} = 1$
- (D)
  $\vec{b} \times \vec{a} = 2$
19
Projection of $\vec{v} = x \hat{i} + y \hat{j} + z \hat{k}$ along $\hat{i}$ is:
- (A)
  $x$
- (B)
  $y$
- (C)
  $z$
- (D)
  $0$
20
$\hat{i} \cdot \hat{k} \times \hat{j}$ is:
- (A)
  $1$
- (B)
  $0$
- (C)
  $2$
- (D)
  $- 1$

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