10th Class Mathematics First half Book Paper

Q1. Multiple choice questions (Attempt all · 15 × 1 = 15)

1. Which of the following is a quadratic equation?
   1. ax + b = c
   2. ax² + bx + c
   3. ax² + bx + c = 0
   4. ax² + bx + c = 0, a = 0
2. $\frac{2}{1 - i}$ =?
   1. $\frac{1 + i}{2}$
   2. $\frac{(1+i)^2}{2}$
   3. $1 - i$
   4. $1 + i$
3. Which ordered pair is a solution of the system 2x - y ≤ 5 and x + 2y > 2?
   1. (1 , -1)
   2. (4 , 1)
   3. (2 , 0)
   4. (3 , 2)
4. If A and B are two matrices, conformable for the product AB then $(AB)^t =$
   1. $A^tB^t$
   2. $(BA)^t$
   3. $B^tA^t$
   4. AB
5. An expression which is the ratio of two polynomials but the polynomial in denominator is non-zero is called.
   1. polynomial
   2. rational Expression
   3. compound Expression
   4. irrational Expression
6. If $f(x) =\frac{1}{2} x$, what is $f^2 (x)$ ?
   1. $\frac{1}{4x}$
   2. $\frac{1}{4} x$
   3. 2x
   4. $\frac{1}{4} x^2$
7. Which of the following is a reciprocal equation?
   1. $x^2 + 2x + 2 = 0$
   2. $x^4 + x^3 + x^2 + x + 1 = 0$
   3. $\sqrt{2x + 3}$
   4. $x^4 + 2x^3 + x^2 + 4x = 0$
8. $1 + (i)^9$ = ?
   1. $1 + i$
   2. $1 +\sqrt{-1}$
   3. $1 - i$
   4. $-i$
9. The solution of the $\frac{x}{-2}$ < 3 - x is:
   1. x < 2
   2. x < 6
   3. x > 2
   4. x < -2
10. Matrix equation for y + x = 144 + y and x + 2y = x + 13 is
    1. $$\begin{bmatrix} 1 & 1 \\ 1 & 2 \end{bmatrix} \times \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 144 \\ 13 \end{bmatrix}$$
    2. $$\begin{bmatrix} 1 & 0 \\ 1 & 2 \end{bmatrix} \times \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 144 \\ 13 \end{bmatrix}$$
    3. d) $$\begin{bmatrix} 1 & 0 \\ 1 & 2 \end{bmatrix} \times \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 14 \\ 13 \end{bmatrix}$$
    4. $$\begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix} \times \begin{bmatrix} y \\ x \end{bmatrix} = \begin{bmatrix} 144 \\ 13 \end{bmatrix}$$
11. Coefficients in the polynomial $\sqrt{16x^2y} - \frac{1}{2}y^3 + \frac{22}{7}z$ are the elements of the set of:
    1. Integers
    2. Irrational numbers
    3. Odd numbers
    4. Rational numbers
12. Which of the following is an exponential function?
    1. $\left(\frac{1}{3}\right)^x$
    2. $e^x$
    3. $2^x$
    4. All of these
13. Roots of the equation (x – 1)² – 9 are:
    1. –2, 4
    2. 2, 4
    3. –4, 2
    4. –2, –4
14. $(-xi)19$ = ?
    1. $-x^{19}i$
    2. $x^{19}i$
    3. $-i^{19}$
    4. $-x^{19}$
15. (7 , -2) is a solution of the inequality;
    1. x - y < -4
    2. 2x + y < 10
    3. x + 10y < 1
    4. #NAME?