2nd Year Mathematics 1st Quarter Book Paper

Q1. Multiple choice questions (Attempt all · 12 × 1 = 12)

1. The logarithmic function $f(x) = \log_b x$
   1. all real numbers
   2. x < 0
   3. x > 0
   4. x ≥ 0
2. If $f$ is differentiable for every x, then $f$ is
   1. Discontinuous
   2. Continuous
   3. inite
   4. Infinite
3. $\text{If } f \text{ is integrable, then it is .}$
   1. discontinous
   2. unbounded
   3. continuous
   4. linear
4. Scaling refers to:
   1. increasing the size of an object.
   2. decreasing the size of an object.
   3. maintaining the properties while resizing an object.
   4. changing the shape of an object.
5. If $f(2) = 2$, $g(x) = x^2$, then $\frac{d}{dx} \left[ \frac{3g(x)}{f(2)} \right]$
   1. 2x
   2. 3x
   3. $\frac{3}{2}x$
   4. $\frac{3}{2}x^2$
6. $\int \sqrt{x} \, dx$ is:
   1. $x^{3/2} + C$
   2. $\frac{2}{3} x^{3/2} + C$
   3. $\frac{3}{2} x^{3/2} + C$
   4. $x^{1/2} + C$
7. Which of the following is an example of exponential growth function?
   1. f(x) = 3x + 4
   2. $f(x) = 3^x \times 5$
   3. f(x) = x³
   4. f(x) = x²
8. If $f$ is differentiable for every value of x, then $f$ is continuous for:
   1. Some value of x
   2. [0 , ∞)
   3. Every value of x
   4. [−∞ , 0]
9. If ' f(x) = 3x² + 2x , then f(x) is :
   1. 6x + 2 + c
   2. x³ + x² + c
   3. 3x³ + 2x² + c
   4. $1.5x³ + x^2 + c$
10. The function f: R → [0 , ∞) defined by f(x) = x²+ 1, is:
    1. onto but not one-to-one
    2. one-to-one but not onto
    3. neither one-to-one nor onto
    4. both one-to-one and onto
11. ∫ sin2x dx is:
    1. $\frac{\cos 2x}{2} + c$
    2. 2cos2x + c
    3. $-\frac{\sin 2x}{2} + c$
    4. $-\frac{\cos 2x}{2} + c$
12. The exponential decay function is expressed by:
    1. $f(x) = a⋅ b^x; 0 < b < 1$
    2. $f(x) = a⋅ b^x; b > 1$
    3. $f(x) = a⋅ b^x ; 0 < a < 1$
    4. $f(x) = a⋅ b^x; a > 1$