1. Number of nonempty singleton subsets from the elements of the set {l,m,n,p} is

2. Let f : A→B, then f is invertible if

3. Let $f : \mathbb{R} \to \mathbb{R}$ be defined by $f(x) = 3x - 4$. Then what is $f^{-1}(x)$?

4. What is the value of the limit?$\lim_{x \to \infty} \left(1 + \frac{3}{x}\right)^x$

5. lim x→∞ sinx/x is equal to

6. Analyze the properties of the function $f(x)$ defined as: $f(x) = \begin{cases} 2x & \text{if } x < 2 \\ 2 & \text{if } x = 2 \\ x^2 & \text{if } x > 2 \end{cases}$

7. d/dx(log|x| is equal to )

8. The derivative of $\sin^3(x)$ with respect to $\cos^3(x)$ is?

9. If $f(x) = \log(\log x)$, then what is $f'(e)$ equal to?

10. The minimum value of f(x) = sinx.cosx is

11. ∫ logx dx is equal to

12. What is the value of the definite integral $\int_{0}^{\sqrt{3}/2} \frac{dx}{\sqrt{1-x^2}}$?

13. The area bounded by the parabola y2 = x, the line y = 4 and y-axis is

14. The modulus of $\frac{(1-i)^3}{1-i^3}$ is equal to?

15. The roots of the equation $2x^2-3x+1 = 0$ are

16. If A=(1 2; 3 4) and B=(5 6; 7 8) then (AB)` is :

17. The two lines of the system 6x - 4y = 10, 3x - 2y = 5 are

18. If the A.M. and G.M. between two given numbers are 81 and 18, respectively, then H.M. is

19. The most general value of $\theta$ satisfying the equation $3 \tan^2(\theta) = 1$ is?

20. $\tan^{-1}(x) - \tan^{-1}\left(\frac{1}{x}\right)$ is equal to

21. In a $\triangle ABC$, the inradius $r$ is equal to?

22. Find the distance between the two parallel lines $3x + 4y = 6$ and $6x + 8y = 16$.

23. For what value of $\lambda$ does the equation $12x^2 - 10xy + 2y^2 + 11x - 5y + \lambda = 0$ represent a pair of straight lines?

24. The equation of the circle having the ends of its diameter at $(1, -1)$ and $(0, 2)$ is?

25. The direction cosines of a line equally inclined to the axes are