Questions covered in Mock Test 1: Full Syllabus

Review the question prompts below before starting the timed test. Try each problem independently, then use the interactive test to record your answers and review the worked solutions.

1. If $A = \{1, 2, 3, 4, 5\}$ and $B = \{4, 5, 6, 7\}$, then $A - B$ is
2. The value of $\sin 75^\circ$ is
3. The multiplicative inverse of $4 - 3i$ is
4. The number of terms in the expansion of $(x + a)^{100} + (x - a)^{100}$ is
5. The distance between the lines $3x + 4y = 9$ and $6x + 8y = 15$ is
6. $\lim_{x \to 0} \frac{\sin ax}{\sin bx}$ is equal to
7. The derivative of $\sin x \cos x$ with respect to $x$ is
8. If $P(A) = 1/2, P(B) = 1/3$ and $P(A \cap B) = 1/4$, then $P(A \cup B)$ is
9. The coordinates of the focus of the parabola $y^2 = -8x$ are
10. The 10th term of the G.P. $5, 25, 125, \dots$ is
11. Which of the following relations on set $\{1, 2, 3\}$ is reflexive but not symmetric?
12. The value of $\tan 15^\circ$ is
13. The modulus of the complex number $z = \frac{1+i}{1-i}$ is
14. The solution set of the inequality $|x-1| \le 2$ is
15. The value of $^nC_r + ^nC_{r-1}$ is
16. The coefficient of $x^n$ in the expansion of $(1+x)^{2n}$ is
17. If AM and GM of two numbers are 10 and 8 respectively, the numbers are
18. The slope of a line perpendicular to the line $x - y + 1 = 0$ is
19. The point $(-2, 3, 5)$ lies in which octant?
20. The median of the data: 3, 5, 7, 9, 11, 13, 15 is
21. Find the domain and range of the real function $f(x) = \sqrt{9-x^2}$.
22. Solve the inequality $3(1-x) < 2(x+4)$.
23. Find the derivative of $f(x) = x \sin x$ from first principles.
24. Find the equation of the line passing through $(-3, 5)$ and perpendicular to the line through the points $(2, 5)$ and $(-3, 6)$.
25. Three coins are tossed once. Find the probability of getting at least two heads.
26. Prove that $\frac{\sin 5x + \sin 3x}{\cos 5x + \cos 3x} = \tan 4x$.
27. Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse $\frac{x^2}{36} + \frac{y^2}{16} = 1$.
28. Insert 3 numbers between 1 and 256 so that the resulting sequence is a G.P.
29. In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?
30. Find the derivative of $\frac{x + \cos x}{\tan x}$.
31. Show that the points $P(-2, 3, 5)$, $Q(1, 2, 3)$ and $R(7, 0, -1)$ are collinear.
32. Find the coefficient of $x^5$ in the product $(1+2x)^6 (1-x)^7$ using binomial expansion.
33. Calculate the mean and standard deviation for the following distribution:
    Class: 0-10, 10-20, 20-30, 30-40, 40-50
    Frequency: 5, 8, 15, 16, 6
34. Solve the system of linear inequalities graphically: $x + 2y \le 10, x + y \ge 1, x - y \le 0, x \ge 0, y \ge 0$.
35. Find the number of words with or without meaning which can be made using all the letters of the word AGAIN. If these words are written as in a dictionary, what will be the 50th word?
36. Case Study (Sets): In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee.
    (i) Find how many students were taking neither tea nor coffee?
    (ii) How many were taking tea only?
37. Case Study (Limits): The distance $s$ meters covered by a particle in $t$ seconds is given by $s = 4t^3 + 2t^2 + 5t + 3$.
    (i) Find the velocity at $t=2$ sec.
    (ii) Find the acceleration at $t=2$ sec.
38. Case Study (Conic Sections): A satellite dish is shaped like a paraboloid of revolution. The receiver is located at the focus. The dish is 10 ft across at its opening and 2 ft deep at its center.
    (i) Find the equation of the parabola.
    (ii) How far from the vertex is the receiver located?