SELF EVALUATION -1
1. SETS
If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, then A ∩ B is:
A) {1, 2}
B) {3, 4}
C) {5, 6}
D) {1, 6}
2. Relations & Functions
If f(x) = 2 x + 3, then f(4) is:
A) 8
B) 10
C) 11
D) 12
3. Trigonometric Identities
The value of sin²θ + cos²θ is:
A) 0
B) 1
C) 2
D) –1
4. Complex Numbers
i² equals:
A) 1
B) –1
C) 0
D) i
5. Quadratic Equations
The nature of roots of ax² + bx + c = 0 depends on:
A) b² – 4 ac
B) a + b + c
C) a – b
D) c²
6. Permutations & Combinations
The value of 5P2 is:
A) 10
B) 20
C) 5
D) 25
7. Statistics
Mean of first 5 natural numbers is:
A) 2
B) 2.5
C) 3
D) 4
8. Straight Lines
Slope of the line 2 x + 3 y = 6 is:
A) 2/3
B) –2/3
C) 3/2
D) –3/2
SELF EVALUATION -2
1. Sets
If A = {x : x is a prime number less than 10}, then A is:
A) {1, 2, 3, 5, 7}
B) {2, 3, 5, 7}
C) {2, 4, 6, 8}
D) {1, 3, 5, 7}
2. Relations
If A = {1, 2, 3}, then the total number of relations on A is:
A) 3
B) 6
C) 9
D) 512
3. Functions
If f(x) = x² – 1, then f(–2) is:
A) 3
B) –3
C) 5
D) –5
4. Trigonometry
The value of tan 45° is:
A) 0
B) 1
C) √3
D) –1
5. Complex Numbers
If z = 3 + 4 i, then |z| is:
A) 5
B) 7
C) 25
D) 1
6. Permutations
The number of ways to arrange the letters of the word “MATH” is:
A) 4
B) 12
C) 24
D) 16
7. Binomial Theorem
The coefficient of x² in (1 + x)⁴ is:
A) 4
B) 6
C) 12
D) 24
8. Straight Line
Distance between points (1,2) and (4,6) is:
A) 5
B) 4
C) √13
D) 6
9. Limits
lim x→0 (sin x)/x equals:
A) 0
B) 1
C) ∞
D) –1
10. Statistics
If the mean of 10 numbers is 20, then their total sum is:
A) 200
B) 20
C) 100
D) 10
SELF EVALUATION -3
1. If A = {1,2,3} and B = {2,3,4}, then A ∪ B is:
A) {1,2,3}
B) {2,3}
C) {1,2,3,4}
D) {4}
2. Number of subsets of a set containing 4 elements is:
A) 4
B) 8
C) 16
D) 32
3. If n(A) = 3, then number of relations on A is:
A) 9
B) 27
C) 512
D) 64
4. If f(x) = x³, then f(2) equals:
A) 6
B) 8
C) 4
D) 10
5. Value of sin 90° is:
A) 0
B) 1
C) –1
D) √3
6. sin²θ + cos²θ =
A) 0
B) 1
C) 2
D) –1
7. If i² =
A) 1
B) –1
C) i
D) 0
8. Modulus of 1 + i is:
A) 1
B) √2
C) 2
D) 0
9. Discriminant of 2 x² + 3 x + 1 = 0 is:
A) 1
B) –1
C) 5
D) 0
10. Roots of x² – 4 = 0 are:
A) ±2
B) ±4
C) 2
D) –2
11. Value of 5! is:
A) 20
B) 60
C) 120
D) 720
12. ⁶C₂ equals:
A) 12
B) 15
C) 30
D) 6
13. Coefficient of x² in (1 + x)³ is:
A) 3
B) 6
C) 9
D) 1
14. Distance between (0,0) and (3,4) is:
A) 5
B) 4
C) 7
D) 3
15. Slope of line y = 3 x + 2 is:
A) 2
B) 3
C) –3
D) 1
16. If mean of 5 numbers is 10, their sum is:
A) 50
B) 15
C) 5
D) 10
17. lim x→0 (sin x)/x equals:
A) 0
B) 1
C) ∞
D) –1
18. If tan θ = 1, then θ =
A) 30°
B) 45°
C) 60°
D) 90°
19. Domain of f(x) = 1/x is:
A) All real numbers
B) x ≠ 0
C) x = 0
D) x > 0
20. (a + b)² equals:
A) a² + b²
B) a² + 2ab + b²
C) a² – b²
D) 2ab
21. If A = {1,2} and B = {3,4}, number of elements in A × B is:
A) 2
B) 4
C) 6
D) 8
22. Equation of x-axis is:
A) x = 0
B) y = 0
C) x = y
D) y = 1
23. Value of cos 0° is:
A) 0
B) 1
C) –1
D) 1/2
24. If |z| = 0, then z is:
A) 1
B) i
C) 0
D) –1
25. Number of diagonals in a quadrilateral is:
A) 2
B) 4
C) 6
D) 1
26. 7P2 equals:
A) 14
B) 42
C) 21
D) 49
27. If variance = 9, then standard deviation is:
A) 9
B) 3
C) 81
D) 6
28. Solution of 2 x – 4 = 0 is:
A) 2
B) –2
C) 4
D) 0
29. If n(A) = 5, number of proper subsets is:
A) 31
B) 32
C) 30
D) 25
30. Value of sec 60° is:
A) 1
B) 2
C) √3
D) 1/2
SELF EVALUATION -4
- All possible subsets of set A = {2,3,4} are
- P(A) = {2},{3}, {4}
- P(A) = {{2},{3}, {4}, {2,3,4}}
- P(A) = {ϕ,{2},{3}, {4},{2,3},{3,4},{4,2} ,{2,3,4}}
- none of these
- If A' is the complement of set A, then
- A' = U - A
- A' = U + A
- A' - A = U
- A' = A
- If A and B are two sets such that n(A)= 27, n(B) = 35 and n(A ∪ B) = 50, then find n(A ∩ B).
- 10
- 12
- 14
- 16
- Find a and b when (a - 2 b, 13) = (7,2a - 3 b).
- a = 4, b = 1
- a = 5, b = 2
- a = 5, b = -1
- a = 6, b = 7
- If f:R→R : f(x) = x² + 3 = 19, then find the pre-image of the function.
- 4
- -4
- ±4
- 0
- Find the domain of the function f(x) = ( x² + 1)/(x² - 1)
- R - {1}
- R - {-1,1}
- R - {-1}
- R
- Range of the modulus function f(x)= |x| is
- Range(f) = [0,∞)
- Range(f) = (0,∞)
- Range(f) = (-∞,∞)
- none of these
- The value of 1+ i² + i⁴ + i⁶ is
- 1
- -1
- 0
- -2
- Conjugate of z = 5 - 2 i is
- -5 - 2 i
- 5 + 2 i
- -5 + 2 i
- 5 + i
- If 2 y + (3 x - y)i = (5 - 2 i) then find the value of x and y.
- x = 3/2, y = 5/2
- x = 1/6, y = 5/2
- x = 3/2, y = 4/3
- x = 5/3, y = 1/6
- If z = 4 - 3 i then the multiplicative inverse of z is
- 4/25 + 3 i/25
- 3/25 + 4 i/25
- -4/25 - 3 i/25
- 4/25 - 3 i/25
- Polar form of Z = (-√3 - i) is
- 2(Cos 5 π/6 - i sin 5 π/6)
- 2(- Cos 5 π/6 + i sin 5 π/6)
- 2(Cos 5 π/6 + isin 5 π/6)
- none of these
- Imaginary roots of the equation x² + 3 x + 9 = 0 are
- x = (-3 ± i3√3)/2
- x = (3 ± i3√3)/2
- x = (-3 - i3√3)/2
- x = (-3 + i3√3)/2
- Let a is a positive integer then |x| > a is
- x < -a or x > a
- x > -a or x < a
- x < -a or x > -a
- none of these
- ⁿP₅ = 42 × ⁿP₃ , n > 4 find n.
- 12
- 10
- 14
- 16
- If 1/4! + 1/5! = x/6!, then value of x is
- 40
- 36
- 38
- 32
- ⁿCᵣ + ⁿCᵣ₋₁ = ?
- ⁿ⁺¹Cᵣ
- ⁿ⁻¹Cᵣ
- ⁿ⁺¹Cᵣ₊₁
- none of these
- Relation between permutation and combination is
- ⁿCᵣ = ⁿPᵣ/r!
- ⁿCᵣ × r! = 1
- ⁿCᵣ/r! = ⁿPᵣ
- none of these
- If ⁿC₈ = ⁿC₆ then the value of ⁿC₃ is
- 350
- 346
- 364
- 580
- Find the 6th term of the expansion (4x/5 − 5/2x)⁹
- 5040/x
- 4050/x
- -5040/x
- -4050/x
- Which term of the A.P. 9, 14, 19, 24, 29, ... is 379 ?
- 80 th
- 78 th
- 75 th
- 60 th
- What will be the sum of all natural numbers between 100 and 1000 which are divisible by 5?
- 94850
- 98450
- 99450
- 94950
- For what value of x are the numbers -2/7, x , -7/2 are in G.P. ?
- x = 1, x = - 1
- x = -1, x = 3
- x = 0, x = 2
- none of these
- Degree measure of (3/4)ᶜ is
- 42°50"
- 42°57'16"
- 49°61'
- 41°57'18"
- Find the degree of the angle subtended at the centre of a circle of diameter 50 cm by an arc of length 11 cm.
- 30°
- 22°17'
- 25°12'
- none of these
- Value of Cos 15 π is
- 1
- 0
- -1
- 2
- Cosec(-41 π/4) is
- √2
- -√2
- 1/2
- -1/2
- tan(x + y) is equal to
- (tan x + tan y) / (1 - tan x • tan y)
- (tan x - tan y) / (1 + tan x • tan y)
- (1-tan x • tany) / (tan x + tan y)
- (1 + tan x • tan y) / (tan x - tan y)
- The value of tan(13 π/12) is
- (2 + √3)
- (2 - √3)
- (2 ± √3)
- (2 ∓ √3)
- If Cos²θ = Cos²α then general solution is
- θ = n π + α
- θ = n π - α
- θ = n π ± α
- none of these
- When two lines L₁ and L₂ are perpendicular to each other then their slopes m₁ and m₂ are related as
- m₁ × m₂ = 1
- m₁ × m₂ = -1
- m₁/m₂ = ∞
- m₂/m₁= ∞
- Intercept form of a straight line is
- x/a + y/b = 1
- x/a - y/b = 1
- x/a + y/b = -1
- none of these
- A circle passes through the points A(2,-4), B(5,-8) and C(2,1). The centre of the circle is
- (2,-4)
- (-3,4)
- (3,-16/3)
- none of these
- For the parabola x² = 6 y , the focus and the equation of directrix are respectively
- F(0, -3/2), y = 3/2
- F(0, 3/2), y = 3/2
- F(0, 3/2), y = -3/2
- none of these
- The vertices of an ellipse are (±5,0)
and its foci are (±4,0). The equation of the ellipse is
- x² /25 + y² /16 = 1
- x² /9 + y² /25 = 1
- x² /25 + y² /9 = 1
- x² /16 + y² /25 = 1
- lim x→0 (Sin ax / Sin bx) is equal to
- b/a
- a/b
- -a/b
- -b/a
- lim x→0 [(3²ˣ − 1)/(2³ˣ − 1) ] is equal to
- log 9/log 8
- log 8/log 9
- log 2/log 3
- log 3/log2
- If y = tan√x then dy/dx = ?
- (sec√x)/2√x
- (secx)/2√x
- (sec²√x)/2√x
- (sec²√x)/√x
- If y = x²sinx then dy/dx =?
- 2 x •sinx +x² cos x
- x² sinx + 2 x•cos x
- 2 x •sinx - x² cos x
- none of these
- Probability of the event is defined as
- P(E) = n(E)/n(S)
- P(E) = [n(E)+n(S)]/n(S)
- P(E) = [P(S)+P(E)]/P(E)
- none of these
