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WorksheetsOPT. Mathematics Students
Total questions: 80
Worksheet time: 31mins
1. For what value of m in y=f(x)= mx+c makes it a constant function?
0
1
-1
2
2. What type of algebraic function is f(x)=ax^2+bx+c?
Cubic
Quadratic
Trigonometric
Linear
3. The minimum value of y = sinx is .......
1
0
-1
-2
4. If f : A→ B and g : B→C be the two functions, then what will denote the composite function A→C ?
Single Function
Composion Function
Composite Function
Double Function
5. If f(x) = a and g(x) = b then what is the value of gbf(x)?
b
a
ab
bb
6. If f(x) = x+a and g(x) = x then, what is the value of fog(x)?
x
a
x+a
x2
7. If f = {(m, n), (a, b)} and g = {(n, a), (b, c)} then what is the value of gof(x)?
a, c
m, n
a,b
a,n
8. If f(x) = 2x+3 and g(x) = 3x-1, find fog(1).
8
9
6
7
9. Under what condition, the inverse function of a function is possible?
one to one function
Inverse function
Composite function
one to one onto function
10. If f = {(a,b), (x,y)} then the inverse function of f is (a)
11. If g(x) = 2x-5 , find g-1(x).
x+5/2
x-5/2
2x+5/4
2x+5
12. If (x-a) is a factor of polynomial p(x) then p(a) = .........
1
a
0
x-a
13. If p(b) = 0 then x-b is a ..............................of p(x).
divisor
Quotient
factor
dividend
14. The relation of among polynomial f(x), Quotient q(x), Divisor d(x) and Remainder R(x) is ..............
f(x) = q(x) +d(x) - r(x)
f(x) = d(x) × q(x) + r(x)
f(x) = d(x) + q(x) + r(x)
f(x) = d(x) × q(x) × r(x)
15. In a polynomial f(x), f(b/a) = 0, what will be its one of the factors?
x-b/a
x_a/b
x+b/a
a-x/b
16. If polynomial f(x) = 4x3 - 3x2 3x - k is divided by (x-2), the remainder is 12. find the value of k.
15
16
14
17
17. What is the sixth AM of AS whose firs term 'a' and common difference is 'd'?
a+5d
a+6d
a+7d
a+4d
18. What is the sum of first n odd natural numbers?
2n
n(n+1)/2
n2
n2/2
19. If eighth term of an AP is 44 and the common difference is 4. Find the seventh term.
42
48
40
45
20. In the formula d = (b-a)/n+1 what does n represents?
No. of means
No. of terms
No. of AP
No. of AS
21. Find the sum of 2+4+........................ 10 terms.
420
320
520
620
22. If 2, k and 14 are in AP, Find the value of k.
9
12
8
10
23. What is the geometric mean between two positive numbers a and b?
√ab
∛ab
(a+b)2
a/b
24. What is the common ratio of the sequence-1-3-9-................?
-2
-3
-4
3
25. If m+2, m+8 and 17+m are in geometric sequence, find the value of m.
12
15
10
20
26. What is the equation of boundary line of the inequality ax + by ≤ c ?
ax+by+c=0
ax+by = c
ax-by = c
by-ax=c
27. In which side from the line y=5 is the solution region of y≤5 lie?
Upward
Left side
Right side
Downwarde
28. Does (0,0) lie on the solution set of inequality 3x+2y≥8 ?
Yes
No
X-axis
Y-axis
29. The smooth curve obtained by the graph of a quadratic equation is called ...........
Circle
Hyperbola
Elipse
Parabola
30. What is the coordinates of vertex of parabola whose equation is y = ax2 ?
(0,1)
(1,0)
(0,0)
(1,1)
31. Find the co-ordinates of the vertex of a quadratic function y = x2 + 2x - 3 ?
(1,1)
(1,-4)
(-1,-4)
(-4,-1)
32. If the graph of a function can be drawn without lifting the pencil from the paper then it is called .............................
Limit
Discontinuity
Function
Continuity
33. Which one of the following is continuity?
Sound from drum beating
Growth of plant
Number line of natural numbers
Number line of integers
34. Write the interval notation of -3≤x≤3.
(-3,3]
(-3,3)
[-3,3]
[-3,3)
35. lim which limit indicates?
x→a-
Right hand limit
Left hand limit
No limit
Both
36. What do the (2,3] interval denote?
Right open
Left open
Open
Closed
37. Which one is correct according to graph as shown in figure?
y = cosx
y = tanx
y= sinx
y= secx
38. If left hand limit= right hand limit = functional value then function is .............
Discontinuity
Continuity
Both
None
39. If matrix Am×n and matrix Bn×p then the order of product of A and B is ...........
p×m
p×n
m×n
m×p
40. Under what condition, the system of simultaneous equation has no unique solution?
Value of determinant = 1
Value of determinant = 0
Value of determinant = -1
Value of determinant is less than 1
41. If matrix A is a singular matrix, what is the determinant of A?
1
-1
0
None of above
42. Which type of matrix is shown in alongside?
Identity Matrix
Zero Matrix
Null Matrix
Singular Matrid
43. What is the determinant value of 2×2 identity matrix?
1
-1
2
0
44. If matrix A = (m) then what is the value of ∣A∣ ?
m
1
0
A
45. What is the determinant of a 2×2 Null matrix?
0
1
-1
2
46. If AB=BA=I then what types of matrices are A and B?
Identity Matrix
Square Matrix
Inverse Matrix
Column Matrix
47. What type of equations can be solved by using Cramer's rule?
Quadratic equation
Simultaneous linear equation
Cubic equation
None of above
48. What should be the formula to calculate x using Cramer's rule when D, Dx and dy are given?
D/Dx
Dx/D
D/Dy
Dx/Dy
49. What value of D makes the solution of equations undefined according to the Cramer's rule?
1
-1
∞
0
50. Find the value of D using Cramer's rule from the equations : 2x+3y = 5 and x+y = 2.
2
1
-1
-2
51. According to Cramer's rule, D=2, Dx = 8 and Dy = 6 then find the value of y.
3
6
4
1/3
52. Find the values of D using Cramer's rule from the equations 3x+2y=1 and 7x+5y=4.
3
2
1
-1
53. In the equations 3x+y=7 and x+2y=4, according to the Cramer's rule the value of D si 5, what is the value of x?
x=2
x =3
x = -1
x= 1
54. In the grouped data, if the first quartile is 20 and the third quartile is 60, find the quartile deviation.
30
20
40
10
55. In a continuous series, the first quartile is 45 and the quartile deviation is 8.5, what is the third quartile?
55
40
52
62
56. By which methods, the standard deviation can be calculated?
Direct Method
Actual Mean Method
Assumed Mean Method
All of the above
57. Mean Deviation can be calculate by using ..........................
Standard Deviation
Mode
Mean and Median
Mode
58. What is the maximum value of y = cosx?
0
1
-1
∞
59. What is the y-intercept of y = tanx?
∞
-1
0
1
60. If f(x) = 2x + 1, then, find ff(2).
10
11
12
15
61. What is the degree of x3 + 4x2 - 9?
2
5
3
0
62. If x+1 is a factor of 2x3 - kx2 -8x + 5, find the value of k.
11
12
13
14
63. What is the difference of degree of dividend and quotient in synthetic division method?
0
1
2
-1
64. What is the degree of divisor in synthetic division method?
2
-1
0
1
65. What is the meaning of 'a' in the formula tn = a+(n-1)d?
Last term
Third term
First term
First mean
66. What is the tenth term of GS whose ninth term is 27 and common ratio is 3?
9
72
27
81
67. Find sum of 1+3+9+ ....................7 terms
1093
1024
1048
1092
68. Which quadrants do the inequality y≥0 represent in a graph?
I and III
II and III
I and II
III and IV
69. The vertex of parabola is ..................................................
(1,1)
(0,1)
(0,0)
X-axis
70. From the graph of alongside, which is the correct value of x?
-1 and 7
-1 and -3
3 and -1
-1 and 3
71. What is the first natural number?
0
1
10
11
72. Under what condition, the inverse of a matrix is possible?
Value of det. = 0
Value of det. = ∞
Value of det. = 1
Value of det. = Non zero
73. What is the value of 'm' in the equation y = mx + 3 to make it a constant function?
0
1
-1
3
74. Determine the value of 'n' in the equation 2n - 5 = 7 to solve a linear equation.
6
7
8
9
75. What is the determinant of a 3x3 Null matrix?
0
1
-1
3
76. What is the value of sin(π/2)?
1
0
-1
2
77. If f(x) = 3x - 11, find f-1 (4).
4
5
6
7
78. If the sum of two numbers is 15 and their difference is 3, what are the two numbers?
6, 9
7, 8
5, 10
4, 11
79. If matrix A is a singular matrix, what is the determinant of AT?
1
-1
0
None of above
80. What is the sum of the first n even natural numbers?
2n
n(n+1)
n2
n2/2
