1. NUMBER THEORY
1.1 Sequences
1. In a sequence if an = 5n – 4, then a5 is ______________
(a) 29 (b) 21 (c) 6 (d) 14
2. If an = (-1 )n n, then a5 is __________
(a) 5 (b) 25 (c) – 5 (d) – 25
3. The second term of a sequence whose nth term is (-1)n 2n is _________
(a) 0 (b) 4 (c) – 1 (d) – 2
1.2 Arithmetic Progression (A.P)
4. If the nth term of an A.P. is 7n – 3, then the 4th term is _________
(a) 4 (b) 25 (c) 11 (d) 28
5. In an A.P., the first term is 18, common difference is – 4. Then the 5th term is _________
(a) – 2 (b) 2 (c) 34 (d) – 34
6. The nth term of a sequence is 7n – 3. Its common difference is _________
(a) 7 (b) 4 (c) 7n (d) – 7
7. If an A.P, if tn = 7n – 3, then the common difference is __________
(a) 3 (b) 4 (c) 7 (d) 10
8. The common difference of an A.P., tn = 4n + 5 is ___________
(a) 5 (b) 4n (c) 4 (d) 5n
9. The common difference of the A.P. 3, 1, -1, - 3 …………. is _________
(a) 2 (b) – 2 (c) 1/3 (d) 3
10. The common difference of the A.P. 1, 7, 13 …………. is _________
(a) 6 (b) – 6 (c) 1 (d) 13
11. The common difference of the A.P. 5 + 9 + 13 + 17 + …….. is
(a) 3 (b) 2 (c) 5 (d) 4
1.3 Geometric Progression (G.P)
12. The common ratio of the G.P. 3, 6, 12, 24 …………. is _________
(a) 2 (b) – 2 (c) 1/2 (d) – 1/2
13. The common ratio of the G.P. 64, 16, 4 …………. is _________
(a) 4 (b) – 4 (c) 1/4 (d) – 1/4
14. The common ratio of the G.P. 2, 6, 18, …………. is _________
(a) 4 (b) 3 (c) – 3 (d) 12
15. The common ratio of a G.P., 3, 9, 27, ……….. is __________
(a) 4 (b) 3 (c) 27 (d) 9
16. The 8th term of the G.P., 3, 6, 12, ……… is ___________
(a) – 384 (b) 128 (c) – 128 (d) 384
1.4 Sum to n terms of an A.P
17. The number of terms in the series 3, 6, 9,..….. 51 is __________
(a) 18 (b) 32 (c) 19 (d) 17
1.5 Sum to n terms of a G.P
1.6 Summation of some special series
18. The value of 1 + 2 + 3 + ……….. + 20 is __________
(a) 210 (b) 420 (c) 400 (d) 230
19. The sum of the first 10 odd numbers _________
(a) 10 (b) 55 (c) 100 (d) 60
20. The sum of the first 20 odd numbers _________
(a) 144 (b) 147 (c) 400 (d) 168
21. The sum of 1 + 3 + 5 + ……….. 20 terms is __________
(a) 210 (b) 400 (c) – 400 (d) 250
22. The sum of 1 + 3 + 5 + ……. 100 terms is _________
(a) 10000 (b) 450 (c) 5050 (d) 1000
23. The sum of 1 + 3 + 5 + …….. + 27 is _________
(a) 272 (b) 142 (c) 132 (d) 262
24. The sum of the first n natural numbers is 10. The sum of their cubes is________
(a) 20 (b) 100 (c) 1000 (d) 30
25. If the sum of 1 + 2 + 3 + ……….. + 10 is 55, then the sum of 13 + 23 + 33 + ……….. + 103
is ________
(a) 552 (b) 553 (c) 3024 (d) 3026
26. The value of 12 + 22 + 32 + ……….. + 102 is ________
(a) 395 (b) 390 (c) 385 (d) 360
2. MENSURATION
1. If the radius and height of a cylinder are a cm and b cm respectively, then its curved
surface area is_______
(a) 2rhcm2 (b) 2ab cm2 (c) a2bcm2 (d) ab cm2
2. The total surface area of a right circular cylinder of radius r and height h is_______
(a) r (h + r) sq. units (b) 2r (h – r) sq. units
(c) 2r (h + r) sq. units (d) r (h – r) sq. units
3. The radius and the height of a cylinder are equal to those of a cone. If the volume of the
cone is 20cm3, then the volume of the cylinder is_________
(a) 400cm3 (b) 10cm3 (c) 60cm3 (d) 40cm3
4. Curved surface area of a hollow cylinder is_______
(a) 2Rh (b) 2rh (c) rl (d) 2h(R + r)
5. Volume of a hollow cylinder is_______
(a) (R2 – r2) (b) 2h(R + r) (c) r2h (d) h (R2 – r2)
6. The volume of a solid hollow cylinder of external radius R and internal radius r is______
(a) 2RH(R + r) (b) h (R2 + r2) (c) 2h(R + r) (d) h(R + r)(R - r)
7. In a cone l = 13 cm, h = 5 cm, then r = ?
(a) 13 cm (b) 14 cm (c) 12 cm (d) 11 cm
8. For a right circular cone of radius r, height h and slant height, the total surface area is__
(a) 2r (l + r) sq. units (b) r (l + r) sq. units
(c) r (h + r) sq. units (d) 2r (h + r) sq. units
9. The formula to find the total surface area of a hemisphere is_________
(a) 2 r2 sq. units (b) 3 r2 sq. units (c) 4 r2 sq. units (d) r2 sq. units
10. Volume of a hemisphere of radius r cm is_________
(a) 4/3 r3 cubic units (b) 2/3 r3 cubic units
(c) 1/3 r3 cubic units (d) 1/3 r2h cubic units
11. The surface area of a sphere is 100 cm2. Its radius is__________
(a) 25cm (b) 100cm (c) 5cm (d) 10cm
12. The total surface area of a sphere is 144 cm2. Its radius is__________
(a) 36cm (b) 6cm2 (c) 24cm (d) 6cm
13. Total surface area of a sphere of radius 1cm is__________
(a) 4 cm3 (b) 4 r2 cm2 (c) 4 cm2 (d) 3 r2 cm2
14. The volume of the sphere r units is_________
(a) 2/3 r3 cu. units (b) 4/3 r2 cu. units (c) 4/3 r3 cu. units (d) 4 r3 cu. Units
3. SETS AND FUNCTIONS
3.1 SETS
1. A A = (a) { } (b) A (c) (d) A'
2. A A’ = (a) A (b) { } (c) A' (d) ξ
3. A = {p, q, r, s} then A A is (a) {p, q, r, s} (b) 4 (c) {4} (d) A
4. If ξ = {1,2,3,4,5,6}, A = {1,3,5}, then n(A)' is _____
(a) 3 (b) 6 (c) 2 (d) 0
5. If A B = {1,2,3,5}, A B = {2} and A = {1,2,3} find the set B is_____
(a) {2, 5} (b) {1, 2, 3, 5} (c) {2} (d) { }
6. If A B = { a,b,d,g,h }, A B = {a,b,d} and A = { a,b,d,g} find the set B is_____
(a) { a,b,d,h } (b) { a,b,d,g } (c) { a,b,h } (d) { d,g,h }
7. A = {p, r, s}, B = {l, m, o, p, s}, then n (A B) is _____
(a)2 (b) 7 (c) 6 (d) None
8. A = {-2, 3, 5, 7}, B = {3, 7, 11}, then n (A B) is______
(a)7 (b) 5 (c) 1 (d) None
9. If A = {1,2, 3, 6, 9}, B = {2, 4, 6, 8}, then the value of n (A B) is______
(a) {2, 6} (b) {2} (c) 2 (d) 4
10. If A = { a, b, c, d, e }, B = { b, d, f }, then A – B is_____
(a) { a, b, c, d, e } (b) { a, c, e, f } (c) { b, d } (d) { a, c, e }
11. A = { 3, 4, 5, 6 }, B = { 5, 7, 8 }, then A – B is________
(a) {5} (b) {3, 4, 6} (c) {3, 4, 8} (d) {7, 8}
12. A = { 6, 9, 13, 17 }, B = { 5, 9, 17, 18 }, then A – B is________
(a) {6, 13} (b) {5, 18} (c) {5, 6, 9, 13, 17, 18} (d) {9, 17}
13. A = {10, 11, 12, 16, 18}, B = {11, 15, 16, 20 }, then A – B is________
(a) {11, 16} (b) {10, 12, 18} (c) {15, 16, 20} (d) {11}
14. If A = { a, b, c }, B = { c, d, e, f }, then n(A – B) is_____
(a) 2 (b) 3 (c) 4 (d) 7
15. A = {r, s}, (B C) = {p, q, r, s}, then A (B C) = _______
(a) {r, s} (b) {p, q} (c) {p, r, s} (d) {p, q, r, s}
16. The value of A (B C) is ______
(a) A (B C) (b) (A B) (A C)
(c) A (B C) (d) (A B) (A C)
17. A – ( B C ) = ___________
(a) ( A – B ) ( A – C ) (b) ( A – B ) ( A – C )
(c) ( A – B ) C (d) ( A – B ) C
18. (A B)' = (a) A' B' (b) (A B)' (c) A' B' (d) A B'
19. A' B' = (a) A' B' (b) A' B (c) (A B)' (d) A B'
3.2 RELATIONS
20. If P = { 2, 3, 4, 8, 9 }, then the set of ordered pairs representing the relation is a multiple
of 2 on P is _________
(a) {(2,2),(4,2),(8,2),(4,8)} (b) {(2,2),(4,2),(8,2) }
(c) {(2,2),(2,4),(2,8) } (d) {(8,4),(2,8),(2,4),(2,2)}
3.3 FUNCTIONS
21. If f (a) = a for all a A then f is ________ of A.
(a) into function (b) identity function
(c) constant function (d) many to one function
22. If f = {(1,1),(8,2),(27,3),(64,4)}, then the domain of f is _______
(a){ 1, 2, 3, 4 } (b) { 1, 3 } (c) { 1, 8, 27, 64 } (d) { 2, 4 }
23. If R= {(a,r),(a,s),(b,r),(b,s)}, then the domain is _______
(a){ a, b } (b) { b, s } (c) { r, s } (d) { a, r }
24. R = {( -1, 1 ), ( 0, 0 ), ( 2, 4 )}.The domain of R is__________
(a) { -1, 0, 2 } (b) { 1, 0, 4 } (c) { -1, 0, 4 } (d) { 1, 0, 2 }
25. f = { (0, -1), (3, 2), (5, 3), (7, 2) } in this function the image of 5 is___________
(a) -1 (b) 2 (c) 3 (d) 5
26. f = { (0, -1), (3, 2), (5, 3), (7, 2) } in this function the image of 0 is __________
(a) -1 (b) 2 (c) 3 (d) 5
27. The pre – image of 2 under the function f = { (0, -1), (3, 2), (5, 3), (7, 2) } is________
(a) 3 (b) 7 (c) 3, 7 (d) 5, 7
28. Find the pre – image of 2 under the function f = { (0, -1), (3, 2), (5, 3), (6, 1) } is________
(a) 0 (b) 5 (c) 6 (d) 3
29. The pre – image of 4 under the function f = { (-2, 4), (-1, 0), (0, -1), (1, 0) } is________
(a) -1 (b) 0 (c) 1 (d) -2
30. If f (x) = 3x + 1, then the pre – image of 7 is ______
(a) 4 (b) 2 (c) 22 (d) 7
31. If f (x) = x + 5, then the value of f (-3) is ______
(a) 2 (b) -2 (c) -15 (d) 15
32. If f (x) = 4x2, then the range of f (-2) is ______
(a) -8 (b) -16 (c) 16 (d) 64
33. If f (x) = 2x2 - 1, then the range of f (-2) is ______
(a) 3 (b) – 5 (c) 0 (d) 7
34. If f (x) = x2 – x + 7, then the value of f (-3) is ______
(a) 17 (b) 19 (c) 0 (d) 4
35. If f (x) = 4x/(x + 1) , then f (3) is_________
(a) -3 (b) 3 (c) 12 (d) -12
36. If f (x) = (〖(2x)〗^2+ 5)/3, then the value of f (2) is
(a) 13/3 (b) 3 (c) 23 (d) 7
37. If f (x) = 4x/(x + 1) , then f (3) + f (-3) is ________
(a) 0 (b) 9 (c) -3 (d) -6
38. If f (x) = x + 5, g (x) = x2, then f o g (x) = _______
(a) (x + 5)2 (b) x2 + 5 (c) x2 + x (d) x2 - 5
39. If f (x) = x - 5, g (x) = x2, then f o g = _______
(a) (x - 5)2 (b) x2 (c) 3 - 2x2 (d) x2 - 5
40. If f(x) = 2x, g(x) = 1/2 x, then f o g (x) = ____________
(a) x2 (b) 2x2 (c) x (d) 2x
4. ALGEBRA
4.1 Simultaneous Equations
1. x + y = 3, y + z = -5, x + z = 2, then x + y + z = ________
(a) 1 (b) 0 (c) 2 (d) -1
4.2 Polynomial
2. If (ax + b) divides p(x), then remainder is ______
(a) p (-a) (b) p (a) (c) p (-b/a) (d) p (b/a)
3. The value of p (a), If (x - a) is a factor of p(x) is ______
(a) a (b) x (c) 0 (d) 7
4. When x3 + x2 + 5 is divided by (x – 1) the remainder is ______
(a) 10 (b) 0 (c) 7 (d) -7
5. When x3 + x2 – 3x + 5 is divided by (x – 1) the remainder is ______
(a) – 4 (b) 10 (c) – 10 (d) 4
6. When x3 – x2 – 1 is divided by x – 1, then the remainder is _________
(a) -1 (b) -3 (c) 1 (d) 3
7. When x^3+x^2-2x+7 is divided by (x + 4), the remainder is __________
(a) -33 (b) 10 (c) 33 (d) 35
8. If x – 3 is a factor of x2 + mx – 18, then the value of m is______
(a) 3 (b) 6 (c) 2 (d) 4
9. One of the factor of x3 + 2x – 3 is ________
(a) x + 1 (b) x – 1 (c) x – 2 (d) x + 3
4.3 GCD and LCM
10. The G.C.D of a m, a m + 1, a m + 2 is ______
(a)a (b) m (c) a m (d) a m + 2
11. The G.C.D of a 3, a 5 and a 7 is ______
(a) a 3 (b) a 5 (c) a 7 (d) a 15
12. The G.C.D of m 6, m 12, m 18 is ______
(a) m 6 (b) m 18 (c) m 12 (d) m 36
13. The G.C.D of p 8, p 7, p 12 is ______
(a) p 8 (b) p 7 (c) p 12 (d) p 27
14. The G.C.D of x 4, x 6 and x 10 is ______
(a) x 10 (b) x 6 (c) x 16 (d) x 4
15. The G.C.D of x 5, x 7 and x 10 is ______
(a) x 5 (b) x 10 (c) x 22 (d) x 7
16. The G.C.D of 3a2b and 15ab2
(a) 3ab (b) 15a2b2 (c) 3a2b2 (d) 3ab2
17. The G.C.D of 3a4, 9a6, 12a7 is
(a) a4 (b) 3a7 (c) 3a4 (d) 12a4
18. The L.C.M of x 6, x 10 and x 7 is ______
(a) x 6 (b) x 10 (c) x 7 (d) x 23
19. The L.C.M of 15a8, 75a6 is________
(a)75a5 (b) 15a8 (c) 15a5 (d) 75a8
20. The L.C.M of a3 – b3 and a – b is _________
(a) a – b (b) a3 – b3 (c) a2 – ab + b2 (d) a2 – b2
4.4 Rational Expressions
21. The value of x/(x + y) + y/(x + y) is______
(a) 0 (b) -1 (c) 1 (d) 2
22. x/(2- x) - 2/(2 - x) is________
(a) 1 (b) -1 (c) x – 2 (d) 2x
23. x/(5- x) - 5/(5 - x) is________
(a) 1 (b) -1 (c) x – 5 (d) 5x
24. Simplify: (a^(2 ) b)/(b^(2 ) c) x (b^2 c)/(c^2 a) (a^2 b)/(c^2 a)
(a) 〖ab〗^2/c^2 (b) 1 (c)(a^2 b^2)/c^2 (d) a^2 b^2 c
4.5 Square root
25. √(0.0144 ) = ______
(a) 12 (b) 1.2 (c) 0.12 (d) 0.012
26. The value of √(81a^4 b^16 ) = ______
(a) 9ab (b) 9a2b4 (c) 9a2b8 (d) 9 (ab)8
27. The square root of 36a8 is ______
(a) 6a16 (b) 18a8 (c) 6a4 (d) a4
28. The square root of 16x 2 y 4 z 16 is______
(a) 4x y 2 z 4 (b) 8x y 2 z 8 (c) 4x y 2 z 8 (d) 8x y 2 z 4
29. Square root of 16x2y4z8 is _______
(a) 8xy2z4 (b) 4xy2z4 (c) 4x2y2z2 (d) 8x2y2z
30. Square root of 9x2 + 30x + 25 is ______
(a) 3x + 5 (b) 3x – 5 (c) 9x + 5 (d) 9x – 5
4.6 Quadratic Equations
31. The roots of the quadratic equation 3x2 – 75 = 0 are ______
(a) 3 (b) 5 (c) 0 (d) 25
32. The term that has to be added to x2 + 16x to make a perfect square is_______
(a) 16 (b) 64 (c) 8 (d) 36
33. The solution set (x + 1) (x – 2) = 0 is
(a) {1, -2} (b) {-1, -2} (c) {1, 2} (d) {-1, 2}
34. Solutions for (x – 5) (x + 3) = 0
(a) ( -5, 3 ) (b) ( -5, -3 ) (c) ( 5, 3 ) (d) ( 5, -3 )
35. The solution set of (x – 5) (x + 2) = 0 is______
(a) {-5, 2} (b) {5, -2} (c) {5, 2} (d) {-5, -2}
36. If the roots are imaginary, then the value of b2 – 4ac is _______
(a) 0 (b) < 9 =" 0" 4 =" 0">5. APPLIED MATHEMATICS
5.1 Linear Programming
1. Which is linear equation?
(a) 2x + 3y = 5 (b) 2x + 3y 5 (c) 2x + 3y <>5.2 Network Programming
15. The path that takes longest duration is_______
(a) solution path (b) project path (c) critical path (d) correct path
6. GEOMETRY
6.1 Locus
6.2 Circles
1. The number of circles passing through three non- collinear points is_________
(a) 1 (b) 2 (c) 0 (d) 4
2. Two circles of diameters 12 cm and 10 cm touch each other internally. Then the distance
between their centres is
(a) 2 cm (b) 22 cm (c) 1 cm (d) 11 cm
6.3 Angles in a Circle
3. The angle in a semicircle is ________
(a) Obtuse angle (b) Acute angle (c) Right angle (d) Straight angle
4. The angle in a semi – circle is_________
(a) 0 (b) 45 (c) 135 (d) 90
5. The angle in the major segment is ________
(a) Obtuse angle (b) Acute angle (c) Right angle (d) Straight angle
6. Angle in a minor segment is_________
(a) an obtuse angle (b) an acute angle (c) a right angle (d) a reflex angle
7. In the figure the value of x is __________
(a) 120 (b) 60 (c) 180 (d) 240
8. In the figure the value of x is __________
(a) 40 (b) 50 (c) 180 (d) 90
9. In the figure, the value of x is __________
(a) 150 (b) 60 (c) 90 (d) 30
10. If one angle of a cyclic quadrilateral is 70, then the angle opposite to it is ___________
(a) 20 (b) 110 (c) 140 (d) 160
11. If one angle of a cyclic quadrilateral is 65, then the angle opposite to it is ___________
(a) 50 (b) 40 (c) 130 (d) 115
12. In a cyclic quadrilateral ABCD, mA = 5x, mC = 4x, then the value of x is _________
(a) 12 (b) 20 (c) 48 (d) 36
13. In a cyclic quadrilateral ABCD, mA = 72, then mC is _________
(a) 108 (b) 144 (c) 72 (d) 180
14. In a cyclic quadrilateral the sum of the opposite angle is 5x, find x _________
(a) 10 (b) 100 (c) 36 (d) 90
6.4 Circles and Tangents
15. Parallelogram inscribed in a circle is a ________
(a) rectangle (b) square (c) trapezium (d) quadrilateral
16. The tangents at the ends of a diameter are _________
(a) perpendicular (b) parallel (c) equal (d) none
17. Number of tangents that can be drawn at any point on the circle is________
(a) 2 (b) 3 (c) 4 (d) 1
18. The number of tangents that can be drawn from a point outside the circle is________
(a) 1 (b) 2 (c) 4 (d) 0
19. The length of the tangent to a circle of radius 6cm from a point at a distance of 10cm
from the centre of the circle________
(a) 4cm (b) 8cm (c) 16cm (d) 3cm
6.5 Similar Triangle
20. If a line is drawn parallel to one side of a triangle the other two sides are divided in_____
(a) same (b) the same ratio (c) parallel (d) perpendicular
21. The ratio of corresponding sides of two similar triangles is 2 : 5. The ratio of their areas
is _________
(a) 2 : 5 (b) 5 : 2 (c) 4 : 25 (d) 25 : 4
22. If the ratio of the sides of two similar triangles is 3 : 4, then the ratio of their areas
is _________
(a) 3 : 4 (b) 4 : 3 (c) 9 : 16 (d) 27 : 64
23. In a triangle ABC, DE BC, if AD = 3cm, DB = 5cm, AE = 6cm, then EC is_______
(a) 10 cm (b) 8 cm (c) 2 cm (d) 3.6 cm
24. Which are the sides of a right triangle?
(a) 7, 8, 9 (b) 10, 11, 12 (c) 3, 4, 5 (d) 6, 6, 7
25. If 7 and 24 are the two sides of a right angled triangle, then the hypotenuse is ______
(a) 25 (b) 31 (c) 168 (d) 17
26. In the figure, BD = 4, DC = 9, the length of AD is _________
(a) 36 (b) 6 (c) 13 (d) 5
27. The length of the diagonal of a square is 4√2 m, then the length of the side is_________
(a) 4 m (b) 8√2 m (c) √2 m (d) 8 m
28. The length of the side of a square whose diagonal 5√2 is ________
(a) 5 (b) 2√2 (c) 3√3 (d) 3√5
7. ANALYTICAL GEOMETRY
7.1 Ratio Formula
1. The midpoint of the line segment joining the origin and (4, 8) is________
(a) (0, 4) (b) (0, 8) (c) (2, 4) (d) (4, 2)
2. The midpoint of the line segment joining the origin and (2, -4) is________
(a) (2, 0) (b) (0, -4) (c) (1, -2) (d) (0, 0)
3. The midpoint of the line segment, joining the points (3, 5) and (1, 3) is________
(a) (4, 2) (b) (2, 4) (c) (1, 2) (d) (2, 1)
4. The midpoint of the line segment, joining the points (8, 2) and (4, 6) is________
(a) (2, 2) (b) (6, 4) (c) (4, 6) (d) (2, -2)
5. The midpoint of the line segment, joining the points (0, 4) and (4, 2) is________
(a) (0, 4) (b) (4, 2) (c) (4, 6) (d) (2, 3)
6. The midpoint of the line segment, joining the points (1, -3) and (-5, 7) is________
(a) (-3, -5) (b) (-2, 2) (c) (3, 5) (d) (-4, 4)
7. The co-ordinates of the midpoint of the line segment joining the points A (-3, 2) and
B (7, 8) is________
(a) (5, 5) (b) (-5, 5) (c) (-2, 5) (d) (2, 5)
8. The midpoint of the line segment PQ is (5, 1). If P is (8, 4), then point Q is _______
(a) (2, -2) (b) (3, 3) (c) (-2, 2) (d) (-3, -3)
9. The centre of a circle is (-6, 4). A diameter of the circle has its one end at the origin then
the other end is _________
(a) (-12, 8) (b) (6, -4) (c) (12, -8) (d) (-6, 4)
10. The centroid of the triangle whose vertices are the points (-2, 3), (5, -5) and (6, 2)
is________
(a) (0, 3) (b) (-3, 0) (c) (3, 0) (d) (0, -3)
7.2 Area of a Triangle
11. If the three vertices of a triangle are collinear, then the area of the triangle is______
(a) 1 (b) 0 (c) 2 (d) 4
12. The area of the triangle whose vertices are (0, 0), (1, 0) and (0, 1) is___________
(a) 1 sq. unit (b) 1/2 sq. unit (c) 2 sq. units (d) 0 sq. units
13. Area of the triangle whose vertices are (0, 0), (2, 0) and (0, 2) is _______
(a) 1 sq. unit (b) 1/2 sq. unit (c) 2 sq. units (d) 0 sq. unit
14. The area of the triangle whose vertices are (-1, 1), (1, -1) and (0, 0) is _______
(a) -2 (b) 2 (c) 1 (d) 0
7.3 Straight Lines
15. The equation of X – axis is _______
(a) x = 0 (b) y = 0 (c) x + y = 0 (d) x - y = 0
16. The equation of straight line parallel to X – axis_______
(a) x = 0 (b) x = a (c) y = a (d) y = 0
17. The equation of straight line parallel to x – axis and passing through (3, 2) is_______
(a) y – 2 = 0 (b) x – 2 = 0 (c) x + 3 = 0 (d) y + 2 = 0
18. The equation of straight line passing through (2, -3) and parallel to x – axis is_______
(a) x = 3 (b) x = -3 (c) y = -3 (d) y = 3
19. The equation of straight line parallel to x – axis and which passes through the point
(2, -3) is_______
(a) y – 3 = 0 (b) y + 3 = 0 (c) x + 3 = 0 (d) x – 3 = 0
20. The equation of line, which is parallel to x – axis and passes through the point
(3, -2) is_______
(a) y = 0 (b) y = -2 (c) x = 0 (d) x = 3
21. Equation of a line, which is parallel to y – axis and passes through the point (5, 4)
is_______
(a) y = 0 (b) x = 0 (c) x = 5 (d) y = 4
22. The equation of line parallel to y – axis and passes through the point (3, 2) is_______
(a) y – 2 = 0 (b) x – 2 = 0 (c) y – 3 = 0 (d) x – 3 = 0
23. The equation of a straight line whose slope is 5 and which passes through the origin
is__
(a) 5y = -x (b) 5y = x (c) y = 5x (d) y = -5x
24. Slope of 2y = 3x is_______
(a) 3 (b) 2 (c) 3/2 (d) -3
25. Slope of the line 2x = y
(a) -2 (b) 1 (c) 2 (d) 1/2
26. The slope of the line y = mx + c is_____________
(a) m (b) c (c) m/c (d) c/4
27. The slope of y = 5x – 5 is___________
(a) 5 (b) -5 (c) 1 (d) -1
28. The slope of the straight line 3x + 2y = 4 is___________
(a) 1/2 (b) 4/3 (c) (-3)/2 (d) 3/2
29. The slope of a line which is parallel to the line 2x – 3y + 5 = 0 is___________
(a) - 2/3 (b) 2/3 (c) 3/2 (d) - 3/2
30. The slope of the straight line 3x + 4y + 10 = 0 is___________
(a) (-4)/3 (b) 4/3 (c) 3/4 (d) (-3)/4
31. The slope of the line 3x + 2y = 5 is________
(a) 3/2 (b) - 3/2 (c) 2/3 (d) - 2/3
32. If the straight line 7x – 5y = k passes through the point (1, 1) then the value of k is_____
(a) 2 (b) -2 (c) 1 (d) -1
33. If the straight line 4x – 3y = k passes through the point (1, 1) then the value of k is_____
(a) 2 (b) -2 (c) 1 (d) -1
34. Equation of a straight line with x and y intercepts is __________
(a) x/a + y/b = 1 (b) x/a + y/b = -1 (c) x/a - y/b = 1 (d) a/x + b/y = 1
35. If the two straight lines are perpendicular, then_________
(a) m1 x m2 = -1 (b) m1 x m2 = 1 (c) m1 = m2 (d) m1 = -m2
7.4 Some Properties of Straight Lines
36. The point of intersection of the lines x + y = 8 and x – y = 2 is _________
(a) (-5, -3) (b) (5, -3) (c) (5, 3) (d) (3, 5)
8. TRIGONOMETRY
8.1 Use of Trigonometric Tables
1. The first mathematician to use algebra in trigonometry was ________
(a) Brahmagupta (b) Ptolemy (c) Bhaskaracharya (d) Ramanujam
2. If sin θ = 0.5 then the value of θ is_______
(a) 60 (b) 30 (c) 90 (d) 45
3. If sin θ = 1/√2 , then the value of θ is _________
(a) 0 (b) 30 (c) 60 (d) 45
4. If sin θ = √3/2 , then the value of θ is _________
(a) 60 (b) 30 (c) 45 (d) 90
5. If sin θ = cos θ, then the value of θ is__________
(a) 0 (b) 45 (c) 30 (d) 90
6. If sin θ = tan θ, then the value of θ is__________
(a) 45 (b) 90 (c) 1 (d) 0
7. If sin θ = cos θ, then the value of tan θ is__________
(a) 0 (b) 1/2 (c) √3 (d) 1
8. If the value of cos θ = 1/√2 , then the value of tan θ is _________
(a) 0 (b) 2 (c) 1 (d) 3
9. If tan θ =√3 , then the value of θ is _________
(a) 30 (b) 45 (c) 60 (d) 90
10. 1 – tan245 = ____________
(a) 1 (b) 0 (c) 2/3 (d) 2
11. If tan A = 8/15 , Sin A =
(a) 7/15 (b) 8/15 (c) 8/17 (d) 7/8
8.2 Heights and Distances
12. The angle of depression of a stone from the top of a building is 30. The angle of
elevation of the top of the building from the stone is__________
(a) 15 (b) 30 (c) 60 (d) 0
13. The elevation of the sun, when the length of the shadow of a plane pole is √3 times the
height of the pole is __________
(a) 60 (b) 45 (c) 30 (d) 90
14. The angle of elevation of the top of a tower at a distance of 60 m. is found to be 45°.
The height of the tower is___________
(a) 60 m (b) 20 √3 m (c) 45 m (d) 60 √3 m
15. The length of the shadow of a wall of 5m height, when the sun is in 45° elevation is
(a) 10 m (b) 25 m (c) 5 m (d) 15 m
10. STATISTICS
10.1 Dispersion
1. The range of the data 27, 35, 25, 45, 67 is__________
(a) 40 (b) 42 (c) 10 (d) 89
2. The range of the data 36, 27, 28, 34, 59, 39 is__________
(a) 3 (b) 32 (c) 20 (d) 86
3. The largest value of the data is 98. If the range of the data is 73, then the smallest value
is __________
(a) 25 (b) 171 (c) 95 (d) 28
4. The largest value of the data is 25. If the range of the data is 15, then the smallest value
is __________
(a) 10 (b) -10 (c) 40 (d) -40
5. The largest value of the data is 89, If the range of the data is 37, then the smallest value
of the data is __________
(a) 126 (b) 37 (c) 89 (d) 52
6. The range and the smallest run of 10 tests of a person is 15. The highest run is_______
(a) 10 (b) 15 (c) 30 (d) 5
7. Standard deviation of the data 5, 10, 15, 20, 25 is 5 √2 . If we add 3 to each item, then
the new standard deviation is__________
(a) 3 + 5 √2 (b) 8 √2 (c) 5 √2 (d) 2√2
8. The standard deviation of 10 values is 4. If each value is increased by 3, then the
standard deviation of the new set of values is_____________
(a) 3 (b) 4 (c) 9 (d) 7
9. The standard deviation of a given data is 4. If each value is multiplied by 3, then the new
standard deviation is _________
(a) 4 (b) 12 (c) 7 (d) 1
10. The standard deviation of 10 values is 4. If each value is multiplied by 3, then the new
standard deviation is _________
(a) 4 (b) 12 (c) 7 (d) 1
11. The standard deviation of 8 values is 9. If each value is divided by 3, then the new
standard deviation is_________
(a) 3 (b) 1 (c) 9 (d) 8
12. The S.D is 25 and its variance is _________
(a) 5 (b) 600 (c) 50 (d) 625
13. If the variance of a data is 1.44, then the standard deviation is_________
(a) 1.2 (b) 12 (c) 72 (d) 44
14. If the variance of a data is 1.69, then the standard deviation is_________
(a) 1.3 (b) 13 (c) 3.38 (d) 69
15. The variance of 5 scores is 16. If each one of them is divided by 2, then the standard
deviation of the new scores is_______
(a) 4 (b) 8 (c) 2 (d) 16
16. The coefficient of variation of a series is 80% . The arithmetic mean is 20. Then the
standard deviation is ______________
(a) 160 (b) 16 (c) 1600 (d) 0.16
10.2 Probability
__
17. The sum of P(A) + P (A) is
(a) 1 (b) 1/2 (c) 1/4 (d) 3/4
18. When a coin is tossed the sample space is _______
(a) { T } (b) { H, T } (c) { } (d) { H }
19. The probability of getting head while tossing a coin is____________
(a) 1/2 (b) 1 (c) 2 (d) 1/3
20. Two coins are tossed simultaneously. The probability of getting two heads is________
(a) 2/4 (b) 1/4 (c) 3/4 (d) 1
21. When two coins are tossed at a time, the number of sample spaces is________
(a) 2 (b) 4 (c) 8 (d) 16
22. The probability of an event of getting more than two heads in are tossing two coins
simultaneously is________
(a) 1 (b) 0 (c) 1/4 (d) 3/4
23. When a fair die is rolled, then the probability of getting 3 on the face of the die is ______
(a) 1/2 (b) 1/4 (c) 1/6 (d) 1/3
24. A die is rolled once, the probability of getting an even number is _________
(a) 1/3 (b) 2/3 (c) 1/2 (d) 1/4
25. A die is rolled once. The probability of getting prime number is __________
(a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
26. When a coin and a die are thrown at a time, the numbers of elements in the sample
space is________
(a) 2 (b) 6 (c) 12 (d) 36
27. One card is drawn at random from a shuffled pack of 52 cards. Then the probability
that it will be a spade is_____
(a) 1/13 (b) 1/4 (c) 1/2 (d) 1/52
28. What is the probability of getting a red card when one card is drawn at random from a
shuffled pack of 52 cards?
(a) 1/2 (b) 2/3 (c) 3/4 (d) 1/3
ALL THE BEST @ All the best @ all the best @ All the best @ All the best @All the best
1.1 Sequences
1. In a sequence if an = 5n – 4, then a5 is ______________
(a) 29 (b) 21 (c) 6 (d) 14
2. If an = (-1 )n n, then a5 is __________
(a) 5 (b) 25 (c) – 5 (d) – 25
3. The second term of a sequence whose nth term is (-1)n 2n is _________
(a) 0 (b) 4 (c) – 1 (d) – 2
1.2 Arithmetic Progression (A.P)
4. If the nth term of an A.P. is 7n – 3, then the 4th term is _________
(a) 4 (b) 25 (c) 11 (d) 28
5. In an A.P., the first term is 18, common difference is – 4. Then the 5th term is _________
(a) – 2 (b) 2 (c) 34 (d) – 34
6. The nth term of a sequence is 7n – 3. Its common difference is _________
(a) 7 (b) 4 (c) 7n (d) – 7
7. If an A.P, if tn = 7n – 3, then the common difference is __________
(a) 3 (b) 4 (c) 7 (d) 10
8. The common difference of an A.P., tn = 4n + 5 is ___________
(a) 5 (b) 4n (c) 4 (d) 5n
9. The common difference of the A.P. 3, 1, -1, - 3 …………. is _________
(a) 2 (b) – 2 (c) 1/3 (d) 3
10. The common difference of the A.P. 1, 7, 13 …………. is _________
(a) 6 (b) – 6 (c) 1 (d) 13
11. The common difference of the A.P. 5 + 9 + 13 + 17 + …….. is
(a) 3 (b) 2 (c) 5 (d) 4
1.3 Geometric Progression (G.P)
12. The common ratio of the G.P. 3, 6, 12, 24 …………. is _________
(a) 2 (b) – 2 (c) 1/2 (d) – 1/2
13. The common ratio of the G.P. 64, 16, 4 …………. is _________
(a) 4 (b) – 4 (c) 1/4 (d) – 1/4
14. The common ratio of the G.P. 2, 6, 18, …………. is _________
(a) 4 (b) 3 (c) – 3 (d) 12
15. The common ratio of a G.P., 3, 9, 27, ……….. is __________
(a) 4 (b) 3 (c) 27 (d) 9
16. The 8th term of the G.P., 3, 6, 12, ……… is ___________
(a) – 384 (b) 128 (c) – 128 (d) 384
1.4 Sum to n terms of an A.P
17. The number of terms in the series 3, 6, 9,..….. 51 is __________
(a) 18 (b) 32 (c) 19 (d) 17
1.5 Sum to n terms of a G.P
1.6 Summation of some special series
18. The value of 1 + 2 + 3 + ……….. + 20 is __________
(a) 210 (b) 420 (c) 400 (d) 230
19. The sum of the first 10 odd numbers _________
(a) 10 (b) 55 (c) 100 (d) 60
20. The sum of the first 20 odd numbers _________
(a) 144 (b) 147 (c) 400 (d) 168
21. The sum of 1 + 3 + 5 + ……….. 20 terms is __________
(a) 210 (b) 400 (c) – 400 (d) 250
22. The sum of 1 + 3 + 5 + ……. 100 terms is _________
(a) 10000 (b) 450 (c) 5050 (d) 1000
23. The sum of 1 + 3 + 5 + …….. + 27 is _________
(a) 272 (b) 142 (c) 132 (d) 262
24. The sum of the first n natural numbers is 10. The sum of their cubes is________
(a) 20 (b) 100 (c) 1000 (d) 30
25. If the sum of 1 + 2 + 3 + ……….. + 10 is 55, then the sum of 13 + 23 + 33 + ……….. + 103
is ________
(a) 552 (b) 553 (c) 3024 (d) 3026
26. The value of 12 + 22 + 32 + ……….. + 102 is ________
(a) 395 (b) 390 (c) 385 (d) 360
2. MENSURATION
1. If the radius and height of a cylinder are a cm and b cm respectively, then its curved
surface area is_______
(a) 2rhcm2 (b) 2ab cm2 (c) a2bcm2 (d) ab cm2
2. The total surface area of a right circular cylinder of radius r and height h is_______
(a) r (h + r) sq. units (b) 2r (h – r) sq. units
(c) 2r (h + r) sq. units (d) r (h – r) sq. units
3. The radius and the height of a cylinder are equal to those of a cone. If the volume of the
cone is 20cm3, then the volume of the cylinder is_________
(a) 400cm3 (b) 10cm3 (c) 60cm3 (d) 40cm3
4. Curved surface area of a hollow cylinder is_______
(a) 2Rh (b) 2rh (c) rl (d) 2h(R + r)
5. Volume of a hollow cylinder is_______
(a) (R2 – r2) (b) 2h(R + r) (c) r2h (d) h (R2 – r2)
6. The volume of a solid hollow cylinder of external radius R and internal radius r is______
(a) 2RH(R + r) (b) h (R2 + r2) (c) 2h(R + r) (d) h(R + r)(R - r)
7. In a cone l = 13 cm, h = 5 cm, then r = ?
(a) 13 cm (b) 14 cm (c) 12 cm (d) 11 cm
8. For a right circular cone of radius r, height h and slant height, the total surface area is__
(a) 2r (l + r) sq. units (b) r (l + r) sq. units
(c) r (h + r) sq. units (d) 2r (h + r) sq. units
9. The formula to find the total surface area of a hemisphere is_________
(a) 2 r2 sq. units (b) 3 r2 sq. units (c) 4 r2 sq. units (d) r2 sq. units
10. Volume of a hemisphere of radius r cm is_________
(a) 4/3 r3 cubic units (b) 2/3 r3 cubic units
(c) 1/3 r3 cubic units (d) 1/3 r2h cubic units
11. The surface area of a sphere is 100 cm2. Its radius is__________
(a) 25cm (b) 100cm (c) 5cm (d) 10cm
12. The total surface area of a sphere is 144 cm2. Its radius is__________
(a) 36cm (b) 6cm2 (c) 24cm (d) 6cm
13. Total surface area of a sphere of radius 1cm is__________
(a) 4 cm3 (b) 4 r2 cm2 (c) 4 cm2 (d) 3 r2 cm2
14. The volume of the sphere r units is_________
(a) 2/3 r3 cu. units (b) 4/3 r2 cu. units (c) 4/3 r3 cu. units (d) 4 r3 cu. Units
3. SETS AND FUNCTIONS
3.1 SETS
1. A A = (a) { } (b) A (c) (d) A'
2. A A’ = (a) A (b) { } (c) A' (d) ξ
3. A = {p, q, r, s} then A A is (a) {p, q, r, s} (b) 4 (c) {4} (d) A
4. If ξ = {1,2,3,4,5,6}, A = {1,3,5}, then n(A)' is _____
(a) 3 (b) 6 (c) 2 (d) 0
5. If A B = {1,2,3,5}, A B = {2} and A = {1,2,3} find the set B is_____
(a) {2, 5} (b) {1, 2, 3, 5} (c) {2} (d) { }
6. If A B = { a,b,d,g,h }, A B = {a,b,d} and A = { a,b,d,g} find the set B is_____
(a) { a,b,d,h } (b) { a,b,d,g } (c) { a,b,h } (d) { d,g,h }
7. A = {p, r, s}, B = {l, m, o, p, s}, then n (A B) is _____
(a)2 (b) 7 (c) 6 (d) None
8. A = {-2, 3, 5, 7}, B = {3, 7, 11}, then n (A B) is______
(a)7 (b) 5 (c) 1 (d) None
9. If A = {1,2, 3, 6, 9}, B = {2, 4, 6, 8}, then the value of n (A B) is______
(a) {2, 6} (b) {2} (c) 2 (d) 4
10. If A = { a, b, c, d, e }, B = { b, d, f }, then A – B is_____
(a) { a, b, c, d, e } (b) { a, c, e, f } (c) { b, d } (d) { a, c, e }
11. A = { 3, 4, 5, 6 }, B = { 5, 7, 8 }, then A – B is________
(a) {5} (b) {3, 4, 6} (c) {3, 4, 8} (d) {7, 8}
12. A = { 6, 9, 13, 17 }, B = { 5, 9, 17, 18 }, then A – B is________
(a) {6, 13} (b) {5, 18} (c) {5, 6, 9, 13, 17, 18} (d) {9, 17}
13. A = {10, 11, 12, 16, 18}, B = {11, 15, 16, 20 }, then A – B is________
(a) {11, 16} (b) {10, 12, 18} (c) {15, 16, 20} (d) {11}
14. If A = { a, b, c }, B = { c, d, e, f }, then n(A – B) is_____
(a) 2 (b) 3 (c) 4 (d) 7
15. A = {r, s}, (B C) = {p, q, r, s}, then A (B C) = _______
(a) {r, s} (b) {p, q} (c) {p, r, s} (d) {p, q, r, s}
16. The value of A (B C) is ______
(a) A (B C) (b) (A B) (A C)
(c) A (B C) (d) (A B) (A C)
17. A – ( B C ) = ___________
(a) ( A – B ) ( A – C ) (b) ( A – B ) ( A – C )
(c) ( A – B ) C (d) ( A – B ) C
18. (A B)' = (a) A' B' (b) (A B)' (c) A' B' (d) A B'
19. A' B' = (a) A' B' (b) A' B (c) (A B)' (d) A B'
3.2 RELATIONS
20. If P = { 2, 3, 4, 8, 9 }, then the set of ordered pairs representing the relation is a multiple
of 2 on P is _________
(a) {(2,2),(4,2),(8,2),(4,8)} (b) {(2,2),(4,2),(8,2) }
(c) {(2,2),(2,4),(2,8) } (d) {(8,4),(2,8),(2,4),(2,2)}
3.3 FUNCTIONS
21. If f (a) = a for all a A then f is ________ of A.
(a) into function (b) identity function
(c) constant function (d) many to one function
22. If f = {(1,1),(8,2),(27,3),(64,4)}, then the domain of f is _______
(a){ 1, 2, 3, 4 } (b) { 1, 3 } (c) { 1, 8, 27, 64 } (d) { 2, 4 }
23. If R= {(a,r),(a,s),(b,r),(b,s)}, then the domain is _______
(a){ a, b } (b) { b, s } (c) { r, s } (d) { a, r }
24. R = {( -1, 1 ), ( 0, 0 ), ( 2, 4 )}.The domain of R is__________
(a) { -1, 0, 2 } (b) { 1, 0, 4 } (c) { -1, 0, 4 } (d) { 1, 0, 2 }
25. f = { (0, -1), (3, 2), (5, 3), (7, 2) } in this function the image of 5 is___________
(a) -1 (b) 2 (c) 3 (d) 5
26. f = { (0, -1), (3, 2), (5, 3), (7, 2) } in this function the image of 0 is __________
(a) -1 (b) 2 (c) 3 (d) 5
27. The pre – image of 2 under the function f = { (0, -1), (3, 2), (5, 3), (7, 2) } is________
(a) 3 (b) 7 (c) 3, 7 (d) 5, 7
28. Find the pre – image of 2 under the function f = { (0, -1), (3, 2), (5, 3), (6, 1) } is________
(a) 0 (b) 5 (c) 6 (d) 3
29. The pre – image of 4 under the function f = { (-2, 4), (-1, 0), (0, -1), (1, 0) } is________
(a) -1 (b) 0 (c) 1 (d) -2
30. If f (x) = 3x + 1, then the pre – image of 7 is ______
(a) 4 (b) 2 (c) 22 (d) 7
31. If f (x) = x + 5, then the value of f (-3) is ______
(a) 2 (b) -2 (c) -15 (d) 15
32. If f (x) = 4x2, then the range of f (-2) is ______
(a) -8 (b) -16 (c) 16 (d) 64
33. If f (x) = 2x2 - 1, then the range of f (-2) is ______
(a) 3 (b) – 5 (c) 0 (d) 7
34. If f (x) = x2 – x + 7, then the value of f (-3) is ______
(a) 17 (b) 19 (c) 0 (d) 4
35. If f (x) = 4x/(x + 1) , then f (3) is_________
(a) -3 (b) 3 (c) 12 (d) -12
36. If f (x) = (〖(2x)〗^2+ 5)/3, then the value of f (2) is
(a) 13/3 (b) 3 (c) 23 (d) 7
37. If f (x) = 4x/(x + 1) , then f (3) + f (-3) is ________
(a) 0 (b) 9 (c) -3 (d) -6
38. If f (x) = x + 5, g (x) = x2, then f o g (x) = _______
(a) (x + 5)2 (b) x2 + 5 (c) x2 + x (d) x2 - 5
39. If f (x) = x - 5, g (x) = x2, then f o g = _______
(a) (x - 5)2 (b) x2 (c) 3 - 2x2 (d) x2 - 5
40. If f(x) = 2x, g(x) = 1/2 x, then f o g (x) = ____________
(a) x2 (b) 2x2 (c) x (d) 2x
4. ALGEBRA
4.1 Simultaneous Equations
1. x + y = 3, y + z = -5, x + z = 2, then x + y + z = ________
(a) 1 (b) 0 (c) 2 (d) -1
4.2 Polynomial
2. If (ax + b) divides p(x), then remainder is ______
(a) p (-a) (b) p (a) (c) p (-b/a) (d) p (b/a)
3. The value of p (a), If (x - a) is a factor of p(x) is ______
(a) a (b) x (c) 0 (d) 7
4. When x3 + x2 + 5 is divided by (x – 1) the remainder is ______
(a) 10 (b) 0 (c) 7 (d) -7
5. When x3 + x2 – 3x + 5 is divided by (x – 1) the remainder is ______
(a) – 4 (b) 10 (c) – 10 (d) 4
6. When x3 – x2 – 1 is divided by x – 1, then the remainder is _________
(a) -1 (b) -3 (c) 1 (d) 3
7. When x^3+x^2-2x+7 is divided by (x + 4), the remainder is __________
(a) -33 (b) 10 (c) 33 (d) 35
8. If x – 3 is a factor of x2 + mx – 18, then the value of m is______
(a) 3 (b) 6 (c) 2 (d) 4
9. One of the factor of x3 + 2x – 3 is ________
(a) x + 1 (b) x – 1 (c) x – 2 (d) x + 3
4.3 GCD and LCM
10. The G.C.D of a m, a m + 1, a m + 2 is ______
(a)a (b) m (c) a m (d) a m + 2
11. The G.C.D of a 3, a 5 and a 7 is ______
(a) a 3 (b) a 5 (c) a 7 (d) a 15
12. The G.C.D of m 6, m 12, m 18 is ______
(a) m 6 (b) m 18 (c) m 12 (d) m 36
13. The G.C.D of p 8, p 7, p 12 is ______
(a) p 8 (b) p 7 (c) p 12 (d) p 27
14. The G.C.D of x 4, x 6 and x 10 is ______
(a) x 10 (b) x 6 (c) x 16 (d) x 4
15. The G.C.D of x 5, x 7 and x 10 is ______
(a) x 5 (b) x 10 (c) x 22 (d) x 7
16. The G.C.D of 3a2b and 15ab2
(a) 3ab (b) 15a2b2 (c) 3a2b2 (d) 3ab2
17. The G.C.D of 3a4, 9a6, 12a7 is
(a) a4 (b) 3a7 (c) 3a4 (d) 12a4
18. The L.C.M of x 6, x 10 and x 7 is ______
(a) x 6 (b) x 10 (c) x 7 (d) x 23
19. The L.C.M of 15a8, 75a6 is________
(a)75a5 (b) 15a8 (c) 15a5 (d) 75a8
20. The L.C.M of a3 – b3 and a – b is _________
(a) a – b (b) a3 – b3 (c) a2 – ab + b2 (d) a2 – b2
4.4 Rational Expressions
21. The value of x/(x + y) + y/(x + y) is______
(a) 0 (b) -1 (c) 1 (d) 2
22. x/(2- x) - 2/(2 - x) is________
(a) 1 (b) -1 (c) x – 2 (d) 2x
23. x/(5- x) - 5/(5 - x) is________
(a) 1 (b) -1 (c) x – 5 (d) 5x
24. Simplify: (a^(2 ) b)/(b^(2 ) c) x (b^2 c)/(c^2 a) (a^2 b)/(c^2 a)
(a) 〖ab〗^2/c^2 (b) 1 (c)(a^2 b^2)/c^2 (d) a^2 b^2 c
4.5 Square root
25. √(0.0144 ) = ______
(a) 12 (b) 1.2 (c) 0.12 (d) 0.012
26. The value of √(81a^4 b^16 ) = ______
(a) 9ab (b) 9a2b4 (c) 9a2b8 (d) 9 (ab)8
27. The square root of 36a8 is ______
(a) 6a16 (b) 18a8 (c) 6a4 (d) a4
28. The square root of 16x 2 y 4 z 16 is______
(a) 4x y 2 z 4 (b) 8x y 2 z 8 (c) 4x y 2 z 8 (d) 8x y 2 z 4
29. Square root of 16x2y4z8 is _______
(a) 8xy2z4 (b) 4xy2z4 (c) 4x2y2z2 (d) 8x2y2z
30. Square root of 9x2 + 30x + 25 is ______
(a) 3x + 5 (b) 3x – 5 (c) 9x + 5 (d) 9x – 5
4.6 Quadratic Equations
31. The roots of the quadratic equation 3x2 – 75 = 0 are ______
(a) 3 (b) 5 (c) 0 (d) 25
32. The term that has to be added to x2 + 16x to make a perfect square is_______
(a) 16 (b) 64 (c) 8 (d) 36
33. The solution set (x + 1) (x – 2) = 0 is
(a) {1, -2} (b) {-1, -2} (c) {1, 2} (d) {-1, 2}
34. Solutions for (x – 5) (x + 3) = 0
(a) ( -5, 3 ) (b) ( -5, -3 ) (c) ( 5, 3 ) (d) ( 5, -3 )
35. The solution set of (x – 5) (x + 2) = 0 is______
(a) {-5, 2} (b) {5, -2} (c) {5, 2} (d) {-5, -2}
36. If the roots are imaginary, then the value of b2 – 4ac is _______
(a) 0 (b) < 9 =" 0" 4 =" 0">5. APPLIED MATHEMATICS
5.1 Linear Programming
1. Which is linear equation?
(a) 2x + 3y = 5 (b) 2x + 3y 5 (c) 2x + 3y <>5.2 Network Programming
15. The path that takes longest duration is_______
(a) solution path (b) project path (c) critical path (d) correct path
6. GEOMETRY
6.1 Locus
6.2 Circles
1. The number of circles passing through three non- collinear points is_________
(a) 1 (b) 2 (c) 0 (d) 4
2. Two circles of diameters 12 cm and 10 cm touch each other internally. Then the distance
between their centres is
(a) 2 cm (b) 22 cm (c) 1 cm (d) 11 cm
6.3 Angles in a Circle
3. The angle in a semicircle is ________
(a) Obtuse angle (b) Acute angle (c) Right angle (d) Straight angle
4. The angle in a semi – circle is_________
(a) 0 (b) 45 (c) 135 (d) 90
5. The angle in the major segment is ________
(a) Obtuse angle (b) Acute angle (c) Right angle (d) Straight angle
6. Angle in a minor segment is_________
(a) an obtuse angle (b) an acute angle (c) a right angle (d) a reflex angle
7. In the figure the value of x is __________
(a) 120 (b) 60 (c) 180 (d) 240
8. In the figure the value of x is __________
(a) 40 (b) 50 (c) 180 (d) 90
9. In the figure, the value of x is __________
(a) 150 (b) 60 (c) 90 (d) 30
10. If one angle of a cyclic quadrilateral is 70, then the angle opposite to it is ___________
(a) 20 (b) 110 (c) 140 (d) 160
11. If one angle of a cyclic quadrilateral is 65, then the angle opposite to it is ___________
(a) 50 (b) 40 (c) 130 (d) 115
12. In a cyclic quadrilateral ABCD, mA = 5x, mC = 4x, then the value of x is _________
(a) 12 (b) 20 (c) 48 (d) 36
13. In a cyclic quadrilateral ABCD, mA = 72, then mC is _________
(a) 108 (b) 144 (c) 72 (d) 180
14. In a cyclic quadrilateral the sum of the opposite angle is 5x, find x _________
(a) 10 (b) 100 (c) 36 (d) 90
6.4 Circles and Tangents
15. Parallelogram inscribed in a circle is a ________
(a) rectangle (b) square (c) trapezium (d) quadrilateral
16. The tangents at the ends of a diameter are _________
(a) perpendicular (b) parallel (c) equal (d) none
17. Number of tangents that can be drawn at any point on the circle is________
(a) 2 (b) 3 (c) 4 (d) 1
18. The number of tangents that can be drawn from a point outside the circle is________
(a) 1 (b) 2 (c) 4 (d) 0
19. The length of the tangent to a circle of radius 6cm from a point at a distance of 10cm
from the centre of the circle________
(a) 4cm (b) 8cm (c) 16cm (d) 3cm
6.5 Similar Triangle
20. If a line is drawn parallel to one side of a triangle the other two sides are divided in_____
(a) same (b) the same ratio (c) parallel (d) perpendicular
21. The ratio of corresponding sides of two similar triangles is 2 : 5. The ratio of their areas
is _________
(a) 2 : 5 (b) 5 : 2 (c) 4 : 25 (d) 25 : 4
22. If the ratio of the sides of two similar triangles is 3 : 4, then the ratio of their areas
is _________
(a) 3 : 4 (b) 4 : 3 (c) 9 : 16 (d) 27 : 64
23. In a triangle ABC, DE BC, if AD = 3cm, DB = 5cm, AE = 6cm, then EC is_______
(a) 10 cm (b) 8 cm (c) 2 cm (d) 3.6 cm
24. Which are the sides of a right triangle?
(a) 7, 8, 9 (b) 10, 11, 12 (c) 3, 4, 5 (d) 6, 6, 7
25. If 7 and 24 are the two sides of a right angled triangle, then the hypotenuse is ______
(a) 25 (b) 31 (c) 168 (d) 17
26. In the figure, BD = 4, DC = 9, the length of AD is _________
(a) 36 (b) 6 (c) 13 (d) 5
27. The length of the diagonal of a square is 4√2 m, then the length of the side is_________
(a) 4 m (b) 8√2 m (c) √2 m (d) 8 m
28. The length of the side of a square whose diagonal 5√2 is ________
(a) 5 (b) 2√2 (c) 3√3 (d) 3√5
7. ANALYTICAL GEOMETRY
7.1 Ratio Formula
1. The midpoint of the line segment joining the origin and (4, 8) is________
(a) (0, 4) (b) (0, 8) (c) (2, 4) (d) (4, 2)
2. The midpoint of the line segment joining the origin and (2, -4) is________
(a) (2, 0) (b) (0, -4) (c) (1, -2) (d) (0, 0)
3. The midpoint of the line segment, joining the points (3, 5) and (1, 3) is________
(a) (4, 2) (b) (2, 4) (c) (1, 2) (d) (2, 1)
4. The midpoint of the line segment, joining the points (8, 2) and (4, 6) is________
(a) (2, 2) (b) (6, 4) (c) (4, 6) (d) (2, -2)
5. The midpoint of the line segment, joining the points (0, 4) and (4, 2) is________
(a) (0, 4) (b) (4, 2) (c) (4, 6) (d) (2, 3)
6. The midpoint of the line segment, joining the points (1, -3) and (-5, 7) is________
(a) (-3, -5) (b) (-2, 2) (c) (3, 5) (d) (-4, 4)
7. The co-ordinates of the midpoint of the line segment joining the points A (-3, 2) and
B (7, 8) is________
(a) (5, 5) (b) (-5, 5) (c) (-2, 5) (d) (2, 5)
8. The midpoint of the line segment PQ is (5, 1). If P is (8, 4), then point Q is _______
(a) (2, -2) (b) (3, 3) (c) (-2, 2) (d) (-3, -3)
9. The centre of a circle is (-6, 4). A diameter of the circle has its one end at the origin then
the other end is _________
(a) (-12, 8) (b) (6, -4) (c) (12, -8) (d) (-6, 4)
10. The centroid of the triangle whose vertices are the points (-2, 3), (5, -5) and (6, 2)
is________
(a) (0, 3) (b) (-3, 0) (c) (3, 0) (d) (0, -3)
7.2 Area of a Triangle
11. If the three vertices of a triangle are collinear, then the area of the triangle is______
(a) 1 (b) 0 (c) 2 (d) 4
12. The area of the triangle whose vertices are (0, 0), (1, 0) and (0, 1) is___________
(a) 1 sq. unit (b) 1/2 sq. unit (c) 2 sq. units (d) 0 sq. units
13. Area of the triangle whose vertices are (0, 0), (2, 0) and (0, 2) is _______
(a) 1 sq. unit (b) 1/2 sq. unit (c) 2 sq. units (d) 0 sq. unit
14. The area of the triangle whose vertices are (-1, 1), (1, -1) and (0, 0) is _______
(a) -2 (b) 2 (c) 1 (d) 0
7.3 Straight Lines
15. The equation of X – axis is _______
(a) x = 0 (b) y = 0 (c) x + y = 0 (d) x - y = 0
16. The equation of straight line parallel to X – axis_______
(a) x = 0 (b) x = a (c) y = a (d) y = 0
17. The equation of straight line parallel to x – axis and passing through (3, 2) is_______
(a) y – 2 = 0 (b) x – 2 = 0 (c) x + 3 = 0 (d) y + 2 = 0
18. The equation of straight line passing through (2, -3) and parallel to x – axis is_______
(a) x = 3 (b) x = -3 (c) y = -3 (d) y = 3
19. The equation of straight line parallel to x – axis and which passes through the point
(2, -3) is_______
(a) y – 3 = 0 (b) y + 3 = 0 (c) x + 3 = 0 (d) x – 3 = 0
20. The equation of line, which is parallel to x – axis and passes through the point
(3, -2) is_______
(a) y = 0 (b) y = -2 (c) x = 0 (d) x = 3
21. Equation of a line, which is parallel to y – axis and passes through the point (5, 4)
is_______
(a) y = 0 (b) x = 0 (c) x = 5 (d) y = 4
22. The equation of line parallel to y – axis and passes through the point (3, 2) is_______
(a) y – 2 = 0 (b) x – 2 = 0 (c) y – 3 = 0 (d) x – 3 = 0
23. The equation of a straight line whose slope is 5 and which passes through the origin
is__
(a) 5y = -x (b) 5y = x (c) y = 5x (d) y = -5x
24. Slope of 2y = 3x is_______
(a) 3 (b) 2 (c) 3/2 (d) -3
25. Slope of the line 2x = y
(a) -2 (b) 1 (c) 2 (d) 1/2
26. The slope of the line y = mx + c is_____________
(a) m (b) c (c) m/c (d) c/4
27. The slope of y = 5x – 5 is___________
(a) 5 (b) -5 (c) 1 (d) -1
28. The slope of the straight line 3x + 2y = 4 is___________
(a) 1/2 (b) 4/3 (c) (-3)/2 (d) 3/2
29. The slope of a line which is parallel to the line 2x – 3y + 5 = 0 is___________
(a) - 2/3 (b) 2/3 (c) 3/2 (d) - 3/2
30. The slope of the straight line 3x + 4y + 10 = 0 is___________
(a) (-4)/3 (b) 4/3 (c) 3/4 (d) (-3)/4
31. The slope of the line 3x + 2y = 5 is________
(a) 3/2 (b) - 3/2 (c) 2/3 (d) - 2/3
32. If the straight line 7x – 5y = k passes through the point (1, 1) then the value of k is_____
(a) 2 (b) -2 (c) 1 (d) -1
33. If the straight line 4x – 3y = k passes through the point (1, 1) then the value of k is_____
(a) 2 (b) -2 (c) 1 (d) -1
34. Equation of a straight line with x and y intercepts is __________
(a) x/a + y/b = 1 (b) x/a + y/b = -1 (c) x/a - y/b = 1 (d) a/x + b/y = 1
35. If the two straight lines are perpendicular, then_________
(a) m1 x m2 = -1 (b) m1 x m2 = 1 (c) m1 = m2 (d) m1 = -m2
7.4 Some Properties of Straight Lines
36. The point of intersection of the lines x + y = 8 and x – y = 2 is _________
(a) (-5, -3) (b) (5, -3) (c) (5, 3) (d) (3, 5)
8. TRIGONOMETRY
8.1 Use of Trigonometric Tables
1. The first mathematician to use algebra in trigonometry was ________
(a) Brahmagupta (b) Ptolemy (c) Bhaskaracharya (d) Ramanujam
2. If sin θ = 0.5 then the value of θ is_______
(a) 60 (b) 30 (c) 90 (d) 45
3. If sin θ = 1/√2 , then the value of θ is _________
(a) 0 (b) 30 (c) 60 (d) 45
4. If sin θ = √3/2 , then the value of θ is _________
(a) 60 (b) 30 (c) 45 (d) 90
5. If sin θ = cos θ, then the value of θ is__________
(a) 0 (b) 45 (c) 30 (d) 90
6. If sin θ = tan θ, then the value of θ is__________
(a) 45 (b) 90 (c) 1 (d) 0
7. If sin θ = cos θ, then the value of tan θ is__________
(a) 0 (b) 1/2 (c) √3 (d) 1
8. If the value of cos θ = 1/√2 , then the value of tan θ is _________
(a) 0 (b) 2 (c) 1 (d) 3
9. If tan θ =√3 , then the value of θ is _________
(a) 30 (b) 45 (c) 60 (d) 90
10. 1 – tan245 = ____________
(a) 1 (b) 0 (c) 2/3 (d) 2
11. If tan A = 8/15 , Sin A =
(a) 7/15 (b) 8/15 (c) 8/17 (d) 7/8
8.2 Heights and Distances
12. The angle of depression of a stone from the top of a building is 30. The angle of
elevation of the top of the building from the stone is__________
(a) 15 (b) 30 (c) 60 (d) 0
13. The elevation of the sun, when the length of the shadow of a plane pole is √3 times the
height of the pole is __________
(a) 60 (b) 45 (c) 30 (d) 90
14. The angle of elevation of the top of a tower at a distance of 60 m. is found to be 45°.
The height of the tower is___________
(a) 60 m (b) 20 √3 m (c) 45 m (d) 60 √3 m
15. The length of the shadow of a wall of 5m height, when the sun is in 45° elevation is
(a) 10 m (b) 25 m (c) 5 m (d) 15 m
10. STATISTICS
10.1 Dispersion
1. The range of the data 27, 35, 25, 45, 67 is__________
(a) 40 (b) 42 (c) 10 (d) 89
2. The range of the data 36, 27, 28, 34, 59, 39 is__________
(a) 3 (b) 32 (c) 20 (d) 86
3. The largest value of the data is 98. If the range of the data is 73, then the smallest value
is __________
(a) 25 (b) 171 (c) 95 (d) 28
4. The largest value of the data is 25. If the range of the data is 15, then the smallest value
is __________
(a) 10 (b) -10 (c) 40 (d) -40
5. The largest value of the data is 89, If the range of the data is 37, then the smallest value
of the data is __________
(a) 126 (b) 37 (c) 89 (d) 52
6. The range and the smallest run of 10 tests of a person is 15. The highest run is_______
(a) 10 (b) 15 (c) 30 (d) 5
7. Standard deviation of the data 5, 10, 15, 20, 25 is 5 √2 . If we add 3 to each item, then
the new standard deviation is__________
(a) 3 + 5 √2 (b) 8 √2 (c) 5 √2 (d) 2√2
8. The standard deviation of 10 values is 4. If each value is increased by 3, then the
standard deviation of the new set of values is_____________
(a) 3 (b) 4 (c) 9 (d) 7
9. The standard deviation of a given data is 4. If each value is multiplied by 3, then the new
standard deviation is _________
(a) 4 (b) 12 (c) 7 (d) 1
10. The standard deviation of 10 values is 4. If each value is multiplied by 3, then the new
standard deviation is _________
(a) 4 (b) 12 (c) 7 (d) 1
11. The standard deviation of 8 values is 9. If each value is divided by 3, then the new
standard deviation is_________
(a) 3 (b) 1 (c) 9 (d) 8
12. The S.D is 25 and its variance is _________
(a) 5 (b) 600 (c) 50 (d) 625
13. If the variance of a data is 1.44, then the standard deviation is_________
(a) 1.2 (b) 12 (c) 72 (d) 44
14. If the variance of a data is 1.69, then the standard deviation is_________
(a) 1.3 (b) 13 (c) 3.38 (d) 69
15. The variance of 5 scores is 16. If each one of them is divided by 2, then the standard
deviation of the new scores is_______
(a) 4 (b) 8 (c) 2 (d) 16
16. The coefficient of variation of a series is 80% . The arithmetic mean is 20. Then the
standard deviation is ______________
(a) 160 (b) 16 (c) 1600 (d) 0.16
10.2 Probability
__
17. The sum of P(A) + P (A) is
(a) 1 (b) 1/2 (c) 1/4 (d) 3/4
18. When a coin is tossed the sample space is _______
(a) { T } (b) { H, T } (c) { } (d) { H }
19. The probability of getting head while tossing a coin is____________
(a) 1/2 (b) 1 (c) 2 (d) 1/3
20. Two coins are tossed simultaneously. The probability of getting two heads is________
(a) 2/4 (b) 1/4 (c) 3/4 (d) 1
21. When two coins are tossed at a time, the number of sample spaces is________
(a) 2 (b) 4 (c) 8 (d) 16
22. The probability of an event of getting more than two heads in are tossing two coins
simultaneously is________
(a) 1 (b) 0 (c) 1/4 (d) 3/4
23. When a fair die is rolled, then the probability of getting 3 on the face of the die is ______
(a) 1/2 (b) 1/4 (c) 1/6 (d) 1/3
24. A die is rolled once, the probability of getting an even number is _________
(a) 1/3 (b) 2/3 (c) 1/2 (d) 1/4
25. A die is rolled once. The probability of getting prime number is __________
(a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
26. When a coin and a die are thrown at a time, the numbers of elements in the sample
space is________
(a) 2 (b) 6 (c) 12 (d) 36
27. One card is drawn at random from a shuffled pack of 52 cards. Then the probability
that it will be a spade is_____
(a) 1/13 (b) 1/4 (c) 1/2 (d) 1/52
28. What is the probability of getting a red card when one card is drawn at random from a
shuffled pack of 52 cards?
(a) 1/2 (b) 2/3 (c) 3/4 (d) 1/3
ALL THE BEST @ All the best @ all the best @ All the best @ All the best @All the best
