PRACTICE SET
1. The HCF of 455 and 42 is
a) 21 b) 14 c) 7 d) 35
2. The value of is
a) b) c) d)
3. The zero of the linear polynomial 2x + 3 is
a) b) c) 1 d)
4. If α and β are the roots of the quadratic polynomial p(x) = 𝑎𝑥2 + bx + c, a ≠ 0 then α + β =
a) b) c) d)
5. If the pair of equations 𝑎1𝑥 + 𝑏1𝑦 + 𝑐1=0 𝑎𝑛𝑑 𝑎2𝑥 + 𝑏2𝑦 + 𝑐2= 0 has a unique solution, then
a) 𝑎2𝑏1 ≠ 𝑎1𝑏2 b) 𝑎2𝑏1 = 𝑎1𝑏2 c) 𝑎2𝑐1 ≠ 𝑎1𝑐2 d) 𝑐2𝑏1 = 𝑐1𝑏2
6. The roots of a quadratic equation 𝑎𝑥2 + bx + c = 0 are given by
a) b) c) d)
7. The degree of a quadratic polynomial is
a) 0 b) 1 c) 2 d) 4
8. Which of the following is not a similarity criterion for two triangles?
a) SSS b) AA c) ASA d) SAS
9. The distance of the point P(x, y) from the origin is
a) b) c) 𝑥2 + 𝑦2 d) x + y
10. sinA = 1 and cosA = 0 when A is
a) 0° b) 30° c) 60° d) 90°
11. The value of is _______.
a) 0 b) 30 c) 60 d) 90
12. In ΔABC, AB = 6√3 cm, AC = 12cm, BC = 6cm then ∠B = ______.
a) 0° b) 30° c) 60° d) 90°
13. The value of is _______.
a) 0 b) 23 c) 19 d) 99
14. Complete the identity: 𝑐𝑜𝑠2𝐴 + _____ = 1
a) 𝑠𝑒𝑐2𝐴 b) 𝑠𝑖𝑛2𝐴 c) 𝑐𝑜𝑠𝑒𝑐2𝐴 d) 𝑐𝑜𝑡2𝐴
15. Complete the identity: 𝑠𝑒𝑐2𝐴 – _____= 𝑡𝑎𝑛2𝐴
a) 1 b) –1 c) 2 d) 0
16. The coordinates of the mid- point of a line segment joining P(𝑥1, 𝑦1) and Q(𝑥2, 𝑦2) are
a) b)
c) d)
17. The quadratic polynomial whose sum of zeroes is 3 and product of zeroes is –2 is:
(a) x2 + 3x – 2 (b) x2 – 2x + 3 (c) x2 – 3x + 2 (d) x2 – 3x – 2
18. If (x + 1) is a factor of 2x3 + ax2 + 2bx + 1, then find the values of a and b given that
2a – 3b = 4
(a) a = –1, b = –2 (b) a = 2, b = 5
(c) a = 5, b = 2 (d) a = 2, b = 0
19. If p(x) is a polynomial of at least degree one and p(k) = 0, then k is known as
(a) value of p(x) (b) zero of p(x)
(c) constant term of p(x) (d) none of these
20. A polynomial of degree n has
(a) only 1 zero (b) exactly n zeroes
(c) atmost n zeroes (d) more than n zeroes
21. For any positive integer a and 3, there exist unique integers q and r such that a = 3q + r, where r must satisfy:
(a) 0 ≤ r < 3 (b) 1 < r < 3 (c) 0 < r < 3 (d) 0 < r ≤ 3
22. L.C.M. of 23 × 32 and 22 × 33 is:
(a) 23 (b) 33 (c) 23 × 33 (d) 22 × 32
23. The HCF and LCM of two numbers are 33 and 264 respectively. When the first number is completely divided by 2 the quotient is 33. The other number is:
(a) 66 (b) 130 (c) 132 (d) 196
24. If two positive integers a and b are written as a = x3y2 and b = xy3; x, y are prime numbers, then HCF (a, b) is
(a) xy (b) xy2 (c) x3y3 (d) x2y2
25. If two positive integers p and q can be expressed as p = ab2 and q = a3b; a, b being prime numbers, then LCM (p, q) is
(a) ab (b) a2b2 (c) a3b2 (d) a3b3
26. Find the value of P for which the point (–1, 3), (2, p) and (5, –1) are collinear.
(a) 4 (b) 3 (c) 2 (d) 1
27. Find the distance of the point (–6, 8) from the origin.
(a) 8 (b) 11 (c) 10 (d) 9
28. Find the value of p for which the points (–5, 1), (1, p) and (4, –2) are collinear.
(a) –3 (b) –2 (c) 0 (d) –1
29. Find the value of k if the points A(2, 3), B(4, k) and C(6, –3) are collinear.
(a) 2 (b) 3 (c) 0 (d) 1
30. In what ratio of line x – y – 2 = 0 divides the line segment joining (3, –1) and (8, 9)?
(a) 1 : 2 (b) 2 : 1 (c) 2 : 3 (d) 1 : 3
31. Every quadratic polynomial can have at most
(a) three zeros (b) one zero (c) two zeros (d) none of these
32. If p = 1 and q = –2 are roots of equation x2 – px + q = 0, then the quadratic equation will be
(a) x2 + 2x –1= 0 (b) x2 – x – 2 = 0
(c) x2 – 2x + 1= 0 (d) x2 + x + 2 = 0
33. Roots of the quadratic equation x2 – 3x = 0, will be
(a) 3 (b) 0, –3 (c) 0, 3 (d) 0, 0
34. Which of the following is not a quadratic equation
(a) x² + 3x – 5 = 0 (b) x² + x3 + 2 = 0
(c) 3 + x + x² = 0 (d) x² – 9 = 0
35. A linear equation has degree
(a) 0 (b) 1 (c) 2 (d) 3
36. A cubic equation has degree
(a) 1 (b) 2 (c) 3 (d) 4
37. A bi-quadratic equation has degree
(a) 1 (b) 2 (c) 3 (d) 4
38. The polynomial equation x(x + 1) + 8 = (x + 2) (x – 2) is
(a) linear equation (b) quadratic equation
(c) cubic equation (d) bi-quadratic equation
39. The equation (x – 2)² + 1 = 2x – 3 is a
(a) linear equation (b) quadratic equation
(c) cubic equation (d) bi-quadratic equation
40. sin 2B = 2 sin B is true when B is equal to
(a) 90° (b) 60° (c) 30° (d) 0°
41. 5 tan² A – 5 sec² A + 1 is equal to
(a) 6 (6) –5 (c) 1 (d) –4
42. In a right triangle ABC, the right angle is at B. Which of the following is true about the other two angles A and C?
a) There is no restriction on the measure of the angles
b) Both the angles should be obtuse
c) Both the angles should be acute
d) One of the angles is acute and the other is obtuse
43. (cos A / cot A) + sin A = ____________
a) cotA b) 2sin A c) 2cos A d) secA
44. If 5tanθ=4, then value of (5sinθ – 4cosθ)/(5sinθ + 4cosθ) is:
a)1/6 b)5/6 c)0 d)5/3
45. Which of the following is the area of a rhombus?
(i) Product of its diagonals (ii) (sum of its diagonals)
(iii) ½ (Product of its diagonals) (iv) 2 (Product of its diagonals)
46. If the edge of a cube is 1 cm then which of the following is its volume?
(i) 6 m3 (ii) 3 m3 (iii) 1 m3 (iv) none of these
47. If the parallel sides of a parallelogram are 2 cm apart and their sum is 10 cm then its area is:
(i) 20 cm2 (ii) 5 cm2 (iii) 10 cm2 (iv) none of these
48. The length of the parallel sides of a trapezium are 7cm and 5cm and its height is 4cm. Find the area of the trapezium.
(i) 24 square cm (ii) 42 square cm
(iii) 20 square cm (iv) 40 square cm
49. If the edge of a cube is 1 cm then which of the following is its total surface area?
(i) 1 cm2 (ii) 4 cm2 (iii) 6 cm2 (iv) none of these
50. If the dimensions of a room are I, b and h, (l → length, b → breadth and h → height) then which of the following is the total surface area the room?
(i) 2(lb + bh + hl) (ii) 2h (1 + h)
(iii) 2(bh + lh) (iv) 2h + l + b
QB. PROJECT: (10)
Solve a pair of linear equations by graphical method and verify the result by any other algebraic method.
QC. Do as directed:
1. Solve the following pair of linear equations: (2)
y – 4x = 1
6x – 5y = 9
2. A part of monthly Hostel charge is fixed and the remaining depends on the number of days one has taken food in the mess. When Swati takes food for 20 days, she has to pay Rs 13000 as hostel charges whereas, Mansi who takes food for 25 days pays Rs 3500 as hostel charges. Find the fixed charges and the cost of food per day. (3)
3. Solve using cross multiplication method: (2)
x + y = 1
2x – 3y = 11
4. Find whether the lines representing the following pair of linear equations intersect at a point, are parallel or coincident: (2)
2x – 3y + 6 = 0
4x – 5y + 2 = 0
5. Solve for x and y: (2)
6(ax + by) = 3a + 2b
6(bx – ay) = 3b – 2a
6. Solve for x and y: (2)
2x = 5y + 4;
3x – 2y + 16 = 0
7. In a two digit number, the digit in the unit place is twice of the digit in the tenth place. If the digits are reversed, the new number is 27 more than the given number. Find the number. (2)
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