Class 09 – Mathematics
Maximum Marks: 40 Time Allowed: 90 minutes
General Instructions:-
1. Section A consists of 42 questions of 1 mark each. Attempt any 40 questions.
2. There is no negative marking.
Question 1. An exterior angle of a triangle is 80° and the interior opposite angles are in the ratio 1 : 3, measure of interior opposite angles are
(a) 30°, 90°
(b) 40°, 120°
(c) 20°, 60°
(d) 30°, 60°
Question2. In figure if ∠A + ∠B + ∠C + ∠D + ∠E + ∠F = k right angles, then find value of k.
(а) 2
(b) 3
(c) 4
(d) 5
Question3. In the given figure, the measure of ∠ABC is
(a) 80°
(b) 20°
(c) 100°
(d) 60°
Question4. The angle of a triangle are in the ratio 5 : 3 : 7, the triangle is
(а) an acute-angled triangle
(b) an obtuse angled triangle
(c) an right angled triangle
(d) an isosceles triangle.
Question5. In figure l1 || l2, the value of x is
(a) 80°
(b) 100°
(c) 110°
(d) 70°
Question6. If one angle of triangle is equal to the sum of the other two, then the triangle is
(a) an isosceles triangle
(b) an obtuse-angled triangle
(c) an equilateral triangle
(d) a right triangle
Question7. One of the angles of a triangle is 75°. If the difference of other two is 35°, then the largest angle of other two angles has a measure
(a) 80°
(b) 75°
(c) 70°
(d) 135°
Question8. Which number is divisible by 11?
(a) 1516
(b) 1452
(c) 1011
(d) 1121
Question9. LCM of the given number ‘x’ and ‘y’ where y is a multiple of ‘x’ is given by
(a) x
(b) y
(c) xy
(d) x/y
Question10. The largest number that will divide 398,436 and 542 leaving remainders 7,11 and 15 respectively is
(a) 17
(b) 11
(c) 34
(d) 45
Question11. There are 312, 260 and 156 students in class X, XI and XII respectively. Buses are to be hired to take these students to a picnic. Find the maximum number of students who can sit in a bus if each bus takes equal number of students
(a) 52
(b) 56
(c) 48
(d) 63
Question12. There is a circular path around a sports field. Priya takes 18 minutes to drive one round of the field. Harish takes 12 minutes. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet ?
(a) 36 minutes
(b) 18 minutes
(c) 6 minutes
(d) They will not meet
Question13. Express 98 as a product of its primes
(a) 2² × 7
(b) 2² × 7²
(c) 2 × 7²
(d) 23 × 7
Question14. Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively. Find the maximum capacity of a bag so that the wheat can be packed in exact number of bags.
(a) 98 kg
(b) 290 kg
(c) 200 kg
(d) 350 kg
Question15. If P(E) = 0.07, then what is the probability of ‘not E’?
(a) 0.93
(b) 0.95
(c) 0.89
(d) 0.90
Question16. A bag has 3 red balls and 5 green balls. If we take a ball from the bag, then what is the probability of getting red balls only?
(a) 3
(b) 8
(c) ⅜
(d) 8/3
Question17. A bag has 5 white marbles, 8 red marbles and 4 purple marbles. If we take a marble randomly, then what is the probability of not getting purple marble?
(a) 0.5
(b) 0.66
(c) 0.08
(d) 0.77
Question18. A dice is thrown in the air. The probability of getting odd numbers is
(a) ½
(b) 3/2
(c) 3
(d) 4
Question19. If we throw two coins in the air, then the probability of getting both tails will be:
(a) ½
(b) ¼
(c) 2
(d) 4
Question20. If two dice are thrown in the air, the probability of getting sum as 3 will be
(a) 2/18
(b) 3/18
(c) 1/18
(d) 1/36
Question21. The base of a right triangle is 48 cm and its hypotenuse is 50 cm. The area of the triangle is
(a) 168 cm²
(b) 252 cm²
(c) 336 cm²
(d) 504 cm²
Question22. The area of ΔABC is:
a) 20 cm2
b) 10 cm2
c) 4√5 cm2
d) 2√5 cm2
Question23. The area of a triangular sign board of sides 5 cm, 12 cm and 13 cm is:
a) 60 cm2
b) 30 cm2
c) 12 cm2
d) 65/2 cm2
Question24. The sides of a triangle are in a ratio of 25:14:12 and its perimeter is 510 m. The greatest side of the triangle is:
a) 270 m
b) 250 m
c) 170 m
d) 120 m
Question25. The perimeter of a right triangle is 60 cm and its hypotenuse is 26 cm. The other two sides of the triangle are:
a) 26 cm, 8 cm
b) 25 cm, 9 cm
c) 24 cm, 10 cm
d) 20 cm, 14 cm
Question26. The area of the quadrilateral ABCD in the adjoining figure is:
a) 14.8 cm2
b) 15 cm2
c) 15.2 cm2
d) 16.4 cm2
Question27. The area of trapezium in the adjoining figure is:
a) 286 m2
b) 296 m2
c) 306 m2
d) 316 m2
Question28. The width of each of five continuous classes in a frequency distribution is 5 and the lower class-limit of the lowest class is 10. The lower class-limit of the highest class is:
(a) 15
(b) 30
(c) 35
(d) 40
Question 29. Let m be the mid-point and 1 be the lower class limit of a class in a continuous frequency distribution. The upper class limit of the class is:
(a) 2m + l
(b) 2m – l
(c) m – l
(d) m – 2l
Question 30. The class marks of a frequency distribution are given as follows:15, 20, 25, …The class corresponding to the class mark 15 is:
(a) 12.5 – 17.5
(b) 17.5 – 22.5
(c) 18.5 – 21.5
(d) 19.5 – 20.5
Question 31. In the class intervals 10-20, 20-30, the number 20 is included in:
(a) 10-20
(b) 20-30
(c) both the intervals
(d) none of these intervals
Question 32. A grouped frequency table with class intervals of equal sizes using 250-270 (270 not included in this interval) as one of the class interval is constructed for the following data:268, 220, 368, 258, 242, 310, 272, 342, 310, 290, 300, 320, 319, 304,402, 318, 406, 292, 354, 278, 210, 240, 330, 316, 406, 215, 258, 236.The frequency of the class 370-390 is:
(a) 0
(b) 1
(c) 3
(d) 5
Question 33. A grouped frequency distribution table with classes of equal sizes using 63-72 (72 included) as one of the class is constructed for the following data:30, 32, 45, 54, 74, 78, 108, 112, 66, 76, 88, 40, 14, 20, 15, 35, 44, 66, 75, 84, 95, 96, 102, 110, 88, 74, 112, 14, 34, 44. The number of classes in the distribution will be:
(a) 9
(b) 10
(c) 11
(d) 12
Question 34. To draw a histogram to represent the following frequency distribution:
the adjusted frequency for the class 25-45 is:
(a) 6
(b) 5
(c) 3
(d) 2
Question 35. The mean of five numbers is 30. If one number is excluded, their mean becomes 28. the excluded number is:
(a) 28
(b) 30
(c) 35
(d) 38
Q36. One of the linear factors of 3x2+8x+5 is
a. (x+1)
b. (x-2)
c. (x+2)
d. (x-4)
Q37. The coefficient of x in 7x2+6x-2 is
a. 2
b. 6
c. -2
d. 7
Q38. Which of the following is an example of the quadratic polynomial?
a. 7x+3
b. 2x2+x-1
c. x+3x3-9
d. None of the above
Q39. Find the value of 72-52.
a. 22
b. 23
c. 24
d. 25
Q40. If x2+kx+6 = (x+2)(x+3) for all k, find the value of k.
a. -1
b. 1
c. 3
d. 5
Q41. What is the zero of the polynomial p(x)=cx+d?
a. -c
b. -d
c. -d/c
d. d/c
Q42. The zero of the polynomial p(x) = -5x+5 is
a. 0
b. -5
c. -1
d. 1
Answer: 1(c) 20°, 60°
Answer: 2(c) 4
Answer: 3(a) 80°
Answer: 4(а) an acute-angled triangle
Answer: 5(a) 80°
Answer:6 (d) a right triangle
Answer: 7(c) 70°
Answer:8 (b) 1452
Answer:9(b) y
Answer: 10(a) 17
Explanation:(a); [Hint. Algorithm 398 – 7 – 391; 436 – 11 = 425; 542 – 15 = 527; HCF of 391, 425, 527 = 17]
Answer:11(a) 52
Explanation:(a); [Hint. HCF of 312, 260, 156 = 52]
Answer: 12(a) 36 minutes
Explanation: (a); [Hint. LCM of 18 and 12 = 36]
Answer: 13(c) 2 × 7²
Answer: 14(a) 98 kg
Explanation:(a); [Hint. HCF of 490, 588, 882 = 98 kg]
Answer: 15(a) 0.93
Explanation: P(E) + P(not E) = 1
Since, P(E) = 0.05
So, P(not E) = 1 – P(E)
Or, P(not E) = 1 – 0.07
∴ P(not E) = 0.93
Answer:16 (c) ⅜
Explanation: Number of red balls = 3
Number of green balls = 5
Total balls in bag = 3+5 = 8
Probability of getting red balls = number of red balls/total number of balls
= ⅜
Answer: 17(d) 0.77
Explanation: Total number of purple marbles = 4
Total number of marbles in bag = 5 + 8 + 4 = 17
Probability of getting purple marbles = 4/17
Hence, the probability of not getting purple marbles = 1-4/17 = 0.77
Answer: 18(a) ½
Explanation: A dice has six faces having values 1, 2, 3, 4, 5 and 6.
There are three odd numbers and three even numbers.
Therefore, the probability of getting only odd numbers is = 3/6 = ½
Answer:19 (b) ¼
Explanation: When two coins are tossed, the total outcomes will be = 2 x 2 = 4
Hence, the probability of getting both tails = ¼
Answer: 20(c) 1/18
Answer: 21(c) 336 cm²
Answer: 22(d) 2√5 cm2
Answer: 23(b) 30 cm2
Answer: 24(b) 250 m.
Answer:25( c) 24 cm, 10 cm
Answer: 26(c) 15.2 cm2
Answer: 27(c) 306 m2
Answer: 28(b) 30
Answer: 29(b) 2m – l
Answer: 30(a) 12.5 – 17.5
Answer: 31(b) 20-30
Answer: 32(a) 0
Answer: 33(b) 10
Answer: 34(d) 2
Answer:35 (d) 38
Answer: 36(a)
Explanation: 3x2+8x+5 = 3x2+ 3x+5x+5
3x2+8x+5 = 3x(x+1)+5(x+1)
3x2+8x+5 = (3x+5)(x+1)
Therefore, (x+1) is one of the factors of 3x2+8x+5.
Answer: 37(b)
Explanation: The coefficient of x in 7x2+6x-2 is 6. Because the number
multiplied by x is 6.
Answer: 38(b)
Explanation: 2x2+x-1 is a quadratic polynomial because the highest
degree of the polynomial is 2.
Answer: 39(c)
Explanation: 72-52 = 49 – 25 = 24.
Answer: 40(d)
Explanation: x2+kx+6 = (x+2)(x+3)
x2+kx+6 = x2+3x+2x+6
x2+kx+6 = x2+5x+6
Hence, the value of k is 5.
Answer: 41(c)
Explanation: The zero of the polynomial p(x)= cx+d is -d/c.
cx+d = 0
cx = -d
x = -d/c.
Answer: 42(d)
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