## SOE MERITORIOUS ANSWER KEY CLASS 9 MATHEMATICS 2024

31. If the abscissa of a point x is zero then where will be the point locate?

Explanation: The abscissa of a point is its x-coordinate. If the x-coordinate is zero, then the point lies on the y-axis.

32. In the given figure find the percentage of shaded region.

(A) 45% (B) 33.34% (C) 35% (D) 37.5%

33. If the sum of two numbers is 6 and difference is 4 then what will be the numbers.

(A) -5, 1 (B) -5, -1 (C) 5, 1 Correct Answer (D) 5,-1

Explanation: Let the two numbers be x and y. We know that x + y = 6 and x - y = 4. Solving these two equations, we get x = 5 and y = 1.

34. If 15 workers can build a wall in 48 hours then how many workers will be required to do the same wall in 30 hours.

(A) 12 (B) 24 Correct Answer (C) 96 (D) 54

Explanation: Let the number of workers required be w. The more workers you have, the less time it takes to complete the job. This is an inverse proportion relationship. We can express this relationship as w * 48 = 15 * 30. Solving for w, we get w = 24.

35. If a number is 64 times the reciprocal of its square then find the number.

(A) 4 Correct Answer (B) 5 (C) 8  (D) 16

36. What is the multiplicative inverse of -7/19

(A) 0 (B) -19/7 Correct Answer (C) 7/19 (D) -7/19

Explanation: The multiplicative inverse of a number is the number that you multiply by to get 1. The multiplicative inverse of -7/19 is -19/7.

37. What will be the solution of 4x-3 = 9

(A) 12 (B) 3 Correct Answer (C) 2 (D) 4

Explanation: Add 3 to both sides and then divide both sides by 4 to get x = 3.

38. What are the factors of 3x-9

(A) 3x(x+3) (B) x(x-3)  (C) x(3x-3) (D) 3(x-3) Correct Answer

Explanation: Factor out a 3 to get 3(x-3).

39. The multiplicative identity of rational number is:

(A) 0 (B) 2 (C) 1 Correct Answer (D) -1

Explanation: The multiplicative identity of any number system is the number that you multiply by to get the same number. The multiplicative identity of rational numbers is 1.

40. Which of the following point is on x-axis

(A) (0,3) (B) (3,0) Correct Answer (C) (1, 1) (D) (2, 5)

Explanation: A point on the x-axis has a y-coordinate of 0.

Sure, all the multiple choice questions (MCQs) and their answers from the image you sent are:

41. What will be added to 2 - 3x for get 2

(A) 3x Correct Answer (B) -3x (C) 25  (D) -2

42. With which number 533163 is divisible

(A) 5 (B) 3 Correct Answer (C) 4 (D) 2

Explanation: A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the digits of 533163 is 21 which is divisible by 3.

43. The diagonals of a rectangle are (2x+1) and (3x-1). Find the value of x.

(A) 1 (B) 2 Correct Answer (C) 3 (D) 4

Explanation: In a rectangle, the diagonals bisect each other at right angles. When two squares bisect each other, their sides are proportional. Set up a proportion to find x: (2x + 1) / (3x - 1) = 1. Solve for x to get x = 2.

44. ABCD is a parallelogram. If ∠A = 45°, then what will be the adjacent angle

(A) 135° Correct Answer (B) 120° (C) 115° (D) 180°

Explanation: In a parallelogram, opposite angles are equal and supplementary angles add up to 180°. Since angle A is 45 degrees, its opposite angle (the angle adjacent to it) must also be 45 degrees. Angles on a straight line add up to 180 degrees, so the sum of the two angles adjacent to a pair of opposite angles must be 180 degrees. Therefore, the adjacent angle to the 45-degree angle must be 180 - 45 = 135 degrees. However, the question asks for the adjacent angle, which is the angle next to it on the parallelogram, and not the opposite angle. In a parallelogram, adjacent angles are supplementary, so the adjacent angle must be 180° - 45° = 135°.

45. What will be the graph of x = 2

(A) A line parallel to x-axis  (B) A line parallel to y-axis Correct Answer (C) A line crossing the main point (D) None of these

Explanation: The equation of a vertical line is always x = a constant, where a is any real number. So the graph of x = 2 is a vertical line that intersects the x-axis at x = 2 and extends infinitely upwards and downwards.

46. What is the value of (2×3)^0 × 6

(A) 1  (B) 0 (C) 6 Correct Answer (D) -6

Explanation: Anything to the 0th power equals 1, except for 0 itself. Since we have 2 x 3 in the equation before taking it to the 0th power, we are not dividing by zero and so anything to the 0th power equals 1. Then we multiply by 6 to get 1 x 6 = 6.

47. What is the product of (x²+x+1) and (x-1)?

(A) x³-1 Correct Answer (B) x³+1 (C) x³-2 (D) 2x²+1

48. The perimeter of a rectangle is 180 cm. If the length is double than the breadth then what will be the length?

(A) 60 cm Correct Answer (B) 9 cm (C) 90 cm (D) 30 cm

Explanation: Let the breadth be x cm. Then the length is 2x cm. The perimeter is the total length of all the sides of the shape added together. So the perimeter is 2x + x + 2x + x = 6x. We are given that the perimeter is 180 cm, so set up the equation 6x = 180 and solve for x. Divide both sides by 6 to get x = 30. Since the length is double the breadth, the length is 2 * 30 cm = 60 cm.

49. 0.08 × 10¹⁰ is equals to

(A) 80000000 (B) 800 (C) 8000  (D) 8

Correct Answer 800000000 all options wrong

50. How many numbers are there between squares of 15 and 16?

(A) 30 (B) 31  (C) 32 Correct Answer (D) 33

Explanation: The square of 15 is 15 × 15 = 225 and the square of 16 is 16 × 16 = 256. So we need to find how many integers there are between 225 and 256 (inclusive). Counting 225 and 256, there are 32 integers.

51. What will be the value of 5(³√8000)?

(A) 10 (B) 5000 (C) 100 Correct Answer (D) 500

Sure, all the multiple choice questions (MCQs) and their answers from the image you sent are:

52. ABC is a right angled triangle. If AB=12 cm. BC=5 cm. What will be the length of AC?

(A) 13 (B) 12

(C) 5 (D) 169

53. In a class of 80 students if 40% of the students passed in subject of English, then how many students not passed in the subject of English?

(A) 32 (B) 48 Correct Answer (C) 22 (D) 52

Explanation: We can find the number of students who did not pass by subtracting the number who passed from the total number of students. Since 40% of the students passed, then 100% - 40% = 60% of the students did not pass. Multiply the total number of students by 60% to find the number who did not pass: 80 students * 60% = 48 students.

54. How many rational numbers are there between two rational numbers?

(A) Infinite (B) 1

(C) 2 (D) 3

Explanation: There are infinitely many rational numbers between any two rational numbers. This is because between any two rational numbers, you can find another rational number by taking the average of the two original numbers. You can then repeat this process infinitely many times, always finding a new rational number between the two original numbers.

55. Write the rational number which is equal to its negative.

(A) 0 Correct Answer (B) 1

(C) 2 (D) 3

Explanation: The only rational number that is equal to its negative is 0. Any other rational number, positive or negative, will have a different opposite.

56. The area of a trapezium is 480 cm². If the distance between two parallel sides is 15 cm and one of them is 20 cm long, find the length of the another parallel side.

(A) 50 (B) 40  (C) 36 (D) 44 Correct Answer

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