ctet objective math sample paper

Test of Numerical Ability for Forthcomming Exam

1. Let A = (x + 1)/(x – 1 ) and B = (x – 1)/(x + 1). Determine the value of A – B
a. 0
b. x/(x² - 1)
c. 4x/(x² - 1)
d. None of these

2. Ashok had to do a multiplication. Instead of taking 35 as one of the multipliers, he took 53. As a result, the product went up by 540. What is the new product ?
a. 1050
b.1590
c. 1440
d. none of these

3. A ladder on a road when inclined on a wall reaches a point 12 m above ground. Placing at the same position if it is inclined on to other side of a road, it reaches a point 9m above the ground. If the length of ladder is 15 m, what is the width of the road ?
a. 17 m
b. 23 m
c. 19 m
d. 21 m

4. The rate of interest on two bonds is in the ratio of 4 : 5. A person wants to invest his savings in these bonds in such a way that he received equal half yearly interest from both the bonds. He should invest in these bonds in the ratio :
a. 5 : 2
b. 2 : 5
c. 4 : 5
d. 5 : 4

5. A student secured 60, 75 and 85 in Mathematics monthly test. If monthly scores were given equal weightage and final scores are given double weightage , what are his average marks in Mathematics ?
a. 65
b. 75
c. 80
d. None of these

6. A sells a product having a printed price of Rs.2,400 at a discount of 10% on printed price. He earns a profit of 25% in this sale. What was the purchase price on which A purchased this product ?
a. Rs.1980
b. Rs.1728
c. Rs.2160
d. Rs.1800

7. A wheel travels a distance of 22 km in 2500 revolutions. Find the diameter of the wheel.
a. 1.4 m
b. 2.8 m
c. 5.6 m
d. None of these

8. The difference between the compound interest and simple interest on a sum of money at the rate of 10% p.a. for 2 years is Rs.50. Find the principal amount.
a. Rs.5,500
b. Rs.4,000
c. Rs.5,000
d. None of these

9. If the numerator of a fraction is doubled and the denominator is increased by 3, the new fraction is 3/5. What is the original fraction if its denominator is more than twice the numerator by 1 ?
a. 3/7
b. 6/13
c. 1/3
d. 5/11

10. Three taps A, B and C can fill the tank in 30 minutes, 45 minutes and 60 minutes respectively. All the three taps are opened simultaneously and after 10 minutes, tap C is closed and another tap D is opened. It took another 20 minutes to fill the tank. How much time does tap D take to empty a full tank ?
a. 18 minutes
b. 24 minutes
c. 30 minutes
d. 36 minutes

11. A rod of length 300 inches is to be cut into three pieces of integer length such that length of the first piece is square of the second and that of the second is square of the third. What is the length of the left out portion, if the left out portion has to be the least ?
a. 12 inches
b. 24 inches
c. 8 inches
d. 30 inches

12. The amount on a certain sum for 3 and 4 years at a certain rate of compound interest are Rs.18250.50 and Rs.20988.10 respectively. What is the rate of interest ?
a. 10%
b. 12%
c. 13%
d. None of these

13. The difference between simple interest and compound interest on a certain sum of money for 2 years at 10% p.a. is Rs.4200. The sum is :
a. Rs.20,000
b. Rs.16,000
c. Rs.24,000
d. None of these

14. In an examination A gets 40% of total marks and B gets 80% of that of A. C gets 60% of A’s and B’s marks taken together. D gets 45% of A’s and C’s marks taken together. If the required pass percentage is 36, how many of these four students passed the examination ?
a. 1
b. 2
c. 3
d. 4

15. In a school, the number of girls exceeds the number of boys by 60. If the number of girls is increased by 15% and the number o boys is increased by 50%, there would be 15 boys more than girls. Find the original strength of the class ?
a. 540
b. 360
c. 720
d. 600

16. An investor invested a sum of Rs.10 lakhs in shares of company X and of company Y. Company X’s share yields 24% in cash each year and the rate of interest on company Y’s debentures is 16%. He received a total of Rs.2,08,000 in the form of dividend and interest from these two companies. How much money was invested in company X ?
a. 400000
b. 600000
c. 650000
d. None of these

17. A dry fruit seller purchased 3 kinds of nuts at the rate of Rs.100/kg, Rs.80/kg and Rs.60/kg respectively. He then mixed them in the ratio of 3 : 4 : 5 by weight and sold the same to a customer at 50% profit. The price per kg at which he sold the mix to the customer is :
a. Rs.110
b. Rs.90
c. Rs.70
d. None of these

18. A, B and C were partners sharing profits in the ratio of 2 : 3 : 4 : 6. D died and his share was distributed equally among the surviving partners. What will be the new profits sharing ratio ?
a. 4 : 5 : 6
b. 2 : 3 : 4
c. 3 : 4 : 5
d. None of these

19. A vehicle changed hands 3 times and at each time the loss to the earlier owner was 10%. If the overall loss was Rs.4,065, find the original price of the vehicle (in rupees).
a. 10,000
b. 10,500
c. 15,000
d. 5,000

20. What is the three digit number which is a 2 more than a perfect square and 2 less than a perfect cube ?
a. 627
b. 402
c. 123
d. None of these

21. If it costs Rs.Y to whitewash the 4 walls of a room, how much would it cost(in rupees), if all the dimensions were to be 5 times the original dimensions ?
a. 5 Y
b. 25 Y
c. 25 Y²
d. 20 Y

22. A sum of Rs.4000 was lent partly at 6% and partly at 8% simple interest. If the interest received after one year is Rs.272, find the ratio in which the money was lent.
a. 2 : 3
b. 3 : 2
c. 1 : 2
d. None of these

23. A man pays off 3/20 of his debt every month . At the end of 6 months, his remaining debt is Rs.290. How much amount (in rupees) has he cleared off every month ?
a. 400
b. 435
c. 450
d. 500

24. Y wanted to borrow Rs.1000 from a moneylender for a period of one year. However, the moneylender deducted Rs.200 as interest charges and gave Rs.800 to him. What is the rate of interest at which Y has borrowed the money ?
a. 20%
b. 22.5%
c. 25%
d. 27.5%

25. If the interest compounded annually on a certain sum at a certain rate of interest for 2 years is equal to 55% of the simple interest on the same amount at the same rate of interest for twice the time period, find the rate of interest.
a. 12%
b. 20%
c. 24%
d. None of these

ANSWER
1. c 2. b 3. d 4. d 5. d
6. b 7. b 8. c 9. a 10. b

11. b 12. d 13. d 14. c 15. a
16. b 17. d 18. a 19. c 20. c
21. b 22. b 23. b 24. c 25. b