Mathematics MCQ with answer for CTET, WBPTET exams

QUESTION SET-1

1. A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length is 1 m.

(a) 1850 m2
(b) 1420 m2
(c) 1980 m2
(d) 1998 m2

2. In the Roman numeration system, there are only _______ basic numerals.

(a) 10
(b) 9
(c) 7
(d) 1

3. What is 29 - 28 + 27 - 26 + 25 - 24 + 23- 22 =

(a) 4
(b) 48
(c) 11
(d) 1

4. The number of 25 paise coins in Rs. 100 is _____.

(a) 40
(b) 100
(c) 400
(d) None of these

5. Pushpa is arranging her brother’s books in a new bookshelf which has 3 shelves. After
putting 15 books in each shelf, she found that 5 books are still left outside. How many books are there in total?

(a) 40
(b) 50
(c) 30
(d) 225

6. What is the greatest number that will divide 2930 and 3250 and will leave as remainders 7 and 11 respectively?

(a) 75
(b) 79
(c) 80
(d) 83

7. Mahesh took a loan at 10% P.A. simple interest. After 4 years he returned the principal along with the interest. If he returns in all Rs. 3500, what is the principal amount?

(a) Rs. 3250
(b) Rs. 2500
(c) Rs. 3150
(d) Rs. 2100

8. 77.74 + 25.12 - ? = 90.05

(a) 12.51
(b) 37.43
(c) 12.81
(d) 52.62

9. Pawan prepared 50 show pieces of sandalwood. The cost of production of each piece was Rs. 10. Apart from this he has to pay Rs. 5 per piece as commission to the selling  agent and Rs. 1 per piece to the workshop assistant. What should be the selling price of each article if he wishes to sell them at 30% profit?

(a) Rs. 14.43
(b) Rs. 16.48
(c) Rs. 20.80
(d) Rs. 84.50

10. What least number should be added to 3500 to make it exactly divisible by 42, 49, 56 and 63?

(a) 25
(b) 26
(c) 27
(d) 28

ANSWERS: 1. (c), 2. (c), 3. (a), 4. (c), 5. (b) , 6. (b),  7. (b), 8. (c),  9. (c), 10. (d)

QUESTION SET-2

Q1: 2, 4, 6, 8, 10 ... are
(a) prime numbers
(b) even numbers
(c) odd numbers
(d) none of these

Q2: The roman number CD in decimal form is
(a) 100
(b) 500
(c) 400
(d) 0

Q3: Total number of prime numbers up to 100 are:
(a) 20
(b) 24
(c) 25
(d) 28

Q4: The only even number which is prime
(a) 2
(b) 0
(c) 0 and 2
(d) none

Q5: If 'p' is an odd number, 'q' is an even number and 'r' is an odd number. Then p+q+r is
(a) odd number
(b) even number
(c) any non-prime number
(d) always a prime number

Q6: The two numbers which have only '1' as the common factor are called
(a) prime numbers
(b) composite numbers
(c) primary numbers
(d) co-prime numbers

Q7: The two consecutive natural numbers will always be
(a) odd numbers

(b) composite numbers
(c) co-primes
(d) even numbers

Q8: The smallest number of four digits is:

(a) 0001
(b) 0010
(c) 1000
(d) 1001

Q9: The product of two prime numbers is
(a) composite number
(b) prime number
(c) odd number
(d) even number

Q10: In the series 13,16,49,169, 256, ... what shall be the next number
(a) 512
(b) 169
(c) 361
(d) 289

Q11: Sum of of first 'n' even numbers is:
(a) n×(n+1)/2
(b) n×(n+1)
(c) n2
(d) n2+1

Answers:

1: (b) even numbers
2: (c) 400
3: (c) 25
4: (a) 2
5: (b) even number
6: (d)co-prime numbers
7: (c) co-primes
8: (c) 1000
9: (a) composite number
10: (b) 169
11: (b) n×(n+1)

QUESTION SET -3

Square and Square Roots

Perfect Square

1. A number is called a perfect square if it is expressed as the square of a number.
2. E.g. 1, 4, 9, 16, 25, ... are called perfect squares (1x1 = 1, 2x2 = 4, 3 x 3 = 9...)
3. In square numbers, the digits at the unit’s place are always 0, 1, 4, 5, 6 or 9.
4. The numbers having 2, 3, 7 or 8 at its units' place are not perfect square numbers.
Q1: Which one of the following number is a perfect square:

a) 622
b) 393
c) 5778
d) 625
Answer: d.

5. If a number ends with odd number of zeros then it is not a perfect square.
Q2: Check which of the following is a not a perfect square.
a) 81000
b) 8100
c) 900
d) 6250000
Answer: a) 81000 smile emoticon 92 x 102 x 10)

6. The square of an even number is an even number while the square of an odd number is an odd number.

7. If n is a positive whole number then (n+1)2 - n2 = 2n + 1
or 2n numbers in between the squares of the numbers n and (n + 1)

Q3: Which of the following perfect square numbers, is the square of an odd number?

289, 400, 900, 1600

a) 289
b) 400
c) 900
d) 1600

Answer: a) 289

Q5: Which of the following perfect square numbers, is the square of a even number?
361, 625, 4096, 65536

a) 361
b) 625
c) 4096
d) 2601

Answer: c)

Q6: How many natural numbers lie between squares of 12 and 13.
a) 22
b) 23
c) 24
d) 25

Answer: c) 24 (2x12 = 24)

Q7: A yoga instructor wants to arrange maximum possible number of 6000 students in a ground so that the number of rows is same as the number of columns. How many rows will be there if 71 students were left out after the arrangement.

a) 80
b) 88
c) 77
d) 78

Answer: c) 77. (Hint: Remaining students = 6000 - 71 = 5929 = 11 x 11 x 7 x 7 = 11 x 7 = 77)

Q8: The perfect square number between 30 and 40 is:

a) 32
b) 35
c) 36
d) 39

Answer: c) 36

Q9: Can a prime number be a perfect square?

a) True
b) False

Answer: b) False

8. Unit digits of xn where x, n ∈ W
Units Digit of
Number (x) Units Digit of
the number (xn) No. of possibilities

0 0 1

1 1 1

2 2,4,6,8 4

3 3,9,7,1 4

4 4,6 2

5 5 1

6 6 1

7 7,9,3,1 4

8 8,4,2,6 4

9 9,1 2

Q10: Find the units digit of (564)64 .

a. 2

b. 4

c. 6

d. 8

Answer: (c) 6.

Hint: Option a and d can be easily eliminated, since 2 and 8 never comes in units place in 4x If you see pattern (4 x 4 = 42 = 16 i.e. 42x = 6 at units place) and (4 x 4 x 4 = 43 = 64 i.e. 42x+1 = 4 at units place). Similarly, (4)64 = 6.

9. The sum of first m odd natural numbers is a perfect square and is equal to m2

10. 12 + 22 + 32 + ... + n2 = n(n+1)(2n+1)/6

Q11. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 is a perfect square of number?

a) 8

b) 7

c) 6

d) 9

Answer: a) 8

Q12: The square of an integer is called a perfect square number. If x is a perfect square number, then its next one is

a. x+1,

b. x2 +1,

c. x2 +2x+1,

d. x+2 √x+1.

Answer: d. (Hint: if x is perfect square, then number is √x. Next perfect square will be (√x + 1)2

i.e. x+2 √x+1.

Q12: As shown in figure below, the area of three squares are given. Find the perimeter of ΔABC.

a. 12 units

b. 12.5 units

c. 19.5 units

d. 20 units

Answer: a. (Hint: Length of each side of square is √25 = 5, √9 = 3 and √16 = 4. Perimeter = 5+3+4 = 12units)

11. The sum of 1 and the product of any four consecutive integers is a perfect square.

E.g. 3 x 4 x 5 x 6 + 1 = 360 + 1 = 361 = √361 = 19

12. To find square root of a number, we generally use following two methods:

Factorization Method: Finding prime factors of a number

Long Division method.

Q13: Find the least perfect square number which is divisible 16, 20 and 24?

Answer: Take the LCM of 16, 20 and 24 which is the least number divisible by all three.

i.e. LCM(16,20,24) = 4x4x5x3 = 240

To make 240 perfect square (multiply by 3x5) = 42 x 52 x 32 = 3600 ...(answer)

______

Q14. Compute √0.0016

Answer: √(0.0016) = √(16/10000) = √(42 x 10-4 ) = 4 x 10-2 = 0.04