2251 + Mcqs in Number System Page 8 McqOptions

351.	Let S be the set of integers x such thati. 100 ≤ x ≤ 200ii. x is odd andiii. x is divisible by 3 but not by 7How many elements does S contain?
A.	16
B.	12
C.	11
D.	13
Answer» E.

Discussion

352.	A 6-digit number is formed by repeating a 3-digit number; for example, 256256 or 678678 etc. Any number this form is always exactly divisible by
A.	7 only
B.	11 only
C.	13 only
D.	1001
Answer» E.

Discussion

353.	In a class, Ashwin finds that number of students who have performed better than him is thrice the number of students who have done worse than him. If Ashwin's rank is 61, then the total number of students in the class is equal to
A.	80
B.	81
C.	82
D.	83
Answer» C. 82

Discussion

354.	For real x, the maximum possible value of x/√(1 + x4) is
A.	\(\frac{1}{{\sqrt 2 }}\)
B.	\(\frac{1}{2}\)
C.	\(\frac{1}{{\sqrt 3 }}\)
D.	1
Answer» B. \(\frac{1}{2}\)

Discussion

355.	If the number 89765A4B, where A and B are different digits, is divisible by 9, and the number is even, then the number of possible values of the pair (A, B) is:
A.	4
B.	5
C.	6
D.	11
Answer» C. 6

Discussion

356.	A bag contains 50 p, 25 p and 10 p coins in the ratio 5 : 9 : 4 amounting to Rs. 206. Find the number of coins of each type
A.	100, 250, 120
B.	150, 270, 120
C.	200, 360, 160
D.	250, 450, 200
Answer» D. 250, 450, 200

Discussion

357.	Calculate the sum of squares from 1 to 9.A. 284B. 285C. 385D. 380
A.	B
B.	C
C.	D
D.	A
Answer» B. C

Discussion

358.	A trader purchased 132 dozens of mangoes at Rs. 475 per dozen and could sell only 125 dozens at Rs. 530 per dozen. What is the value of stock of mangoes in hand (in rupees)?
A.	3325
B.	4250
C.	3710
D.	4620
Answer» B. 4250

Discussion

359.	Find the number of prime factors in the product (30)5 × (24)5.
A.	35
B.	45
C.	10
D.	30
Answer» B. 45

Discussion

360.	It r is the remainder when each of 6454, 7306 and 8797 is divided by the greatest number d (d > 1), then (d - r) is equal to:
A.	126
B.	64
C.	137
D.	149
Answer» E.

Discussion

361.	How many numbers between 300 and 700 are divisible by 5, 6 and 8?
A.	3
B.	2
C.	20
D.	5
Answer» B. 2

Discussion

362.	In a group of 100 children, 64 children like to play cricket, 53 children like to play football and 20 children like to play both cricket and football. How many children do NOT like to play cricket or football?
A.	3
B.	5
C.	7
D.	9
Answer» B. 5

Discussion

363.	Consider the following statements in respect of two integers p and q (both > 1) which are relatively prime:1. Both p and q may be prime numbers.2. Both p and q may be composite numbers.3. One of p and q may be prime and the other composite.Which of the above statements are correct?
A.	1 and 2 only
B.	2 and 3 only
C.	1 and 3 only
D.	1, 2 and 3
Answer» E.

Discussion

364.	If 8219x is divisible by 11, what will be the value of x?
A.	5
B.	2
C.	3
D.	4
Answer» C. 3

Discussion

365.	If u2 + (u−2v−1)2 = −4v(u + v), then what is the value of u + 3v?
A.	0
B.	-1/4
C.	1/4
D.	1/2
Answer» C. 1/4

Discussion

366.	P(n): 22N - 1, n ϵ N is divisible by
A.	4
B.	3
C.	5
D.	None of these
Answer» C. 5

Discussion

367.	Find the LCM of x and (x + 3)
A.	x (x + 3)
B.	x2 (x + 3)
C.	(x + 3)
D.	x
Answer» B. x2 (x + 3)

Discussion

368.	How many numbers are there from 500 to 590 which are divisible by both 2 and 7?
A.	6
B.	7
C.	9
D.	8
Answer» C. 9

Discussion

369.	If \(\dfrac{\sqrt{3}-1}{\sqrt{3}+1}-\dfrac{5+2\sqrt{3}}{7+4\sqrt{3}}=a+b\sqrt{3}\), then the value of (a + b) is;
A.	8
B.	-5
C.	9
D.	-4
Answer» E.

Discussion

370.	Find the HCF of 18, 45 and 72?
A.	6
B.	9
C.	3
D.	8
Answer» C. 3

Discussion

371.	A school has 250 students out of which only 50 like to play football, 47 chess and 40 tennis. 35 students like to play both football and tennis, 33 both chess and tennis, 38 football and chess. If 27 students do not like any of the three sports, find the number of students who like all sports.
A.	13
B.	20
C.	23
D.	10
Answer» E.

Discussion

372.	1?3Find the missing digit if it has 11 and 13 as factors?
A.	2
B.	6
C.	8
D.	4
Answer» E.

Discussion

373.	In a Company, the number of engineers doubles itself every 2 years. In how much time will the number of engineers become 1024 times of its original number?
A.	12 years
B.	20 years
C.	15 years
D.	24 years
Answer» C. 15 years

Discussion

374.	If 2343X is completely divisible by 4, then what is the value of X?
A.	2
B.	4
C.	6
D.	2 or 6
Answer» E.

Discussion

375.	An electronic device makes a beep after every 60 seconds. Another device makes a beep after every 62 seconds. They beeped together at 10.00 a.m. The next time when they would beep together at the earliest one is:
A.	10.30 a.m.
B.	10.31 a.m.
C.	10.59 a.m.
D.	11.00 a.m.
Answer» C. 10.59 a.m.

Discussion

376.	If a nine-digit number 43x1145y2 is divisible by 88, then the value of (2x - y), for the largest value of y, is:
A.	1
B.	5
C.	0
D.	-1
Answer» B. 5

Discussion

377.	____ is the product of the maximum number of each prime factor that occurs in either of the numbers.
A.	Unit digit
B.	Least common multiple
C.	Highest common factor
D.	Multiples
Answer» C. Highest common factor

Discussion

378.	HCF of 12, 18, 24 is
A.	6
B.	12
C.	2
D.	18
Answer» B. 12

Discussion

379.	A flask holds \({1{\frac{1}{4}}}\) liters of tea. How many mugs can be filled with the tea from the flask, if each mug can hold 250 ml of tea?
A.	6
B.	4
C.	5
D.	2
Answer» D. 2

Discussion

380.	Divide 44(x4 – 5x3 – 24x2) by 11x (x – 8):
A.	4x(x – 8)
B.	4x(x + 8)
C.	4x(x – 3)
D.	4x(x + 3)
Answer» E.

Discussion

381.	If k is an integer, then x2 + 7x – 14 (k2 – 7/8) = 0 has
A.	Both integral roots
B.	At least one integral roots
C.	No integral roots
D.	Both positive integral roots
Answer» D. Both positive integral roots

Discussion

382.	If 449 × 445× 451 is divided by 6, then what will be the remainder?
A.	5
B.	1
C.	3
D.	2
Answer» B. 1

Discussion

383.	Insert mathematical symbols in the place of ? To get the result.((10 ? 10) ? 25) ? 10 = 10
A.	-, ×, ÷
B.	×, ×, +
C.	+, ÷, ÷
D.	-, ×, +
Answer» E.

Discussion

384.	Find the LCM of two consecutive integers a and b.
A.	4ab
B.	ab/2
C.	ab
D.	2ab
Answer» D. 2ab

Discussion

385.	A teacher wants to arrange maximum possible number of 6000 students in a field such that the number of rows is equal to the number of columns. Find the number of rows, if 71 students were left out after arrangement.
A.	80
B.	77
C.	78
D.	76
Answer» C. 78

Discussion

386.	In a division operation the quotient is 125, divisor is 28 and remainder is 13. The dividend is
A.	3513
B.	3613
C.	3216
D.	3487
Answer» B. 3613

Discussion

387.	If HCF of (p2 - 8p + 12) and (p2 + 4p - 12) is (p - a), then the value of a is
A.	-6
B.	2
C.	-2
D.	6
Answer» C. -2

Discussion

388.	\(\frac{{{{\left( {598 + 479} \right)}^2} - {{\left( {598 - 479} \right)}^2}}}{{598 \times 479}} = \;?\)
A.	4
B.	10
C.	132
D.	8
E.	None of the above/More than one of the above
Answer» B. 10

Discussion

389.	If an 8-digit number 179x091y is divisible by 88, the value of (5x – 8y) is∶
A.	5
B.	4
C.	9
D.	7
Answer» C. 9

Discussion

390.	How many whole numbers are there between 52 and 356 which are exactly divisible by 6?
A.	49
B.	51
C.	53
D.	55
Answer» C. 53

Discussion

391.	Find the values of k for which x2 + 5kx + k2 + 5 is exactly divisible by x + 2 but not divisible by x + 3.
A.	Both 1 and 9
B.	9
C.	1
D.	Neither 1 nor 9
Answer» C. 1

Discussion

392.	In a gathering of 75 people, 35 people can speak English and 50 people can speak Hindi. How many people can speak both the languages?
A.	10
B.	15
C.	25
D.	35
Answer» B. 15

Discussion

393.	A motor runs for 3 mins and then stops to cool down for 2 mins. For each minute the motor runs, it consumes 1.5 units of electricity. In 4 hours, how much electricity would it consume?
A.	144 units
B.	216 units
C.	312 units
D.	388 units
Answer» C. 312 units

Discussion

394.	Convert binary 1010101 to decimal.
A.	85
B.	87
C.	89
D.	91
Answer» B. 87

Discussion

395.	Five bells commence tolling together and toll at intervals of 2, 4, 9, 12 and 15 seconds respectively. In 45 minutes, how many times do they toll together?
A.	10
B.	16
C.	15
D.	8
Answer» C. 15

Discussion

396.	A bag contains an equal number of one rupee, 50 paisa and 25 paisa coins respectively. If the total value is Rs 35, how many coins of each type are there ?
A.	20
B.	16
C.	18
D.	25
Answer» B. 16

Discussion

397.	If m is the number of prime numbers between 0 and 50; and n is the number of prime numbers between 50 and 100, then what is (m – n) equal to?
A.	4
B.	5
C.	6
D.	7
Answer» C. 6

Discussion

398.	Calculate the total numbers of prime factors in the expression (9)11 × (5)7 × (7)5 × (3)2 × (17)2
A.	35
B.	36
C.	37
D.	38
Answer» E.

Discussion

399.	If a positive integer 'n' is divisible by 3, 5 and 7, then what is the next larger integer divisible by all these numbers?
A.	n + 105
B.	n + 21
C.	n + 35
D.	n + 110
Answer» B. n + 21

Discussion

400.	Five bells begin to toll together at intervals of 9 seconds, 6 seconds, 4 seconds, 10 seconds and 8 seconds respectively. Starting together, how many times will the bells toll together in a span of 1 hour?
A.	11
B.	12
C.	5
D.	10
Answer» B. 12

Discussion

Explore topic-wise MCQs in Digital Circuits.

Let S be the set of integers x such thati. 100 ≤ x ≤ 200ii. x is odd andiii. x is divisible by 3 but not by 7How many elements does S contain?

A 6-digit number is formed by repeating a 3-digit number; for example, 256256 or 678678 etc. Any number this form is always exactly divisible by

In a class, Ashwin finds that number of students who have performed better than him is thrice the number of students who have done worse than him. If Ashwin's rank is 61, then the total number of students in the class is equal to

For real x, the maximum possible value of x/√(1 + x4) is

If the number 89765A4B, where A and B are different digits, is divisible by 9, and the number is even, then the number of possible values of the pair (A, B) is:

A bag contains 50 p, 25 p and 10 p coins in the ratio 5 : 9 : 4 amounting to Rs. 206. Find the number of coins of each type

Calculate the sum of squares from 1 to 9.A. 284B. 285C. 385D. 380

A trader purchased 132 dozens of mangoes at Rs. 475 per dozen and could sell only 125 dozens at Rs. 530 per dozen. What is the value of stock of mangoes in hand (in rupees)?

Find the number of prime factors in the product (30)5 × (24)5.

It r is the remainder when each of 6454, 7306 and 8797 is divided by the greatest number d (d > 1), then (d - r) is equal to:

How many numbers between 300 and 700 are divisible by 5, 6 and 8?

In a group of 100 children, 64 children like to play cricket, 53 children like to play football and 20 children like to play both cricket and football. How many children do NOT like to play cricket or football?

Consider the following statements in respect of two integers p and q (both > 1) which are relatively prime:1. Both p and q may be prime numbers.2. Both p and q may be composite numbers.3. One of p and q may be prime and the other composite.Which of the above statements are correct?

If 8219x is divisible by 11, what will be the value of x?

If u2 + (u−2v−1)2 = −4v(u + v), then what is the value of u + 3v?

P(n): 22N - 1, n ϵ N is divisible by

Find the LCM of x and (x + 3)

How many numbers are there from 500 to 590 which are divisible by both 2 and 7?

If \(\dfrac{\sqrt{3}-1}{\sqrt{3}+1}-\dfrac{5+2\sqrt{3}}{7+4\sqrt{3}}=a+b\sqrt{3}\), then the value of (a + b) is;

Find the HCF of 18, 45 and 72?

A school has 250 students out of which only 50 like to play football, 47 chess and 40 tennis. 35 students like to play both football and tennis, 33 both chess and tennis, 38 football and chess. If 27 students do not like any of the three sports, find the number of students who like all sports.

1?3Find the missing digit if it has 11 and 13 as factors?

In a Company, the number of engineers doubles itself every 2 years. In how much time will the number of engineers become 1024 times of its original number?

If 2343X is completely divisible by 4, then what is the value of X?

An electronic device makes a beep after every 60 seconds. Another device makes a beep after every 62 seconds. They beeped together at 10.00 a.m. The next time when they would beep together at the earliest one is:

If a nine-digit number 43x1145y2 is divisible by 88, then the value of (2x - y), for the largest value of y, is:

____ is the product of the maximum number of each prime factor that occurs in either of the numbers.

HCF of 12, 18, 24 is

A flask holds \({1{\frac{1}{4}}}\) liters of tea. How many mugs can be filled with the tea from the flask, if each mug can hold 250 ml of tea?

Divide 44(x4 – 5x3 – 24x2) by 11x (x – 8):

If k is an integer, then x2 + 7x – 14 (k2 – 7/8) = 0 has

If 449 × 445× 451 is divided by 6, then what will be the remainder?

Insert mathematical symbols in the place of ? To get the result.((10 ? 10) ? 25) ? 10 = 10

Find the LCM of two consecutive integers a and b.

A teacher wants to arrange maximum possible number of 6000 students in a field such that the number of rows is equal to the number of columns. Find the number of rows, if 71 students were left out after arrangement.

In a division operation the quotient is 125, divisor is 28 and remainder is 13. The dividend is

If HCF of (p2 - 8p + 12) and (p2 + 4p - 12) is (p - a), then the value of a is

\(\frac{{{{\left( {598 + 479} \right)}^2} - {{\left( {598 - 479} \right)}^2}}}{{598 \times 479}} = \;?\)

If an 8-digit number 179x091y is divisible by 88, the value of (5x – 8y) is∶

How many whole numbers are there between 52 and 356 which are exactly divisible by 6?

Find the values of k for which x2 + 5kx + k2 + 5 is exactly divisible by x + 2 but not divisible by x + 3.

In a gathering of 75 people, 35 people can speak English and 50 people can speak Hindi. How many people can speak both the languages?

A motor runs for 3 mins and then stops to cool down for 2 mins. For each minute the motor runs, it consumes 1.5 units of electricity. In 4 hours, how much electricity would it consume?

Convert binary 1010101 to decimal.

Five bells commence tolling together and toll at intervals of 2, 4, 9, 12 and 15 seconds respectively. In 45 minutes, how many times do they toll together?

A bag contains an equal number of one rupee, 50 paisa and 25 paisa coins respectively. If the total value is Rs 35, how many coins of each type are there ?

If m is the number of prime numbers between 0 and 50; and n is the number of prime numbers between 50 and 100, then what is (m – n) equal to?

Calculate the total numbers of prime factors in the expression (9)11 × (5)7 × (7)5 × (3)2 × (17)2

If a positive integer 'n' is divisible by 3, 5 and 7, then what is the next larger integer divisible by all these numbers?

Five bells begin to toll together at intervals of 9 seconds, 6 seconds, 4 seconds, 10 seconds and 8 seconds respectively. Starting together, how many times will the bells toll together in a span of 1 hour?