Q.1
If the sum of two numbers is 14 and their difference is 10. Find the product of these two numbers.
Q.2
7 is added to a certain number; the sum is multiplied by 5 ; the product is divided by 9 and 3 is subtracted from the quotient. Thus, if the remainder left is 12, what was the original number ?
Q.3
64329 is divided by a certain number, 175, 114 and 213 appears as three successive remainders. The divisor is -
Q.4
$$\frac{{{{\left( {489 + 375} \right)}^2} - {{\left( {489 - 375} \right)}^2}}}{{\left( {489 \times 375} \right)}} = ?$$
Q.5
What minimum value should be assigned to *, so that 2361*48 is exactly divisible by 9 ?
Q.6
In a division sum, the remainder was 71. With the same divisor but twice the dividend, the remainder is 43. Which one of the following is the divisor ?
Q.7
What is the number of prime factors contained in the product 307 × 225 × 3411 ?
Q.8
12345679 × 72 is equal to :
Q.9
If n is an integer, how many values of n will give an integral value of $$\left( {\frac{{16{n^2} + 7n + 6}}{n}} \right)$$   ?
Q.10
A number when divided by three consecutive numbers 9, 11, 13 leaves the remainders 8, 9 and 8 respectively. If the order of divisors is reversed, the remainders will be :
Q.11
n being any odd number greater than 1, n65 - n is always divisible by :
Q.12
The largest natural number, which exactly divides the product of any four consecutive natural numbers, is :
Q.13
If B > A, then which expression will have the highest value (given that A and B are positive integers)
Q.14
If all the numbers from 501 to 700 are written, what is the total number of times the digit 6 appears ?
Q.15
The number (248 - 1) is exactly divisible by two numbers between 60 and 70. The numbers are :
Q.16
A 4-digit number is formed by repeating a 2-digit number such as 2525, 3232 etc. Any number of this form is exactly divisible by :
Q.17
217 × 217 + 183 × 183 = ?
Q.18
1260 ÷ 14 ÷ 9 = ?
Q.19
Consider the following statements :
1. If x and y are composite numbers, then x + y is always composite.
2. There does not exist a natural number which is neither prime nor composite.
Which of the above statements is/are correct ?
Q.20
The number of digits in the smallest number, which when multiplied by 7 yields all nines, is :
Q.21
The digit in the unit's place of the product (2464)1793 × (615)317 × (131)491 is :
Q.22
1234 + 2345 - 3456 + 4567 = ?
Q.23
(461 + 462 + 463 + 464) is divisible by :
Q.24
A number when divided by 3 leaves a remainder 1. When the quotient is divided by 2, it leaves a remainder 1. What will be the remainder when numbers is divided by 6 ?
Q.25
Consider the following statements for the sequence of numbers given below :
11, 111, 1111, 11111, .....
1. Each number can be expressed in the form (4m + 3), where m is a natural number.
2. Some numbers are squares.
Which of the above statements is/are correct ?
Q.26
74844 ÷ ? = 54 × 63
Q.27
When the square of any odd number, greater than 1, is divided by 8, it always leaves remainder :
Q.28
(46351 - 36418 - 4505) ÷ ? = 1357
Q.29
If a and b are positive integers and $$\frac{(a - b)}{3.5}$$  = $$\frac{4}{7}$$, then:
Q.30
2525 is divided by 26, the remainder is :
Q.31
Find the product of all odd natural numbers less than 5000.
Q.32
38649 - 1624 - 4483 = ?
Q.33
884697 - 773697 - 102479 = ?
Q.34
If 11,109,999 is divided by 1111, then what is the remainder ?
Q.35
In the following sum, '?' stands for which digit :
? + 1? + 2? + ?3 + ?1 = 21?
Q.36
A boy multiplies 987 by a certain number and obtains 559981 as his answer. If in the answer both 9's are wrong but the other digits are correct, then the correct answer will be :
Q.37
How many prime numbers are there between 100 to 200 ?
Q.38
The smallest three-digit prime number is :
Q.39
A 3-digit number 4a3 is added to another 3-digit number 984 to give the four-digit number 13b7, which is divisible by 11. Then, (a + b) is :
Q.40
The digits indicated by * in 3422213** so that this number is divisible by 99 are :
Q.41
(xn - an) is divisible by (x - a)
Q.42
8 + 88 + 888 + 8888 + 88888 + 888888 = ?
Q.43
Two numbers when divided by a certain divisor leave the remainders 4375 and 2986 respectively but when the sum of two numbers is divided by the same divisor, the remainder is 2361. The divisor in question is :
Q.44
The numbers from 1 to 29 are written side by side as follows :
1234567891011121314.....2829
If this number is divided by 9, then what is the remainder ?
Q.45
If m = - 4, n = - 2, then the value of m3 - 3m2 + 3m + 3n + 3n2 + n3 is :
Q.46
If a + b + c = 0, (a + b) (b + c) (c + a) equals
Q.47
If x is a rational number and y is an irrational number, then-
Q.48
The digit in the unit's place of [(251)98 + (21)29 - (106)100 + (705)35 - 164 + 259] is :
Q.49
Which of the following numbers is exactly divisible by 24 ?
Q.50
If p is a positive fraction less than 1, then
0 h : 0 m : 1 s