Exercise 2 Higher Skill Level Questions
1. Find the sum of first 25 natural numbers.
(a) 432 (b) 315 (c) 325 (d) 335 (e) None of the above
2. Find the sum of the squares of first 35 natural numbers.
(a) 14910 (b) 15510 (c) 14510 (d) 16510 (e) None of the above
3. Find the sum of the cubes of first 15 natural numbers.
(a) 15400 (b) 14400 (C) 16800 (d) 13300
4. Find the sum of first 37 odd numbers.
(a) 1369 (b) 1295 (C) 1388 (d) 1875 (e) None of the above
5. Find the sum of first 84 even numbers.
(a) 7140 (b) 7540 (C) 6720 (d) 8832 (e) None of the above
6. Sum of first 15 multiples of 8 is
(a)960 (b) 660 (C) 1200 (d) 1060
7. The product of four consecutive natural numbers plus one is
(a) a non-square (b) always sum of two square numbers (c) a square
(d) None of the above
8. Find the unit digit in the product of (268 x 539 X 826x 102).
(a) 5 (b) 3 (c) 4 (d) 2 (e) None of the above
9. Find the unit digit in the product of (4326 x 5321).
(a) 6 (b) 8 (c) 1 (d) 3 (e) None of the above
10. What is the unit digit in (6817) 754
(a) 8 (b) 4 (c) 2 (d) 97 (e) None of the above
11. What is the unit digit in (365 x 659 x 771)?
(a) 6 (b) 4 (c) (d) 1 (e) None of the above
12. Find the last two-digits of 15 x 37 x 63 x 51 x 97 x 17
(a) 35 (b) 45 (C) 55 (d) 85
13. How many rational numbers are there between 1 and 1000?
(a) 998 (b) 999 (c) 1000 d) Infinite
14. The sum of 5 consecutive even numbers A, B, C, D and E is 130. What is the product of A and E?
(a) 720 (6) 616 (c) 660 (d) 672 (e) None of the above
15. The sum of the five consecutive numbers is equal to 170. What is the product of largest and the smallest numbers?
(a) 1512 (6) 1102 (C) 1152 (d) 1210 (e) None of the above
16. Which of the following numbers always divides the difference between the squares of two consecutive odd integers?
(a) 7 (b) 3 (c) 8 (d) 6 (e) None of the above
17. A number divided by 56 gives 29 as remainder. If the same number is divided by 8, the remainder will be ...
(a) 4 (b)5 (c) 6 (d) 7
18. On dividing a certain number by 357 the remainder is 39. On dividing the same number by 17, What will be the remainder?
(a) 5 (b) 3 (c) 7 (d) 6 (e) None of the above
19. A number when divided by 5, leaves 3 remainder. What will be the remain when the square of this number is divided by 5?
(a) 3 46) 4 (c) 5 (d) O (e) None of the above
20. In a question on division with zero remainder, a candidate took 12 as divisor instead of 21. The quotient obtained by him was 35. Find the correct quotient.
(a) 10 (b) 12 (c ) 20 (d) 15 (e) None of the above
21. A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
(a) 13 (b) 59 (c) 35 (d) 37
22. The number 58129745812974 is divisible by
(a) 11 (B) 9 (c) 4 (d) None of these
23. How many numbers between - 11 and 11 are multiples of 2 or 3?
(a) 11 (b) 14 (C) 15 (d) None of these
24. Which one of the following numbers is divisible by 11?
(a) 45678940 (b) 54857266 (c) 87524398 d) 93455120
25. When 17200 is divided by 18, find the remainder.
(a) 1 (b) 4 (c) 5 (d) 3 (e) None of the above
26. What is the remainder when 4100 is divisible by 7?
(a) 1 (b) 2 (c) 4 (d) None of these
27. A common factor of (4143 + 4343) and (4141 + 4341) is...
(a) (43 - 41) (b) (4141 + 4341) (c) (4143 + 4343) (d) (41+ 43) (e) None of the above
28.The remainder when 919 + 6 is divided by 8 is
(a) 2 (b) 3 (c) 5 (d) 7
29. What will be the remainder when 19100 is divided by 20
(a) 19 (b) 20 (c) 3 (d) 1
30. It is given that (232 + 1) is exactly divisible by a certain number. Which of the following is also definitely divisible by the same number?
(a) (216 + 1) (b) (216 - 1) (c) 7 x 213 (d) (296 + 1) (e) None of the above
31. The number (6x + 6x) for natural number x is always divisible by ...
(a) 6 and 12 (b) 12 only (c) 6 only (d) 3 only (e) None of the above
32. 195 + 215 is divisible by
(a) Only 10 (b) Only 20 (c) Both 10 and 20 (d) Neither 10 nor 20
33. If ‘a’ is a natural number, then the largest number dividing (a3 - a) is
(a) 4 (b) 5 (c) 6 (d) 7 (e) None of the above
34. 712 - 412 is exactly divisible by which of the following number?
(a) 34 (b) 33 (c) 36 (d) 35
35. If N, (N + 2) and (N + 4) are prime numbers, then the number of possible solutions for N are
(a) 1 (b) 2 (c) 3 (d) None of these
36. The smallest positive prime (say p) such that 2P - 1 is not a prime is
(a) 5 (b) 11 (C) 17 (d) 29
37. If b is the largest square divisor of c and a2 divides c, then which one of the following is correct? (where, a, b and c are integers)
(a) b divides a (b) a does not divide b (c) a divides b (d) a and b are coprime
38. If n is a whole number greater than 1, then no(n? - 1) is always divisible by
(a) 12 (b) 24 (c) 48 (d) 60
39. What is the sum of all positive integers lying between 200 and 400 that are multiples of 7?
(a) 8729 (b) 8700 (C) 8428 (d) 8278
40. Consider the following statements
I. To obtain prime numbers less than 121, we are to reject all the multiples
of 2, 3, 5 and 7.
II. Every composite number less than 121 is divisible by a prime number less than 11.
Which of the statements given above is/are correct?
(a) Only I (b) Only II (c) Both I and II (d) Neither I nor II
41. Consider the following statements
I. 7710312401 is divisible by 11.
II. 173 is a prime number.
Which of the statements given above is/are correct?
(a) Only I (b) Only II (c) Both I and II (d) Neither | nor II
42. If k is a positive integer, then every square integer is of the form
(a) Only 4k (b) 4k or 4k + 3 (c) 4K + 1 or 4k + 3 (d) 4k or 4k + 1
43. Every prime number of the form 3k + 1 can be represented in the form 6m + 1 (where k, m are integers), when
(a) k is odd (b) k is even (c) k can be both odd and even (d) No such form is possible
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