1. 1. If the following groups of fractions is arranged in ascending order?

A. [latex]\frac{5}{16}[/latex], [latex]\frac{7}{18}[/latex], [latex]\frac{6}{17}[/latex] B. [latex]\frac{7}{18}[/latex], [latex]\frac{6}{17}[/latex], [latex]\frac{5}{16}[/latex] C. [latex]\frac{5}{16}[/latex], [latex]\frac{6}{17}[/latex], [latex]\frac{7}{18}[/latex] D. [latex]\frac{6}{17}[/latex], [latex]\frac{7}{18}[/latex], [latex]\frac{5}{16}[/latex]

Answer - Option C
Explanation -
[latex]\frac{5}{16}[/latex] = 0.312
[latex]\frac{6}{17}[/latex] = 0.352
[latex]\frac{7}{18}[/latex] = 0.388
2. If fractions[latex]\frac{9}{13}[/latex], [latex]\frac{2}{3}[/latex], [latex]\frac{8}{11}[/latex], [latex]\frac{5}{7}[/latex], are arranged in ascending order, then the correct sequenceis

A. [latex]\frac{9}{13}[/latex], [latex]\frac{2}{3}[/latex], [latex]\frac{8}{11}[/latex], [latex]\frac{5}{7}[/latex] B. [latex]\frac{2}{3}[/latex], [latex]\frac{9}{13}[/latex], [latex]\frac{5}{7}[/latex], [latex]\frac{8}{11}[/latex] C. [latex]\frac{2}{3}[/latex], [latex]\frac{8}{11}[/latex], [latex]\frac{5}{7}[/latex], [latex]\frac{9}{13}[/latex] D. [latex]\frac{5}{7}[/latex], [latex]\frac{8}{11}[/latex], [latex]\frac{2}{3}[/latex], [latex]\frac{9}{13}[/latex]

Answer - Option B
Explanation -
[latex]\frac{9}{13}[/latex] = 0.692, [latex]\frac{2}{3}[/latex] = 0.666,
[latex]\frac{8}{11}[/latex] = 0.727, [latex]\frac{5}{7}[/latex] = 0.714
Hence ascending order is [latex]\frac{2}{3}[/latex] = [latex]\frac{9}{13}[/latex], [latex]\frac{5}{7}[/latex], [latex]\frac{8}{11}[/latex]
3. Which one of the following is the largest? 2[latex]\sqrt{5}[/latex], 6[latex]\sqrt{3}[/latex], 3[latex]\sqrt{7}[/latex] and 8[latex]\sqrt{2}[/latex]

A. 8[latex]\sqrt{2}[/latex] B. 2[latex]\sqrt{5}[/latex] C. 6[latex]\sqrt{3}[/latex] D. 3[latex]\sqrt{7}[/latex]

Answer - Option A
Explanation -
2[latex]\sqrt{5}[/latex] = 2 * 2.236 = 4.472
6[latex]\sqrt{3}[/latex] = 6 * 1.732 = 10.392
3[latex]\sqrt{7}[/latex] = 3 * 2.646 = 7.938
8[latex]\sqrt{2}[/latex] = 8 * 1.414 = 11.312
Clearly8[latex]\sqrt{2}[/latex] is largest
4. I f numer at or and denomi nat or of a pr oper fractions are increased by the same quantity, then the resulting fraction is

A. always greater than the original fraction B. always less than the original fraction C. always equal to the original fraction D. none of these

Answer - Option A
Explanation -
Let proper fraction = [latex]\frac{2}{3}[/latex] =
therefore Resulting fraction = [latex]\frac{2 + 1}{3 + 1}[/latex] = [latex]\frac{3}{4}[/latex]
Hence [latex]\frac{2}{3}[/latex] < [latex]\frac{3}{4}[/latex]
[latex]\frac{1}{2}[/latex] < [latex]\frac{2}{3}[/latex]
[latex]\frac{3}{5}[/latex] < [latex]\frac{3 + 1}{5 + 1}[/latex]
[latex]\frac{3}{5}[/latex] < [latex]\frac{4}{6}[/latex] etc.
5. If x + y > 5 and x – y > 3, then which of the following gives all possible values of x ?

A. x > 3 B. x > 4 C. x > 5 D. x < 5

Answer - Option B
Explanation -
Solving x + y > 5 and x – y > 3 we get,
x > 4.
6. I f x and y ar e negat ive, then which of the following statements is/are always true ?

I. x + y is positive II. xy is positive III. x – y is positive

A. I only B. II only C. III only D. I and III only

Answer - Option B
Explanation -
Product of – ve numbers is also +ve.
7. The value of [latex]\sqrt{ \sqrt{0.000064}}^{3}[/latex]

A. 0.02 B. 0.2 C. 2.0 D. None

Answer - Option B
Explanation - Given expression =[latex]\sqrt{0.008}^{3}[/latex] = 0.2
8. If 11, 109, 999 is divided by 1111, then what is the remainder ?

A. 1098 B. 11888 C. 1010 D. 1110

Answer - Option D
Explanation -
9. The value of [latex]\frac {\frac{1}{2}\frac{1}{2}of \frac{1}{2}}{\frac{1}{2}\frac{1}{2}of \frac{1}{2}}[/latex]

A. 2[latex]\frac{2}{3}[/latex] B. 1 C. 1[latex]\frac{1}{3}[/latex] D. 3

Answer - Option A
Explanation -
[latex]\frac {\frac{1}{2}\frac{1}{2} * \frac{1}{2}}{\frac{1}{2}\frac{1}{2} * \frac{1}{2}}[/latex]
= [latex]\frac {\frac {1}{2} \frac{4}{1}}{\frac{3}{4}}[/latex] = 2 * [latex]\frac{4}{3}[/latex]
= [latex]\frac{8}{3}[/latex]
= 2[latex]\frac{2}{3}[/latex]
10. Taking [latex]\sqrt{2}[/latex] = 1.414, [latex]\sqrt{3}[/latex] = 1.732, [latex]\sqrt{5}[/latex] = 2.236 and [latex]\sqrt{6} [/latex] = 2.449,then the value of [latex]\frac{9 +\sqrt{2}}{\sqrt{5} +\sqrt{3}}[/latex] + [latex]\frac{9 -\sqrt{2}}{\sqrt{5} -\sqrt{3}}[/latex] to three places of decimals is

A. 9.2321 B. 13.716 C. 10.723 D. 15.892

Answer - Option C
Explanation -
[latex]\frac{9 +\sqrt{2}}{\sqrt{5} +\sqrt{3}}[/latex] + [latex]\frac{9 -\sqrt{2}}{\sqrt{5} -\sqrt{3}}[/latex]
= [latex]\frac{1}{2}[/latex][15[latex]\sqrt{5}[/latex]- 3[latex]\sqrt{5}[/latex] + 2[latex]\sqrt{6}[/latex]]
= [latex]\frac{1}{2}[/latex] [33.540 – 5.196 – 7.898]
= 10.732
11. The cube root to 1.061208

A. 1.022 B. 10.22 C. 0.102 D. 1.02

Answer - Option D
Explanation -
Here 1.061208 = [latex]{1.02}^{3}[/latex]
Required cube root = 1.02
12. The least number having four digits which is a perfect square is

A. 1004 B. 1016 C. 1036 D. None of these

Answer - Option D
Explanation -
Required number =1024 = [latex]{32}^{2}[/latex]
13. The missing number in the series 8, 24, 12, 36, 18, 54, ______ is

A. 27 B. 108 C. 68 D. 72

Answer - Option A
Explanation -
Second term is 3 times of the first term and third term is half of the second term, repeat this process the missing term is half of 54, i.e. 27
14. What is the eighth term of the sequence 1, 4, 9, 16, 25,_______ ?

A. 8 B. 64 C. 128 D. 200

Answer - Option B
Explanation -
Given sequence can be written as [latex]{1}^{2}, {2}^{2}, {3}^{2}, {4}^{2}, {5}^{2}[/latex], ...
Hence it’s eighth term
=[latex]{8}^{2}[/latex]
= 64
15. Which of the following is the best approximation for the following expression [latex]\sqrt{{7.9986 / 0.115} + 19.97}[/latex]?

A. 15 B. 10 C. 1.0 D. 1.3

Answer - Option B
Explanation -
Rounding off, we get [latex]\sqrt{{\frac{8}{0.1}} + 20}[/latex] = [latex]\sqrt{100}[/latex]

1. The value of (1 +0.1 +0.11 +0.111) is

A. 1.321 B. 1.211 C. 1.111 D. 1.331

Answer - Option A
Explanation -
1 + 0.1000 + 0.110 + 0.111 = 1.321
2. When a number is divided by 5, it gives remainder 3. What is the remainder when square of that number is divided by 5?

A. 9 B. 3 C. 4 D. 1

Answer - Option C
Explanation -
Let the number be 8.
Thus, when [latex] {8}^{2}[/latex] = 64 will be divided by 5, then remainder will be 4.
3. [latex]\sqrt{10}[/latex] = 3.1623(approx). What is the approx, value of [latex]\frac{1}{\sqrt{10}}?[/latex]

A. 0.333 B. 0.3162 C. 0.3221 D. 0.3437

Answer - Option A
Explanation -
[latex]\frac{1}{3.1623}[/latex] will be less than 0.3333
4. . Find the value of [latex]{(2744)}^{\frac{1}{3}}[/latex]?

A. 24 B. 14 C. 34 D. 16

Answer - Option B
2744 is a multiple of 7.
Hence, the answer has to be 14.
Explanation -
5. Find the L.C.M. of 148 and 185.

A. 680 B. 740 C. 2960 D. 3700

Answer - Option B
Explanation -
148 = 37 × 4 and 185 = 37 × 5
LCM = 37 × 4 × 5 = 740
6. If [latex]{2}^{2n - 1}[/latex] = [latex]\frac{1}{{8}^{2n - 1}}[/latex] then the value of 'n' is:

1. A. 3 B. 2 C. 0 D. -2

Answer - Option B
Explanation -
[latex]{2}^{2n - 1}[/latex] = [latex]\frac{1}{3n - 9}[/latex]
[latex]{2}^{2n - 1}[/latex] = [latex]{2}^{3n - 9}[/latex] = [latex]{2}^{0}[/latex]
5n – 10 = 0
n = [latex]\frac{10}{5}[/latex] = 2
7. What is the largest possible length of a scale that can be used to measure exactly the lengths 3 m, 5 m 10 cm and 12 m 90 cm ?

A. 10 cm B. 20 cm C. 25 cm D. 30 cm

Answer - Option A
Explanation -
Required scale has to be of length 10 cm because 10 cm is the shortest length in in given question.
8. After measuring 120 metres of a rope, it was discovered that the metre rod was 3 cm longer. The true length of the rope measured is :

A. 116 m 40 cm B. 121m 20 cm C. 123m D. 123m 60 cm

Answer - Option D
Explanation -
Actual length has to be
120m + (120 × 3) cm = 120 m + 360 cm
= 123 m 60 cm.
9. Solve [latex]\sqrt{0.000064}^{3}[/latex]

A. 0.4 B. 0.04 C. 0.004 D. 0.0004

Answer - Option B
Explanation -
[latex] \sqrt{0.000064}^{3}[/latex] = [latex] \sqrt{\frac{4}{100} * \frac{4}{100} * \frac{4}{100}}^{3}[/latex] = 0.4
10. The HCF of two numbers is 6 and their LCM is 72. If one number is 24, the other number is

1. A. 12 B. 18 C. 36 D. 72

Answer - Option B
Explanation -
We know that, x × y = LCM × HCF (x, y are the two distinct numbers)
x × 24 = 72 × 6
x = 18.
11. The largest number which divides by 72 and 125, leaving remainders 7 and 8 respectively is

A. 13 B. 56 C. 65 D. 900

Answer - Option A
Explanation -
In such a questions it is better to check the options. In this case 13 satisfies the given condition. Rest of the numbers are large enough to be eliminated easily.
12. The HCF of two numbers is 12 and their LCM is 72. If one number is 36, the other number is

A. 12 B. 24 C. 36 D. 48

Answer - Option B
Explanation -
set the number be x
x × 36 = 12 × 72
x = 24
13. The largest number which divides 81 and 108, leaving remainders 6 and 3 respectively is

A. 9 B. 15 C. 18 D. 515

Answer - Option B
Explanation -
Checking the options we get the correct answer as 15.
14. The HCF of two numbers is 15 and their LCM is 270. If one number is 45, the other number is

A. 9 B. 15 C. 18 D. 515

Answer - Option B
Explanation -
HCF × LCM = Product of numbers
Other number =[latex]\frac{15 * 270}{45}[/latex] = 90
15. The largest number which divides 247 and 319, leaving remainders 7 and 4 respectively is

A. 15 B. 30 C. 45 D. 56

Answer - Option A
Numbers = 247, 319
i.e, Remainders = 7 & 4,
i.e, 247 - 7 = 240, 319 - 4 = 315 are divisible
HCF (240, 315) = 15