21). If A and B are any two non-empty subsets of a set E. then what is \( A \cup ( A \cap B) \) equal to?
| A). \( A\cap B \) |
| B). \( A\cup B \) |
| C). A |
| D). B |
|
22). Consider the following in respect of the numbers \( \large \sqrt{2},\sqrt[3]{3},\sqrt[6]{6} \)
1. \( \large\sqrt[6]{6} \)is the greatest number.
2. \( \large\sqrt{2} \)is the smallest number.
Which of the above statements is/are correct?
| A). 1 only |
| B). 2 only |
| C). Both 1 and 2 |
| D). Neither 1 nor 2 |
|
23). A water pipe is cut into two pieces. The longer piece is 70% of the length of the pipe. By how much percentage is the longer piece longer than the shorter piece?
| A). 140% |
| B). 400/3 % |
| C). 40 % |
| D). None of these |
|
24). The sum of two positive numbers at and y is 2.5 times their difference. If the product of the numbers is 84, then what is the sum of the two numbers?
| A). 26 |
| B). 24 |
| C). 22 |
| D). 20 |
|
25). If n is a whole number greater than 1, then \( n^{2}\)\( \left( n^{2}-1\right)\)is always divisible by
| A). 12 |
| B). 24 |
| C). 48 |
| D). 60 |
|
26). If the roots of the equation \(\left( a^{2}-bc\right) \)\( x^{2}\)+\( 2\)\( \left( b^{2}-ac\right)x+\left( c^{2} - ab\right)\) are equal, where \( b\)\( \ne\) \( 0\), then which one of the following is correct?
| A). \( a\)+\( b\)+\( c\) = \( abc\) |
| B). \( a^{2}\)+\( b^{2}\)+\( c^{2}\) = \( 0\) |
| C). \( a^{3}\)+\( b^{3}\)+\( c^{3}\) = \( 0\) |
| D). \( a^{3}\)+\( b^{3}\)+\( c^{3}\)=\( 3abc\) |
|
27). What is the remainder when \( 4^{1000}\) is divided by 7?
| A). 1 |
| B). 2 |
| C). 4 |
| D). None of these |
|
28). A, B and C can do a piece of work individually in 8, 12 and 15 days respectively. A and B start working, but A quits after working for 2 days. After this, C joins B till the completion of work. In how many days will the work be completed?
| A). \( 5\)\( \Large \frac{8}{9} \) days |
| B). \( 4\)\( \Large \frac{6}{7} \) days |
| C). \( 6\)\( \Large \frac{7}{13} \) days |
| D). \( 3\)\( \Large \frac{3}{4} \) days |
|
29). If \( x\)+\( y\)=\( 5\), \( y\)+\( z\) =\( 10\) and \( z\)+\( x\) =\( 15\), then which one of the following is correct?
| A). z>x>y |
| B). z>y>xa |
| C). x>y>z |
| D). x>z>y |
|
30). On a 20% discount sale, an article costs Rs596. What was the original price of the article?
| A). Rs 720 |
| B). Rs 735 |
| C). Rs 745 |
| D). Rs 775 |
|
