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Browse complete papersIf \(x=\frac{1}{\sqrt{13}-3}\), \(y=\frac{1}{\sqrt{7}-\sqrt{3}}\), \(z=\frac{1}{\sqrt{2}(\sqrt{3}-1)}\), then
x < y < z
y < z < x
z < y < x
x < z < y
Correct answer
x < y < z
The smallest of the differences between the perfect squares lying on either side of the least positive integer that is divisible by 3, 4, 5, 6, 8 is
25
35
15
21
Correct answer
25
If \(x=\sqrt{2}+\sqrt[3]{5}\) and y is such that xy is rational, then a value of y is
\((\sqrt[3]{5}-\sqrt{2})(4+2 \sqrt[3]{25}+5 \sqrt[3]{5})\)
\((\sqrt[3]{5}-\sqrt{2})\)
\((\sqrt[3]{5}-\sqrt{2})(2 \sqrt[3]{25}+5 \sqrt[3]{5}-4)\)
\((\sqrt[3]{5}-\sqrt{2})(4-2 \sqrt[3]{25}+5 \sqrt[3]{5})\)
Correct answer
\((\sqrt[3]{5}-\sqrt{2})(4+2 \sqrt[3]{25}+5 \sqrt[3]{5})\)
If the mean proportional of b, c and the 4th proportional of a, b, c are both equal to 8, then abc =
29
27
25
28
Correct answer
29
The greatest number that exactly divides 513, 1134 and 1215 is
9
54
27
81
Correct answer
9
If \(x=1+\frac{1}{2^2}+\frac{1}{2^3}+\ldots \infty\) and \(y=x+\frac{1}{2}+\frac{x}{9}\) + \(\frac{1}{18}+\frac{x}{81}+\frac{1}{162}+\ldots \infty\), then
x = y
x = y2
y = x2
x + y < 1
Correct answer
x = y
The number of ordered pairs (x, y) of positive integers satisfying the inequality 5x + 3y ≤ 15 is
4
5
6
7
Correct answer
4
In a class, the number of boys who can swim is one more than the number of girls who can swim. The number of girls who cannot swim is one more than the number of boys that cannot swim. The difference between number of boys who can swim and number of girls who cannot swim is two. Then which of the following is true?
The number of girls in that class is 2 less than the number of boys
The number of boys in that class is one more than the number of girls
The number of boys and girls in that class is each equal to 2
The difference between the number of girls who can swim and the number of boys who can't swim is 2
Correct answer
The number of girls in that class is 2 less than the number of boys
A book costs Rs. 35 and a pen costs Rs. 20. A person has purchased less number of books · than the number of pens by spending maximum amount out of Rs. 350, that he has. The amount left unspent (in rupees) is
0
5
10
15
Correct answer
0
Which one of the following point does not lie in the region bounded by x + y < 5, 2x - 4y > 1 and x < y is
\(\left(-1.5,-1 \frac{1}{8}\right) \)
\(\left(-\frac{3}{2},-\frac{5}{4}\right) \)
\(\left(-\frac{1}{10},+\frac{1}{10}\right) \)
(-3, -2)
Correct answer
\(\left(-1.5,-1 \frac{1}{8}\right) \)