Recent questions tagged cat2006

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42
An equilateral triangle $\text{BP}$ is drawn inside a square $\text{ABCD}.$ What is the value of the angle $\text{APD}$ in degrees?$75$$90$$120$$135$$150$
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43
If $\log_y x = a \cdot \log_z y = b \cdot \log_x z = ab$ then which of the following pairs of values for $(a,b)$ is not possible?$-2, 1/2$$1,1$$0.4, 2.5$$\pi, 1/\pi$$2,2...
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44
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47
When you reverse the digits of the number $13,$ the number increases by $18.$ How many other two digit numbers increase by $18$ when their digits are reversed?$5$$6$$7$$8...
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50
Let $f(x) = \max (2x +1, 3 – 4x)$ where $x$ is any real number. Then the minimum possible value of $f(x)$ is:$1/3$$1/2$$2/3$$4/3$$5/3$
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51
What values of $x$ satisfy $x^{\frac{2}{3}} + x^{\frac{1}{3}} - 2 \leq 0?$$-8 \leq x \leq 1$$-1 \leq x \leq 8$$1 < x < 8$$1 \leq x \leq 8$$-8 \leq x \leq 8$
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53
Consider the set $\text{S} = \{1, 2, 3, \dots, 1000\}.$ How many arithmetic progressions can be formed from the elements of $\text{S}$ that start with $1$ and with $1000$...
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54
The graph $y-x$ against $y +x$ is as shown as below. (all graphs in this question are drawn to scale and the same scale has been used oneach axis). Then, Which of the opt...
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55
The sum of four consecutive two digit odd numbers, when divided by $10,$ becomes a perfect square. Which of the following can possibly be one of these four numbers?$21$$2...
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57
The number of solutions of the equation $2x+y=40$ where both $x$ and $y$ are positive integers and $x \leq y$ is:$7$$13$$14$$18$$20$
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58
What are the values of $x$ and $y$ that satisfy both the equations?$2^{0.7x} \cdot 3^{-1.25y} = 8\sqrt{6} / 27$$4^{0.3x} \cdot 9^{0.2y} = 8.(81)^{\frac{1}{5}}$$x=2, y=5$$...
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59
A group of $630$ children is arranged in rows for a group photograph session. Each row contains three fewer children than the row in front of it. What numbers of rows is ...
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60
Consider the sequence where the $n^{\text{th}}$ term $t_n = \frac{n}{n+2}, n=1, 2, \dots.$ The value of $t_3 \times t_4 \times t_5 \times \dots \times t_{53}$ equals:$2/4...
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62
If $a/b=1/3, b/c=2, c/d=1/2, d/e=3$ and $e/f=1/4$ then what is the value of $abc/def?$$3/8$$27/8$$3/4$$27/4$$1/4$
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63
Which among $2^{\frac{1}{2}} , 3^{\frac{1}{3}}, 4^{\frac{1}{4}}, 6^{\frac{1}{6}} \text{ and } 12^{\frac{1}{12}}$ is the largest?$2^{\frac{1}{2}}$$3^{\frac{1}{3}}$$4^{\fra...
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64
If $x=-0.5$ then which of the following has the smallest value?$2^{\frac{1}{x}}$$\frac{1}{x}$$\frac{1}{x^2}$$2^x$$\frac{1}{\sqrt{-x}}$