Recent questions tagged cat2020-set1

1 votes
1 answer
51
1 votes
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54
On a rectangular metal sheet of area $135$ sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two-thir...
2 votes
1 answer
55
1 votes
1 answer
57
The number of real$-$valued of the equation $2^{x}+2^{-x}=2-(x-2)^{2}$ isinfinite$1$$0$$2$
1 votes
1 answer
59
How many distinct positive integer-valued solutions exist to the equation $\left ( x^{2}-7x+11 \right )^{(x^{2}-13x+42)} =1$?$6$$8$$2$$4$
1 votes
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60
1 votes
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61
1 votes
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64
The mean of all $4-$digit even natural numbers of the form $\text{‘}aabb\text{’},$ where $a>0,$ is$5050$$4466$$5544$$4864$
2 votes
1 answer
67
1 votes
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68
If $f\left ( 5+x \right )= f\left ( 5-x \right )$ for every real $x,$ and $f\left ( x \right )=0$ has four distinct real roots, then the sum of these roots is$0$$40$$10$$...
1 votes
1 answer
69
If $a, b$ and $c$ are positive integers such that $ab=432, bc=96$ and $c<9,$ then the smallest possible value of $a+b+c$ is$56$$59$$49$$46$
1 votes
1 answer
70
1 votes
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71
A circle is inscribed in a rhombus with diagonals $12$ cm and $16$ cm. The ratio of the area of circle to the area of rhombus is $\frac{5\pi }{18}$ $\frac{6\pi }{25}$ $\f...
1 votes
1 answer
75
The number of distinct real roots of the equation $\left ( x+\frac{1}{x}\right )^{2}-3\left ( x+\frac{1}{x} \right )+2= 0$ equals