Recent questions tagged cat2019-2

A man makes complete use of $405$ cc of iron, $783$ cc of aluminium, and $351$ cc of copper to make a number of solid right circular cylinders of each type of metal. Thes...

Let $A$ be a real number. Then the roots of the equation $x^{2}-4x-\log _{2}A=0$ are real and distinct if and only if$A \frac{1}{16}$$A \frac{1}{8}$$A< \frac{1}{16}$$A< \...

If $5^{x}-3^{y}=13438$ and $5^{x-1}+3^{y+1}=9686$, then $x+y$ equals _______

If $(2n+1)+(2n+3)+(2n+5)+\dots+(2n+47)=5280,$ then what is the value of $1+2+3+\dots+n$ _______

Let $\text{A}$ and $\text{B}$ be two regular polygons having $\text{A}$ and $\text{B}$ sides, respectively. If $b= 2a$ and each interior angle of $\text{B}$ is $3/2$ time...

Let $f$ be a function such that $f (mn) = f (m) f (n)$ for every positive integers $m$and $n$. If $f (1), f (2)$ and $f (3)$ are positive integers, $f (1) < f (2),$ and $...

Let $\text{ABC}$ be a right-angled triangle with hypotenuse $\text{BC}$ of length $20$ cm. If $\text{AP}$ is perpendicular on $\text{BC}$, then the maximum possible lengt...

The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle, length of each side being $20$ cm. The vertical height of the pyram...

Amal invests Rs $12000$ at $8\%$ interest, compounded annually, and Rs $10000$ at $6\%$ interest, compounded semi-annually, both investments being for one year. Bimal inv...

The number of common terms in the two sequences: $15, 19, 23, 27,\dots,415$ and $14, 19, 24, 29,\dots,464$ is$18$$19$$21$$20$