Comments by rhl

Let $a_{n}=46+8 n$ and $b_{n}=98+4 n$ be two sequences for natural numbers $n \leq 100$. Then, the sum of all terms common to both the sequences is$14900$$15000$$14798$$1...

In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is

A rectangle with the largest possible area is drawn inside a semicircle of radius $2 \mathrm{~cm}$. Then, the ratio of the lengths of the largest to the smallest side of ...

Let $\triangle A B C$ be an isosceles triangle such that $A B$ and $A C$ are of equal length. $A D$ is the altitude from $A$ on $B C$ and $B E$ is the altitude from $B$ o...

A merchant purchases a cloth at a rate of Rs. $100$ per meter and receives $5 \mathrm{~cm}$ length of cloth free for every $100 \mathrm{~cm}$ length of cloth purchased by...

Anil mixes cocoa with sugar in the ratio $3: 2$ to prepare mixture $A$, and coffee with sugar in the ratio $7: 3$ to prepare mixture $B$. He combines mixtures $A$ and $B$...

For a real number $x$, if $\frac{1}{2}, \frac{\log _{3}\left(2^{x}-9\right)}{\log _{3} 4}$, and $\frac{\log _{5}\left(2^{x}+\frac{17}{2}\right)}{\log _{5} 4}$ are in an a...

Let $n$ be any natural number such that $5^{n-1}<3^{n+1}$. Then, the least integer value of $m$ that satisfies $3^{n+1}<2^{n+m}$ for each such $n$, is

A boat takes $2$ hours to travel downstream a river from port $\text{A}$ to port $\text{B}$, and $3$ hours to return to port $\text{A}$. Another boat takes a total of $6$...

For some real numbers $a$ and $b$, the system of equations $x+y=4$ and $(a+5) x+\left(b^{2}-15\right) y=8 b$ has infinitely many solutions for $x$ and $y$. Then, the maxi...

Jayant bought a certain number of white shirts at the rate of Rs $1000$ per piece and a certain number of blue shirts at the rate of Rs $1125$ per piece. For each shirt, ...

A container has $40$ liters of milk. Then, $4$ liters are removed from the container and replaced with $4$ liters of water. This process of replacing $4$ liters of the li...

For some positive real number $x$, if $\log _{\sqrt{3}}(x)+\frac{\log _{x}(25)}{\log _{x}(0.008)}=\frac{16}{3}$, then the value of $\log _{3}\left(3 x^{2}\right)$ is

In a right-angled triangle $\triangle A B C$, the altitude $A B$ is $5 \mathrm{~cm}$, and the base $B C$ is $12 \mathrm{~cm} . P$ and $Q$ are two points on $B C$ such tha...

The salaries of three friends Sita, Gita and Mita are initially in the ratio $5: 6: 7$, respectively. In the first year, they get salary hikes of $20 \%, 25 \%$ and $20 \...

The number of integer solutions of equation $2|x|\left(x^{2}+1\right)=5 x^{2}$ is

Answer the following question based on the information given below.The figures below present annual growth rate, expressed as the $\%$ change relative to the previous yea...

Answer the following question based on the information given below.The figures below present annual growth rate, expressed as the $\%$ change relative to the previous yea...

Answer the following question based on the information given below.FEI for a country in a year, is the ratio (expressed as a percentage) of its foreign equity inflows to ...

Answer the following question based on the information given below.FEI for a country in a year, is the ratio (expressed as a percentage) of its foreign equity inflows to ...

Answer the following question based on the information given below.FEI for a country in a year, is the ratio (expressed as a percentage) of its foreign equity inflows to ...