The number of natural numbers $n \le 30$ for which $\sqrt{n + \sqrt{n + \sqrt{n + ...}}}$ is a natural number is
Problem 2 of 20
The number of natural numbers $n \le 30$ for which $\sqrt{n + \sqrt{n + \sqrt{n + ...}}}$ is a prime number is
Problem 3 of 20
The number of squares formed by $5$ vertical and $4$ horizontal lines (all are equispaced) is
Problem 4 of 20
The number of integers $a,\ b,\ c$ for which $a^2 + b^2 - 8c = 3$ is
Problem 5 of 20
If set $X$ consists of three elements then the number of elements in the power set of power set of $X$ is
Problem 6 of 20
In an $n$-sided regular polygon, the radius of the circum-circle is equal in length to the shortest diagonal. The number of values of $n \lt 60$ for which this can happen is
Problem 7 of 20
Number of integers $n$ such that the number $1 + n$ is a divisor of the number $1 + n^2$ is
Problem 8 of 20
If for $x,y \gt 0$ we have $\dfrac{1}{x} + \dfrac{1}{y} = 2$ then the minimum value of $xy$ is
Problem 9 of 20
Tenth term in the sequence $12,\ 18,\ 20,\ 28\ ...$ is
Problem 10 of 20
The probability of a point within an equilateral triangle with side $1$-unit lying outside its in-circle (inscribed circle) is
Problem 11 of 20
A triangle has perimeter $316$ and its sides are of integer length. The maximum possible area for such a triangle is achieved for
Problem 12 of 20
Number of numbers less than $40$ having exactly four divisors is
Problem 13 of 20
The number $3^8(3^{10} + 6^5) + 2^3(2^{12} + 6^7)$ is
Problem 14 of 20
Let the number of rectangles formed by $6$ horizontal and $4$ vertical lines be $n$ and those formed by $5$ vertical and $5$ horizontal lines be $m$ then we have
Problem 15 of 20
If $ABCD$ is a rhombus and $\angle ABC = 60^\circ$ then
Problem 16 of 20
If $a,b \gt 0$ then
Problem 17 of 20
The statement $\unicode{0x201C}a\ is\ not\ less\ than\ 4\unicode{0x201D}$ is correctly represented by
Problem 18 of 20
Two friends $A$ and $B$ watched a car from the top of their buildings. Angle of depression for A was $10^\circ$ more than angle of depression for $B$, then
Problem 19 of 20
Total surface area of a sphere $S$ with radius $\sqrt{2} + \sqrt{3}\ cm$ is
Problem 20 of 20
A craft teacher reshapes the wax from a cylinder of candle with section diameter $6$ cm and the height $6$ cm into a sphere. The radius of this sphere will be