NDA Mathematics 2017 Question Paper

Let $S$ be the set of all persons living in Delhi. We say that $x,y$ in $S$ are related if they were born in Delhi on the same day. Which one of the following is correct?

Let $A=\{1,2,3,4,5,6,7,8,9,10\}$. Then the number of subsets of $A$ containing two or three elements is

The value of $i^{2n}+i^{2n+1}+i^{2n+2}+i^{2n+3}$, where $i=\sqrt{-1}$, is

If the difference between the roots of the equation $x^2+kx+1=0$ is strictly less than $\sqrt{5}$, where $|k|\ge 2$, then $k$ can be any element of the interval

If the roots of the equation $x^2+px+q=0$ are in the same ratio as those of the equation $x^2+lx+m=0$, then which one of the following is correct?

The value of $${\left(\frac{-1+i\sqrt{3}}{2}\right)}^n+{\left(\frac{-1-i\sqrt{3}}{2}\right)}^n$$ where $n$ is not a multiple of $3$ and $i=\sqrt{-1}$, is

Three-digit numbers are formed from the digits 1, 2 and 3 in such a way that the digits are not repeated. What is the sum of such three-digit numbers?

What is the sum of the series $$0.3+0.33+0.333+\dots n\text{ terms?}$$

If $1,\omega ,{\omega }^2$ are the cube roots of unity, then $(1+\omega )(1+{\omega }^2)(1+{\omega }^3)(1+\omega +{\omega }^2)$ is equal to

If the sum of $m$ terms of an AP is $n$ and the sum of $n$ terms is $m$, then the sum of $(m+n)$ terms is