NDA Mathematics 2026 Question Paper

Let $p$, $q$ and $r$ be three unequal numbers such that $p$, $q$ and $r$ are in AP. If $(q-p)$, $(r-q)$ and $p$ are in GP, then $(p+q):(q+r):(r+p)$ equals

If $p$, $g_1$, $g_2$ and $q$ are in GP and $m$ is the arithmetic mean of $p$ and $q$, then $\frac{g_1^2}{g_2}+\frac{g_2^2}{g_1}$ is equal to

Consider the following inequalities :
I. $1+4i>3+2i$
II. $2+3i<3+4i$
III. $4+3i>3+4i$
where $i=\sqrt{-1}$
How many of the above are valid ?

Let $Z_1$ and $Z_2$ be complex numbers such that $\frac{3Z_1}{4Z_2}$ is purely imaginary. What is $\left|\frac{Z_1+Z_2}{Z_1-Z_2}\right|$ equal to ?

If $\alpha$, $\beta$, $\gamma$ are cube roots of $-8$, then what is $\frac{{\alpha }^2{p}^2+{\beta }^2{q}^2+{\gamma }^2{r}^2}{{\beta }^2{p}^2+{\gamma }^2{q}^2+{\alpha }^2{r}^2}$ equal to ?

The sum of the first $n$ terms of an AP is $3n^2+5n$. If the $m^{\text{th}}$ term of the AP is $68$, then what is the value of $m$ ?

A set $S$ contains $(2n+1)$ elements. If the number of subsets of $S$ which contain at most $n$ elements is $1024$, then what is the value of $n$ ?

What is the maximum number of points of intersection of $5$ circles ?

What is the greatest value of $r$ satisfying the inequality ${}^{15}{C}_{r+1}>2\times {}^{15}{C}_r$ ?

If $n={}^m{C}_2$, then what is ${}^n{C}_2$ equal to ?