NDA Mathematics 2017 Question Paper

If $x+{\log }_{10}(1+2^x)=x{\log }_{10}5+{\log }_{10}6$, then $x$ is equal to

The remainder and the quotient of the binary division $(101110{)}_2÷(110{)}_2$ are respectively

The matrix $A$ has $x$ rows and $x+5$ columns. The matrix $B$ has $y$ rows and $11-y$ columns. Both $AB$ and $BA$ exist. What are the values of $x$ and $y$ respectively?

If $S_n=nP+\frac{n(n-1)Q}{2}$, where $S_n$ denotes the sum of the first $n$ terms of an AP, then the common difference is

The roots of the equation $$(q-r)x^2+(r-p)x+(p-q)=0$$ are

If $E$ is the universal set and $A=B\cup C$, then the set $E-(E-(E-(E-(E-A))))$ is same as the set

If $A=\{x:x\text{ is a multiple of }2\}$, $B=\{x:x\text{ is a multiple of }5\}$ and $C=\{x:x\text{ is a multiple of }10\}$, then $A\cap (B\cap C)$ is equal to

If $\alpha$ and $\beta$ are the roots of the equation $1+x+x^2=0$, then the matrix product $$\left[\begin{array}{cc}1& \beta \\ \alpha & \alpha \end{array}\right]\left[\begin{array}{cc}\alpha & \beta \\ 1& \beta \end{array}\right]$$ is equal to

If $|a|$ denotes the absolute value of an integer, then which of the following are correct?

1. $|ab|=|a||b|$
2. $|a+b|\le |a|+|b|$
3. $|a-b|\ge ||a|-|b||$

Select the correct answer using the code given below.

How many different permutations can be made out of the letters of the word 'PERMUTATION'?