Let $a,b,c\in \mathbb{R}$. If $f(x)=ax^{2}+bx+c$ is such that $a+b+c=3$ and $f(x+y)=f(x)+f(y)+xy,\ \forall x,y\in \mathbb{R}$, then $\displaystyle \sum_{n=1}^{10} f(n)$ is equal to :

1

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 ar…

Topic: JEE Main 2017 (Offline)

2

If for a positive integer $n$, the quadratic equation $x(x+1) + (x+1)(x+2) + \ldots + (x+n-1)(x+n) = 10n$ has two conse…

Topic: JEE Main 2017 (Offline)

3

If $S$ is the set of distinct values of $b$ for which the following system of linear equations$x + y + z = 1$$x + ay + …

Topic: JEE Main 2017 (Offline)

4

If $A = \begin{bmatrix} 2 & -3 \\ -4 & 1 \end{bmatrix}$, then $\operatorname{adj}(3A^{2} + 12A)$ is equal to :

Topic: JEE Main 2017 (Offline)

5

The function $f:\mathbb{R}\to\left[-\dfrac12,\dfrac12\right]$ defined as $f(x)=\dfrac{x}{1+x^{2}}$, is

Topic: JEE Main 2017 (Offline)

6

If $5\left(\tan^{2}x-\cos^{2}x\right)=2\cos2x+9$, then the value of $\cos4x$ is:

Topic: JEE Main 2017 (Offline)

7

Let $\omega$ be a complex number such that $2\omega + 1 = z$ where $z = \sqrt{-3}$. If $\begin{vmatrix} 1 & 1 & 1 \\…

Topic: JEE Main 2017 (Offline)

8

If two different numbers are taken from the set {0,1,2,3,...,10} then the probability that their sum as well as absolut…

Topic: JEE Main 2017 (Offline)

9

For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P(Exactly one of C or …

Topic: JEE Main 2017 (Offline)

10

Let $\vec{a}=2\hat{i}+\hat{j}-2\hat{k}$ and $\vec{b}=\hat{i}+\hat{j}$. Let $\vec{c}$ be a vector such that $|\vec{c}-\v…

Topic: JEE Main 2017 (Offline)