Let $\omega$ be a complex number such that $2\omega + 1 = z$ where $z = \sqrt{-3}$. If $\begin{vmatrix} 1 & 1 & 1 \\ 1 & -\omega^{2}-1 & \omega^{2} \\ 1 & \omega^{2} & \omega^{7} \end{vmatrix} = 3k$, then $k$ is equal to :

1

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

Topic: JEE Main 2017 (Offline)

2

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)

3

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

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4

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

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5

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…

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6

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…

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7

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 \math…

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1

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

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2

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 …

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3

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…

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4

Let k be an integer such that the triangle with vertices (k,-3k), (5,k) and (-k,2) has area 28 sq. units. Then the orth…

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5

If $(2+\sin x)\dfrac{dy}{dx}+(y+1)\cos x=0$ and $y(0)=1$, then $y\left(\dfrac{\pi}{2}\right)$ is equal to :

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6

The area (in sq. units) of the region ${(x,y): x\ge 0,\ x+y\le 3,\ x^{2}\le 4y\ \text{and}\ y\le 1+\sqrt{x}}$ is :

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7

Let $I_n=\int \tan^{n}x,dx,\ (n>1)$. If $I_4+I_6=a\tan^{5}x+bx^{5}+C$, where $C$ is a constant of integration, then the…

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8

The integral $\displaystyle \int_{\pi/4}^{3\pi/4}\dfrac{dx}{1+\cos x}$ is equal to :

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9

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area…

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10

If for $x\in\left(0,\dfrac14\right)$, the derivative of $\tan^{-1}\left(\dfrac{6x\sqrt{x}}{1-9x^{3}}\right)$ is $\sqrt{…

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