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 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is:
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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)
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)
If $A = \begin{bmatrix} 2 & -3 \\ -4 & 1 \end{bmatrix}$,
then $\operatorname{adj}(3A^{2} + 12A)$ is equal to :
Topic: JEE Main 2017 (Offline)
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)
If $5\left(\tan^{2}x-\cos^{2}x\right)=2\cos2x+9$,
then the value of $\cos4x$ is:
Topic: JEE Main 2017 (Offline)
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)
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)
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)
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)
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…
Topic: JEE Main 2017 (Offline)
