Consider the following two binary relations on the set $A = {a, b, c}$ : $R_1 = {(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)}$ and $R_2 = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}$. Then :
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If $\lambda \in \mathbb{R}$ is such that the sum of the cubes of the roots of the equation $x^{2} + (2-\lambda)x + (10-…
Topic: JEE Main 2018 (15 April Morning Shift)
Let $A$ be a matrix such that $A \begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix}$ is a scalar matrix and $|3A| = 108$. The…
Topic: JEE Main 2018 (15 April Morning Shift)
Let $S$ be the set of all real values of $k$ for which the system of linear equations$x + y + z = 2$$2x + y - z = 3$$3x…
Topic: JEE Main 2018 (15 April Morning Shift)
If $x_1, x_2,\ldots , x_n$ and $\frac{1}{h_1}, \frac{1}{h_2},\ldots , \frac{1}{h_n}$ are two A.P.s such that
$x_3 = h_2…
Topic: JEE Main 2018 (15 April Morning Shift)
n–digit numbers are formed using only three digits 2,5,7.
The smallest value of n for which 900 such distinct numbers c…
Topic: JEE Main 2018 (15 April Morning Shift)
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The set of all $\alpha \in \mathbb{R}$ for which $w = \dfrac{1 + (1-8\alpha)z}{1-z}$ is purely imaginary number, for al…
Topic: JEE Main 2018 (15 April Morning Shift)
If the tangents drawn to the hyperbola $4y^{2}=x^{2}+1$ intersect the co-ordinate axes at the distinct points $A$ and $…
Topic: JEE Main 2018 (15 April Morning Shift)
If $\tan A$ and $\tan B$ are the roots of the quadratic equation $3x^{2}-10x-25=0$, then the value of
$3\sin^{2}(A+B)-1…
Topic: JEE Main 2018 (15 April Morning Shift)
A box $A$ contains $2$ white, $3$ red and $2$ black balls. Another box $B$ contains $4$ white, $2$ red and $3$ black ba…
Topic: JEE Main 2018 (15 April Morning Shift)
The mean of set of $30$ observations is $75$. If each observation is multiplied by a non-zero number $\lambda$ and then…
Topic: JEE Main 2018 (15 April Morning Shift)
If $\overrightarrow a ,\,\,\overrightarrow b ,$ and $\overrightarrow C $ are unit vectors such that $\overrightarrow a…
Topic: JEE Main 2018 (15 April Morning Shift)
Let y = y(x) be the solution of the differential equation ${{dy} \over {dx}} + 2y = f\left( x \right),$ where $f\left( …
Topic: JEE Main 2018 (15 April Morning Shift)
In a triangle $ABC$, coordinates of $A$ are $(1,2)$ and the equations of the medians through $B$ and $C$ are respective…
Topic: JEE Main 2018 (15 April Morning Shift)
The value of the integral
$\displaystyle \int_{-\pi/4}^{\pi/4} \sin^{4}x \left(1 + \log\left(\dfrac{2 + \sin 2x}{2 - \s…
Topic: JEE Main 2018 (15 April Morning Shift)
The area (in sq. units) of the region
${(x,y)\in \mathbb{R}^{2} : x \ge 0,\ y \ge 0,\ y \ge x-2 \text{ and } y \le \sqr…
Topic: JEE Main 2018 (15 April Morning Shift)
