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 $x_3 = h_2 = 8$ and $x_8 = h_7 = 20$, then $x_5 \cdot h_{10}$ equals :
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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)
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)
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)
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)…
Topic: JEE Main 2018 (15 April Morning Shift)
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)
