JEE MAIN 2018 Previous Year Questions (PYQs) – Page 1 of 9

A value of $\theta \in \left( {0,{\pi \over 3}} \right)$, for which
$\left| {\matrix{ {1 + {{\cos }^2}\theta } & {{{\sin }^2}\theta } & {4\cos 6\theta } \cr {{{\cos }^2}\theta } & {1 + {{\sin }^2}\theta } & {4\cos 6\theta } \cr {{{\cos }^2}\theta } & {{{\sin }^2}\theta } & {1 + 4\cos 6\theta } \cr } } \right| = 0$, is :

n–digit numbers are formed using only three digits 2,5,7. The smallest value of n for which 900 such distinct numbers can be formed is :

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 :

Let $A$ be a matrix such that $A \begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix}$ is a scalar matrix and $|3A| = 108$. Then $A^2$ equals :

If $\lambda \in \mathbb{R}$ is such that the sum of the cubes of the roots of the equation $x^{2} + (2-\lambda)x + (10-\lambda)=0$ is minimum, then the magnitude of the difference of the roots of this equation is :

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 :

The set of all $\alpha \in \mathbb{R}$ for which $w = \dfrac{1 + (1-8\alpha)z}{1-z}$ is purely imaginary number, for all $z \in \mathbb{C}$ satisfying $|z| = 1$ and $\operatorname{Re} z \ne 1$, is :

If the tangents drawn to the hyperbola $4y^{2}=x^{2}+1$ intersect the co-ordinate axes at the distinct points $A$ and $B$ then the locus of the mid point of $AB$ is :

If $\tan A$ and $\tan B$ are the roots of the quadratic equation $3x^{2}-10x-25=0$, then the value of $3\sin^{2}(A+B)-10\sin(A+B)\cos(A+B)-25\cos^{2}(A+B)$ is :