Let $f$ be a differentiable function such that $f'(x) = 7 - \dfrac{3}{4}\,\dfrac{f(x)}{x}$, for $x>0$, and $f(1)\neq 4$. Then $\displaystyle \lim_{x\to 0} x\,f\!\left(\dfrac{1}{x}\right)$ equals:
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Let $f : (-1, 1) \to \mathbb{R}$ be a function defined by $f(x) = \max \{-|x|, -\sqrt{1 - x^2}\}$. If $K$ be the set of…
Topic: JEE Main 2019 (10 January Evening Shift)
The number of values of $\theta \in (0, \pi)$ for which the system of linear equations $x + 3y + 7z = 0$&nbs…
Topic: JEE Main 2019 (10 January Evening Shift)
The curve amongst the family of curves represented by the differential equation
$(x^2 - y^2)dx + 2xy\,dy = 0$
which…
Topic: JEE Main 2019 (10 January Evening Shift)
Let $z = \left(\dfrac{\sqrt{3}}{2} + \dfrac{i}{2}\right)^5 + \left(\dfrac{\sqrt{3}}{2} - \dfrac{i}{2}\right)^5.$
If $…
Topic: JEE Main 2019 (10 January Evening Shift)
The positive value of $\lambda$ for which the coefficient of $x^2$ in the expression
$x^2 \left( \sqrt{x} + \dfrac{\l…
Topic: JEE Main 2019 (10 January Evening Shift)
The value of $\lambda$ such that the sum of the squares of the roots of the quadratic equation
$x^2 + (3 - \lambda)x …
Topic: JEE Main 2019 (10 January Evening Shift)
Let $A =
\begin{bmatrix}
2 & b & 1 \\
b & b^2 + 1 & b \\
1 & b & 2
\end{bmatrix}$ where $b > 0$.
Then the minimum va…
Topic: JEE Main 2019 (10 January Evening Shift)
If $\vec{\alpha} = (\lambda - 2)\vec{a} + \vec{b}$ and $\vec{\beta} = (4\lambda - 2)\vec{a} + 3\vec{b}$ be two given ve…
Topic: JEE Main 2019 (10 January Evening Shift)
Let $S = \{(x, y) \in \mathbb{R}^2 : \dfrac{y^2}{1 + r} - \dfrac{x^2}{1 - r} = 1 ; \, r \neq \pm 1 \}$.
Then $S$ repr…
Topic: JEE Main 2019 (10 January Evening Shift)
The value of $\displaystyle \int_{-\pi/2}^{\pi/2} \dfrac{dx}{[x] + [\sin x] + 4}$,
where $[t]$ denotes the greatest i…
Topic: JEE Main 2019 (10 January Evening Shift)
