Let $x(t) = 2\sqrt{2}\cos t \sqrt{\sin 2t}$ and $y(t) = 2\sqrt{2}\sin t \sqrt{\sin 2t}, \; t \in (0,\tfrac{\pi}{2}).$ Then $\dfrac{1+\left(\tfrac{dy}{dx}\right)^2}{\tfrac{d^2y}{dx^2}}$ at $t=\tfrac{\pi}{4}$ is equal to :
Previous 10 Questions — JEE Main 2022 (28 July Evening Shift)
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The sum of the absolute maximum and absolute minimum values of the function
$$f(x) = \tan^{-1}(\sin x - \cos x)$$
i…
Topic: JEE Main 2022 (28 July Evening Shift)
The function $f(x) = x e^{\,x(1-x)}, \, x \in \mathbb{R}$ is :
Topic: JEE Main 2022 (28 July Evening Shift)
The function $f : \mathbb{R} \to \mathbb{R}$ defined by
$$
f(x) = \lim_{n \to \infty} \frac{\cos(2 \pi x) - x^{2n} \…
Topic: JEE Main 2022 (28 July Evening Shift)
$ \text{Let } f(x)=ax^{2}+bx+c \text{ be such that } f(1)=3,\ f(-2)=\lambda \text{ and } f(3)=4. $
$ \text{If } f(0)+f(…
Topic: JEE Main 2022 (28 July Evening Shift)
$ \text{Let } A \text{ and } B \text{ be any two } 3\times 3 \text{ symmetric and skew-symmetric matrices respectively.…
Topic: JEE Main 2022 (28 July Evening Shift)
$S = \{\, x \in [-6,3] \setminus \{-2,2\} \;:\; \dfrac{|x+3|-1}{|x|-2} \geq 0 \,\}$
$T = \{\, x \in \mathbb{Z} \;:\;…
Topic: JEE Main 2022 (28 July Evening Shift)
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\text{Let } \alpha, \beta \text{ be the roots of the equation } x^{2} - \sqrt{2}x + \sqrt{6} = 0
\text{ and } \dfrac{…
Topic: JEE Main 2022 (28 July Evening Shift)
Next 10 Questions — JEE Main 2022 (28 July Evening Shift)
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Let $I_n(x) = \int_0^x \dfrac{1}{(t^2+5)^n} \, dt, \; n = 1, 2, 3, \dots$
Then :
Topic: JEE Main 2022 (28 July Evening Shift)
$ \text{The area enclosed by the curves } y=\log_{e}(x+e^{2}),; x=\log_{e}!\left(\dfrac{2}{y}\right) \text{ and } x=\lo…
Topic: JEE Main 2022 (28 July Evening Shift)
$ \text{Let } y=y(x) \text{ be the solution curve of the differential equation } \dfrac{dy}{dx}+\dfrac{1}{x^{2}-1},y=\l…
Topic: JEE Main 2022 (28 July Evening Shift)
Let the hyperbola $H : \dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$ pass through the point $(2\sqrt{2}, -2\sqrt{2})$.
A pa…
Topic: JEE Main 2022 (28 July Evening Shift)
$ \text{Let } S \text{ be the set of all } a \in \mathbb{R} \text{ for which the angle between the vectors } \vec{u}=a(…
Topic: JEE Main 2022 (28 July Evening Shift)
$ \text{Let A and B be two events such that } P(B|A)=\frac{2}{5}, P(A|B)=\frac{1}{7},; \text{and } P(A\cap B)=\frac{1}{…
Topic: JEE Main 2022 (28 July Evening Shift)
