Physics, Chemistry, and Mathematics Quizzes

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Questions and Answers

If $y = sin(x) + ln(x) + e^{2x}$ then $\frac{dy}{dx}$ will be:

$cos x + \frac{1}{x} + 2e^{2x}$ (correct)
$cos x + \frac{1}{x} + e^{2x}$
$\frac{-cos x}{2} + e^{2x}$
$cos(x) + \frac{2}{x^2} + e^{2x}$

If $y = \frac{x^2 + 2x}{3x - 4}$, then the value of $\frac{dy}{dx}$ is:

$\frac{x^2 + 8x - 8}{(3x - 4)^2}$
$\frac{3x^2 - 8x - 8}{(3x - 4)^2}$ (correct)
$\frac{3x^2 - 8x - 8}{(3x + 4)^2}$
$\frac{3x^2 + 8x - 8}{(3x - 4)^2}$

Convert 18 degrees into radians.

$\frac{\pi}{180}$ rad
$\frac{\pi}{18}$ rad
$\frac{18}{\pi}$
$\frac{\pi}{10}$ rad (correct)

Value of sin(37°) cos(53°) is:

$\frac{9}{25}$ (D) Signup and view all the answers

Sin(90° + $\theta$) is:

cos$\theta$ (D) Signup and view all the answers

Value of tan 315° is:

-1 (D) Signup and view all the answers

The displacement of a particle is given by the equation $s = t^3 - 6t^2 + 9t$ where t is measured in seconds and s in meters. What is the velocity after 1 sec (velocity is rate of change of displacement with respect to time):

0 m/sec (D) Signup and view all the answers

If f(x) = $sin^2x - cos^2x$ then $\frac{df}{dx}$ is:

-2sin(2x) (A) Signup and view all the answers

Find value of $\frac{d}{dx}$(cos 45°)

0 (B) Signup and view all the answers

In the shown triangle two sides and one angle is given. The third side is:

(Triangle with sides 2, 3, and angle 60° between them)

$\sqrt{7}$ (D) Signup and view all the answers

The displacement of a body at any time 't' after starting is given by $x = \frac{t^3}{3} - \frac{3t^2}{2} + 2t$. The velocity of the body is zero at t: (velocity is rate of change of displacement with respect to time)

2 sec. (C) Signup and view all the answers

The radius 'r' of a cylinder increases with time at a constant rate of 2 m/sec and its height decreases with time at constant rate of 3 m/sec. The rate of change of volume of cylinder at a time when radius and height of cylinder are 3m and 2m respectively will be:

-3$\pi m^3$/sec. (D) Signup and view all the answers

Y = $x^2logx$, then $\frac{dy}{dx}$ will be:

x + 2x log(x) (C) Signup and view all the answers

Equation of this straight line is: (Line passing through (0,10) forming 37° with x-axis)

3x + 4y = 40 (A) Signup and view all the answers

Differentiate $\frac{sin x}{1 + cos x}$ with respect to x

$\frac{1}{1 + cos x}$ (A), $\frac{1}{1 + cos x}$ (C) Signup and view all the answers

Cos2$\theta$ =

All of the above (D) Signup and view all the answers

Value of sin15°· cos15° is:

$\frac{1}{4}$ (C) Signup and view all the answers

If sin θ= $\frac{1}{3}$, then cos$\theta$ will be -

$\frac{2\sqrt{2}}{3}$ (C) Signup and view all the answers

If y = $\sqrt{sin \sqrt{x}}$ then $\frac{dy}{dx}$ is:

$\frac{cos \sqrt{x}}{4\sqrt{x} sin \sqrt{x}}$ (C) Signup and view all the answers

If sides of a rectangle with given perimeter are a & b , then find the relation between a & b for which area of the given rectangle is maximum

a = b (C) Signup and view all the answers

Value of $\sin(37^\circ) \cos(53^\circ)$ is -

$\frac{9}{25}$ (B) Signup and view all the answers

$\sin(90^\circ + \theta)$ is -

$\cos \theta$ (C) Signup and view all the answers

Value of $\tan 315^\circ$ is

-1 (D) Signup and view all the answers

Find value of $\frac{d}{dx} (\cos 45^\circ)$

0 (B) Signup and view all the answers

In the shown triangle two sides and one angle is given. The third side is :

$\sqrt{7}$ (B) Signup and view all the answers

Equation of this straight line is :

3x + 4y = 40 (B) Signup and view all the answers

Flashcards

sin(x) + ln(x) + e^(2x)

The function to differentiate, involving a sine, logarithm, and an exponential function.

dy/dx for y = sin(x) + ln(x) + e^(2x)

The derivative of the function combining trigonometric, logarithmic, and exponential components.