List of practice Questions

Select the figure from the options which will continue the series established by the problem figure:

Which among the following is NOT a scheduling strategy for television programming?

The sum of roots of |x² - 8x + 15| - 2x + 7 = 0 is:

Match List -I with List-II

	List -I		List-II
A	Diamagnetic solid	I	CrO2
B	Ferromagnetic solid	II	Fe3O4
C	Antiferomagnetic solid	III	NaCl
D	Ferrimagnetic solid	IV	MnO

Choose the correct answer from the option given below

Choose the sentence with the correct use of prepositions on the following options.
(A) A few of the glaciers are expected to vanish by 2050.
(B) They never turned up their proposal.
(C) It was the last report filed by the company in last month.
(D) I am indebted for you regarding help.
Choose the correct answer from the option given below:

If \( f(x) = |x - 5| + |x + 5| + |x - 4| + |x + 4| \), then \[ \frac{f'(1) - f'(-6)}{f'(1) + f'(-6)} \]

If \( f(x + ay) + g(x - ay) = 0 \), then \( \frac{dy}{dx} = \):

If the angle between the curves \( y = e^{(x+4)} \) and \( x^2 y = 1 \) at the point \( (1, 1) \) is \( \theta \), then \[ \sin \theta + \cos \theta = \dots \]

If a line is moving between the coordinate axes such that the sum of the intercepts made by it on the coordinate axes is always 12, then the equation of that line which forms a triangle of maximum area with the coordinate axes is:

If \( (2, a) \) and \( (b, 19) \) are two stationary points of the curve \( y = 2x^3 - 15x^2 + 36x + c \), then \( a + b + c = \dots \)

If the points of contact of the tangents drawn from \( (0,0) \) to the curve \( y = x^2 + 3x + 4 \) are \( (\alpha, \beta) \) and \( (\gamma, \delta) \), then \( \beta + \delta = \):

Evaluate the integral: \[ \int \frac{dx}{4 + 5 \cos x} \]

If \( f(x) = \int_0^x \frac{5t^8 + 7t^6}{(t^2 + 2t + 1)^2} dt \) and \( f(0) = 0 \), then the value of \( f(1) \) is:

Evaluate the integral: \[ \int_0^{\frac{\pi}{4}} \frac{\cos^2 x}{\cos^2 x + 4 \sin^2 x} \, dx \]

Evaluate the integral \( \int x^3 (\log x)^2 dx \):

If \[ \int \frac{1}{x(\log x)^2 + 4\log x - 1} \, dx = A \log [ \log x + B ] + K \] where \( K \) is the constant of integration, then \[ \int \frac{1}{x(\log x)^2 + 4\log x - 1} \, dx = A \log [ \log x + C ] + K. \]

If \( f(x) = \int_0^x \left[ (a+1)(t+1)^2 - (a-1)(t^2 + t + 1) \right] dt \), then a possible positive value of \( a \), for which \( f'(x) = 0 \) has equal roots, is:

Evaluate the integral: \[ \int_0^{\frac{\pi}{2}} \frac{\sin \left( \frac{\pi}{4} + x \right) + \sin \left( \frac{3\pi}{4} + x \right)}{\cos x + \sin x} \, dx \]

Evaluate the integral: \[ \int_0^1 \left( \sqrt{10} \right)^{2x} \, dx \]

The area (in sq. units) of the region bounded by the curves \( y = 4 \cos x \) and \( y = -|\cos x| \) from \( x = -\frac{\pi}{2} \) to \( x = \frac{\pi}{2} \) is:

If \[ x^a \frac{dy}{dx} = y^\beta \left( \gamma \log x + \delta y + 1 \right) \] is a homogeneous differential equation, then

The general solution of the differential equation \( \tan x \tan y \, dx + \cos^2 x \csc^2 y \, dy = 0 \) is:

If \( \alpha \) and \( \beta \) are respectively the order and degree of the differential equation \[ y = e^{\frac{d^2y}{dx^2}}, \] then the value of \( \alpha + \alpha^\beta + \alpha^{2\beta} + \dots + \alpha^{2023\beta} \) is:

Among the following, the unit of permeability is NOT represented by