PREVIOUS NEXT
1
MHT CET 2026 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
The value of integral $\displaystyle\int \dfrac{\sqrt{x^2 + 1}\,[\log(x^2 + 1) - 2\log x]}{x^4}\,dx$ is equal to...
A
$\left(1 + \dfrac{1}{x^2}\right)^{3/2}\left[\dfrac{-1}{3}\log\left(1 + \dfrac{1}{x^2}\right) + \dfrac{2}{9}\right] + c$
B
$\left(1 + \dfrac{1}{x^2}\right)^{3/2}\left[\dfrac{-1}{3}\log\left(1 + \dfrac{1}{x^2}\right) - \dfrac{2}{9}\right] + c$
C
$\left(1 + \dfrac{1}{x^2}\right)^{3/2}\left[\dfrac{-1}{3}\log\left(1 + \dfrac{1}{x^2}\right) + \dfrac{2}{3}\right] + c$
D
$\left(1 + \dfrac{1}{x^2}\right)^{3/2}\left[\dfrac{-1}{3}\log\left(1 + \dfrac{1}{x^2}\right) - \dfrac{2}{3}\right] + c$
2
MHT CET 2026 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
If $f(x) = \dfrac{1}{\log x}$ and $g(x) = \dfrac{1}{(\log x)^2}$, then the value of $\displaystyle\int [f(x) - g(x)]\,dx$ is...
A
$(\log x)^2 + c$
B
$x\log x + c$
C
$\dfrac{x}{\log x} + c$
D
$\dfrac{1}{\log x} + c$
3
MHT CET 2026 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
If $\displaystyle\int \dfrac{dx}{x^{7/2}(x^4 + 1)^{3/8}} = m\left(\dfrac{x^4 + 1}{x^4}\right)^n + c$, where $c$ is a constant of integration, then the value of $\dfrac{n}{m}$ is...
A
$-\dfrac{1}{16}$
B
$-\dfrac{25}{16}$
C
$\dfrac{25}{4}$
D
$-\dfrac{25}{4}$
4
MHT CET 2025 5th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$ \int \frac{d x}{\cos x(1+\cos x)}= $$

A

$\quad \log (\sec x+\tan x)+2 \tan \left(\frac{x}{2}\right)+\mathrm{c}$, where c is the constant of integration

B

$\quad \log (\sec x+\tan x)-2 \tan \left(\frac{x}{2}\right)+\mathrm{c}$, where c is the constant of integration

C

$\log (\sec x+\tan x)+\tan \left(\frac{x}{2}\right)+\mathrm{c}$, where c is the constant of integration

D

$\log (\sec x+\tan x)-\tan \left(\frac{x}{2}\right)+\mathrm{c}$, where c is the constant of integration

PREVIOUS NEXT

MHT CET Subjects

Browse all chapters by subject

Mathematics
Algebra
Sets and Relations Logarithms Quadratic Equations Sequences and Series Binomial Theorem Permutations and Combinations Probability Vector Algebra Three Dimensional Geometry Matrices and Determinants Statistics Mathematical Reasoning Linear Programming Complex Numbers
Trigonometry
Trigonometric Ratios & Identities Trigonometric Equations Inverse Trigonometric Functions Properties of Triangles
Calculus
Limits, Continuity and Differentiability Functions Definite Integration Indefinite Integration Application of Derivatives Area Under The Curves Differential Equations Differentiation
Coordinate Geometry
Parabola Ellipse Circle Straight Lines and Pair of Straight Lines Hyperbola
Physics
Mechanics
Units & Measurement and Dimensions Vector Algebra Motion Laws of Motion Circular Motion Work, Energy and Power Center of Mass and Collision Rotational Motion Gravitation Simple Harmonic Motion Fluid Mechanics Elasticity Waves Heat and Thermodynamics
Optics
Ray Optics Wave Optics
Electromagnetism
Electrostatics Current Electricity Capacitor Moving Charges and Magnetism Magnetism and Matter Electromagnetic Waves Electromagnetic Induction Alternating Current
Modern Physics
Atoms and Nuclei Dual Nature of Radiation Semiconductor Devices and Logic Gates Communication Systems
Chemistry
Physical Chemistry
Some Basic Concepts of Chemistry Atomic Structure States of Matter Thermodynamics Chemical Equilibrium Ionic Equilibrium Liquid Solution Redox Reactions Surface Chemistry Solid State Electrochemistry Chemical Kinetics Nuclear Chemistry
Inorganic Chemistry
Periodic Table and Periodicity Chemical Bonding and Molecular Structure Metallurgy Hydrogen and It's Compounds s-Block Elements p-Block Elements d and f Block Elements Coordination Compounds Environmental Chemistry
Organic Chemistry
IUPAC Nomenclatures General Organic Chemistry Isomerism Hydrocarbons Haloalkanes and Haloarenes Alcohol, Phenols and Ethers Aldehyde and Ketone Carboxylic Acids and Its Derivatives Compounds Containing Nitrogen Polymers Biomolecules Chemistry in Everyday Life Practical Organic Chemistry
EXAM MAP

Browse past year questions by exam & subject

Joint Entrance Examination
JEE Main JEE Advanced MHT CET BITSAT COMEDK WB JEE KCET VITEEE AP EAPCET TS EAMCET IAT (IISER)
Medical
NEET AIIMS MHT CET (Biology)
Graduate Aptitude Test in Engineering
GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN GATE Data Science and Artificial Intelligence
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12