ExamSIDE (Powered by ExamGOAL)
Questions
PREVIOUS NEXT
1
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$$\int \frac{\left(x^2+1\right)}{(x+1)^2} \mathrm{~d} x=$$

A
$ x-2 \log |(x+1)|-\frac{1}{x+1}+c$, where $c$ is a constant of integration.
B
$ x-2 \log |(x+1)|-\frac{2}{x+1}+c$, where c is a constant of integration.
C
  $ x-\log |(x+1)|-\frac{2}{x+1}+c$, where $c$ is a constant of integration.
D
$x-\log |(x+1)|-\frac{x}{x+1}+\mathrm{c}$, where c is a constant of integration.
2
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

$\int\left(1+x-\frac{1}{x}\right) e^{x+\frac{1}{x}} d x$ equal to

A
$(x+1) e^{x+\frac{1}{x}}+c$, (where $c$ is a constant of integration)
B
$-x e^{x+\frac{1}{x}}+c$, (where $c$ is a constant of integration)
C
$(x-1) e^{x+\frac{1}{x}}+c$, (where $c$ is a constant of integration)
D
$x e^{x+\frac{1}{x}}+c$, (where $c$ is a constant of integration)
3
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The value of $\mathrm{I}=\int \frac{x^2}{(\mathrm{a}+\mathrm{bx})^2} \mathrm{dx}$ is

A
$\frac{1}{b^3}\left[a+b x+2 a \log |a+b x|-\frac{a^2}{a+b x}\right]+c$, (where c is the constant of integration)
B
$\frac{1}{b^3}\left[a+b x-2 a \log |a+b x|+\frac{a^2}{a+b x}\right]+c$, (where c is the constant of integration)
C
$\frac{1}{b^3}\left[a+b x-2 a \log |a+b x|-\frac{a^2}{a+b x}\right]+c$, (where c is the constant of integration)
D
$\frac{1}{b^3}\left[a+b x+2 a \log |a+b x|+\frac{a^2}{a+b x}\right]+c$, (where c is the constant of integration)
4
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $I=\int e^{\sin \theta}\left(\log \sin \theta+\operatorname{cosec}^2 \theta\right) \cos \theta d \theta$, then $I$ is equal to

A
$\mathrm{e}^{\sin \theta}\left(\log \sin \theta+\operatorname{cosec}^2 \theta\right)+\mathrm{c}$, (where c is a constant of integration)
B
$\mathrm{e}^{\sin \theta}(\log \sin \theta+\operatorname{cosec} \theta)+\mathrm{c}$, (where c is a constant of integration)
C
$\mathrm{e}^{\sin \theta}(\log \sin \theta-\operatorname{cosec} \theta)+\mathrm{c}$, (where c is a constant of integration)
D
$\mathrm{e}^{\sin \theta}\left(\log \sin \theta-\operatorname{cosec}^2 \theta\right)+\mathrm{c}$, (where c is a constant of integration)
PREVIOUS NEXT
MHT CET Subjects
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
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
Functions Limits, Continuity and Differentiability Differentiation Application of Derivatives Indefinite Integration Definite Integration Area Under The Curves Differential Equations
Coordinate Geometry
Straight Lines and Pair of Straight Lines Circle Parabola Ellipse Hyperbola
EXAM MAP
Joint Entrance Examination
JEE MainJEE AdvancedWB JEEBITSATMHT CETKCETCOMEDKVITEEEAP EAPCETTS EAMCET
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12