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KCET 2023
MCQ (Single Correct Answer)
+1
-0

$$\int \sqrt{\operatorname{cosec} x-\sin x} d x$$ is equals to

A
$$\frac{\sqrt{\sin x}}{2}+C$$
B
$$2 \sqrt{\sin x}+C$$
C
$$\frac{2}{\sqrt{\sin x}}+C$$
D
$$\sqrt{\sin x}+C$$
2
KCET 2023
MCQ (Single Correct Answer)
+1
-0

$$\int \sqrt{5-2 x+x^2} d x$$ is equals to

A
$$\begin{aligned} \frac{x}{2} \sqrt{5-2 x+x^2} & +4 \log \mid(x+1)+\sqrt{x^2-2 x+5} \mid+C\end{aligned}$$
B
$$\frac{x-1}{2} \sqrt{5+2 x+x^2}+2 \log \mid(x-1)+\sqrt{5+2 x+x^2} \mid+C$$
C
$$\frac{x-1}{2} \sqrt{5-2 x+x^2}+2 \log \mid(x-1)+\sqrt{5-2 x+x^2} \mid+C$$
D
$$\frac{x-1}{2} \sqrt{5-2 x+x^2}+2 \log \mid(x+1)+\sqrt{x^2+2 x+5}|+C$$
3
KCET 2023
MCQ (Single Correct Answer)
+1
-0

$$\int \frac{1}{1+3 \sin ^2 x+8 \cos ^2 x} d x$$ is equals to

A
$$\tan ^{-1}\left(\frac{2 \tan x}{3}\right)+C$$
B
$$\frac{1}{6} \tan ^{-1}\left(\frac{2 \tan x}{3}\right)+C$$
C
$$6 \tan ^{-1}\left(\frac{2 \tan x}{3}\right)+C$$
D
$$\frac{1}{6} \tan ^{-1}(2 \tan x)+C$$
4
KCET 2022
MCQ (Single Correct Answer)
+1
-0

$$\int \frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha} d x$$ is equal to

A
$$2(\sin x-x \cos \alpha)+c$$
B
$$2(\sin x+x \cos \alpha)+c$$
C
$$2(\sin x-2 x \cos \alpha)+c$$
D
$$2(\sin x+2 x \cos \alpha)+c$$
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KCET Subjects
Physics
Mechanics
Units & Measurement and Dimensions 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 Induction Alternating Current Electromagnetic Waves
Modern Physics
Atoms and Nuclei Semiconductor Devices and Logic Gates Dual Nature of Radiation
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
Inorganic Chemistry
Periodic Table and Periodicity Chemical Bonding and Molecular Structure Hydrogen and It's Compounds s-Block Elements p-Block Elements d and f Block Elements Metallurgy Coordination Compounds
Organic Chemistry
General Organic Chemistry Isomerism IUPAC Nomenclatures 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
Mathematics
Algebra
Logarithms Quadratic Equations Sequences and Series Permutations and Combinations Probability Sets and Relations Binomial Theorem 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 Parabola Ellipse Hyperbola
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