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1
KCET 2018
MCQ (Single Correct Answer)
+1
-0
$\int \frac{1}{\sqrt{3-6 x-9 x^2}} d x$ is equal to
A
$\sin ^{-1}\left(\frac{3 x+1}{2}\right)+C$
B
$\sin ^{-1}\left(\frac{3 x+1}{6}\right)+c$
C
$\frac{1}{3} \sin ^{-1}\left(\frac{3 x+1}{2}\right)+C$
D
$\sin ^{-1}\left(\frac{2 x+1}{3}\right)+C$
2
KCET 2018
MCQ (Single Correct Answer)
+1
-0
$\int e^{\sin x} \cdot\left(\frac{\sin x+1}{\sec x}\right) d x$ is equal to
A
$\sin x \cdot e^{\sin x}+C$
B
$\cos x \cdot e^{\sin x}+C$
C
$e^{\sin x}+C$
D
$e^{\sin x}(\sin x+1)+C$
3
KCET 2017
MCQ (Single Correct Answer)
+1
-0

$$ \int \sqrt{x^2+2 x+5} d x \text { is equal to } $$

A

$$\frac{1}{2}(x+1) \begin{aligned} & \sqrt{x^2+2 x+5}+2 \log \mid x+1+ \sqrt{x^2+2 x+5 \mid}+C \end{aligned} $$

B

$\left.(x+1) \sqrt{x^2+2 x+5}+\frac{1}{2} \log \right\rvert\, x+1+\sqrt{x^2+2 x+5}+C $

C

$(x+1) \sqrt{x^2+2 x+5}+2 \log \mid x+1+\sqrt{x^2+2 x+5}+C $

D

$(x+1) \sqrt{x^2+2 x+5}-2 \log \mid x+1+\sqrt{x^2+2 x+5}+C $

4
KCET 2017
MCQ (Single Correct Answer)
+1
-0
$\int \frac{(x+3) e^x}{(x+4)^2} d x$ is equal to
A
$\frac{e^x}{(x+4)^2}+C$
B
$\frac{e^x}{(x+3)}+C$
C
$\frac{1}{(x+4)^2}+C$
D
$\frac{e^x}{(x+4)}+C$
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Physics
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Units & Measurement and Dimensions Vector Algebra Motion in a Straight Line Motion in a Plane 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
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Ray Optics Wave Optics
Electromagnetism
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Modern Physics
Atoms and Nuclei Dual Nature of Radiation Semiconductor Devices and Logic Gates Communication Systems
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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
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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
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