Mathematics

# The angle made by the tangent line at (1, 3) on the curve $y=4x-{ x }^{ 2 }$ with $\overline{ OX }$ is

$\tan ^{-1}2$

##### SOLUTION
Given,

$y=4x-x^2$

$\dfrac{dy}{dx}=4-2x$

$\dfrac{dy}{dx}_{(1,3)}=4-2(1)=2$

$\tan \theta =2$

$\therefore \theta =\tan ^{-1}2$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Subjective Hard
Solve : $\displaystyle \int ^{\cfrac{\pi}{2}}_{0} \frac{\sin^2 x}{\sin x+\cos x}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Assertion & Reason Hard
##### ASSERTION

STATEMENT-1 : $\displaystyle \int \frac{\left \{ f(x)\phi '(x)-f'(x)\phi (x) \right \}}{f(x)\phi (x)}\left \{ \log \phi (x)-\log f(x) \right \}dx=\frac{1}{2}\left \{ \log \frac{\phi(x)}{f(x)} \right \}^{2}+c$

##### REASON

STATEMENT-2 : $\displaystyle \int (h(x))^{n}h'(x)dx=\frac{(h(x))^{n+1}}{n+1}+c$

• A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
• B. STATEMENT-1 is True, STATEMENT-2 is False
• C. STATEMENT-1 is False, STATEMENT-2 is True
• D. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
The value of $\int _{ 0 }^{ { \sin }^{ 2 }x }{ { \sin }^{ -1 }\sqrt { t } dt+ } \int _{ 0 }^{ { \cos }^{ 2 }x }{ { \cos }^{ -1 }\sqrt { t }dt}$ is
• A. $\pi$
• B. $\dfrac { \pi }{ 4 }$
• C. $1$
• D. $\dfrac { \pi }{ 2 }$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
If $\displaystyle\int \frac{1}{x\left [ \left ( \log x \right ) ^{2}+4\log x-1\right ]}$ integrated gives $\displaystyle =\frac{1}{2\sqrt{\left ( 5 \right )}}\log \frac{\left ( t+2 \right )-\sqrt{5}}{\left ( t+2 \right )+\sqrt{\left ( 5 \right )}}$ , then find t.
• A. $\ln x$
• B. $x$
• C. $\dfrac {1} {\log x}$
• D. $\log x$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
Integrate:
$\int _{ 0 }^{ \infty }{ \dfrac { x\tan ^{ -1 }{ x } }{ { (1+{ x }^{ 2 }) }^{ 2 } } } dx$ equals ?
• A. $\pi/2$
• B. $\pi/6$
• C. $\pi/4$
• D. $\pi/8$