Question
Function $f(x)=\frac{1}{4 x^2+2 x+1}$, then maximum value of function is _________ .
✓
Answer
$\frac{4}{3}$
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Similar questions
If $\vec{a}=2 \hat{i}+\hat{j}+3 \hat{k}$ and $\vec{b}=3 \hat{i}+5 \hat{j}-2 \hat{k}$, then the value of $|\vec{a} \times \vec{b}|$ will be ___________ .
→A mirror in the shape of an ellipse represented by $\frac{\text{x}^2}{9}+-\frac{\text{y}^2}{4}=1$ was hanging on the wall. Arun and his sister were playing with ball inside the house, even their mother refused to do so. All of sudden, ball hit the mirror and got a scratch in the shape of line represented by $\frac{\text{x}}{3}+\frac{\text{y}}{2}=1$
Based on the above information, answer the following questions.
→Based on the above information, answer the following questions.
- Point(s) of intersection of ellipse and scratch (straight line) is (are).
- (0, 2), (3, 0)
- (2, 0), (3, 0)
- (2, 3), (0, 0)
- (0, 3), (3, 0)
- Area of smaller region bounded by the ellipse and line is represented by.
- The value of $\frac{2}{3}\int\limits_{0}^{3}\sqrt{9-\text{x}^2}\text{dx}$ is.
- $\frac{\pi}{2}$
- $\pi$
- $\frac{3\pi}{2}$
- $\frac{\pi}{4}$
- The value of $2\int\limits_{0}^{3}\bigg(1-\frac{\text{x}}{3}\bigg)\text{dx}$ is.
- 0
- 1
- 2
- 3
- Area of the smaller region bounded by the mirror and scratch is.
- $3\Big(\frac{\pi}{2}+1\Big)\text{ sq.units}$
- $\Big(\frac{\pi}{2}+1\Big)\text{ sq.units}$
- $\Big(\frac{\pi}{2}-1\Big)\text{ sq.units}$
- $3\Big(\frac{\pi}{2}-1\Big)\text{ sq.units}$
Fill in the blank.
The value of $\cos^{-1}\Big(\cos\frac{14\pi}{3}\Big)$ is __________.
→The value of $\cos^{-1}\Big(\cos\frac{14\pi}{3}\Big)$ is __________.
Fill in the blanks.
A feasible region of a system of linear inequalities is said to be _________, if it can be enclosed within a circle.
A feasible region of a system of linear inequalities is said to be _________, if it can be enclosed within a circle.
If $A =\left[\begin{array}{ccc}0 & a & 1 \\ -1 & b & 1 \\ -1 & c & 0\end{array}\right]$ has a skew symmetric matrix, then value of $(a+b+c)^2$ ________
→If $P ( A )=\frac{6}{11}, P ( B )=\frac{5}{11}$ and $P ( A \cup B )=\frac{7}{11}$ then value of $P ( A \cap B )$ will be ____________ .
→If the direction cosines of a line are $l, m, n$, then the equations of the line are _____________ .
→If $P ( B )=0.5$ and $P ( A \cap B )=0.32$ then the value of $P ( A \mid B )$ will be ____________ .
→Fill in the blanks.
The solution of the differential equation $\text{ydx}+(\text{x}+\text{xy})\text{dy}=0$ is ________.
→The solution of the differential equation $\text{ydx}+(\text{x}+\text{xy})\text{dy}=0$ is ________.
The value of $\sec ^2\left(\tan ^{-1} 2\right)+\operatorname{cosec}^2\left(\cot ^{-1} 3\right)$ is _______
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