Question
If $y=x+e^x$ then $\frac{d^2 y}{d x^2}=$ _________ .
✓
Answer
$e^x$
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In a LPP if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same _________ value.
In a LPP if the objective function Z = ax + by has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same _________ value.
Those problems in which an attempt is made to discover maximization of profit and minimization of cost are called _________ .
Fill in the blanks.
The solution of $(1+\text{x})^2\frac{\text{dy}}{\text{dx}}+2\text{xy}-4\text{x}^2=0$ is _________.
→The solution of $(1+\text{x})^2\frac{\text{dy}}{\text{dx}}+2\text{xy}-4\text{x}^2=0$ is _________.
If $y=\log |x|, x \neq 0$, then $\frac{d y}{d x}=$ ________ .
→The value of $\int \frac{1-\sin x}{\cos ^2 x} d x=$ _____________
→$P(A)+P(\bar{A})=$_______
→If sides of parallelogram are $\vec{a}=3 \hat{i}+\hat{j}+4 \hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$ then the area is ________
→If A has $3 \times 3$ order square matrix and $| A |=2$, then $\left|- AA ^{ T }\right|=$ ________ .
→Fill in the blanks:
$\int\frac{\text{x}+3}{(\text{x}+4)^2}\text{e}^\text{x}\text{dx}=$ ________.
→$\int\frac{\text{x}+3}{(\text{x}+4)^2}\text{e}^\text{x}\text{dx}=$ ________.
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)
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- 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.
- $3\Big(\frac{\pi}{2}+1\Big)\text{ sq.units}$
- $\Big(\frac{\pi}{2}+1\Big)\text{ sq.units}$
- $\Big(\frac{\pi}{2}-1\Big)\text{ sq.units}$
- $3\Big(\frac{\pi}{2}-1\Big)\text{ sq.units}$