\(\int_{0}^{1} (x^3 + 3x^2)e^x dx =\)

The slope of tangent on the curve \(y=6 x^2-x-12\), at the point where curve meets positive \(x\)-axis is ___________ .

If \(A=\left[\begin{array}{ll}1 & 2 \\ 4 & 5\end{array}\right]\) then
Match List-I with List-II

List-I	List-II
(A) \(\operatorname{det}(A)\)	(I) \(-\frac{1}{3}\)
(B) \(\operatorname{det}\left(A^{-1}\right)\)	(II) \(- 12\)
(C) \(\operatorname{det}(2 A)\)	(III) \(- 3\)
(D) \(\operatorname{det}\left( 3 A ^T\right)\)	(IV) \(- 27\)

Choose the Correct answer from the options given below :

The acute angle between the lines \(\vec{r}=(4 \hat{i}-\hat{j})+\lambda(2 \hat{i}+\hat{j}-3 \hat{k})\) and \(\frac{x-1}{1}=\frac{y+1}{-3}=\frac{z-2}{2}\) is

Which of the following statements are true?
(A) The vector equation of the line through the point (5, 2, -4) and parallel to the vector \(3 \hat{i}+2 \hat{j}-8 \hat{k}\) is \(\vec{r}=(5 \hat{i}+2 \hat{j}-4 \hat{k})+\lambda(3 \hat{i}+2 \hat{j}-8 \hat{k})\)
(B) Vector form of the equation of line \(\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}\) is \(\vec{r}=(5 \hat{i}-4 \hat{j}+6 \hat{k})+\lambda(3 \hat{i}+7 \hat{j}+2 \hat{k})\)
(C) The direction cosines of z-axis are (1, 1, 0).
(D) If a line has direction ratios 2, -1, -2, then its direction cosines are \(-2 / 3,-1 / 3,-2 / 3\).
Choose the correct answer from the options given below:

Match List-l with List-ll

List-l (Matrix A)	List-ll (Determinant of adjA)
(A) \(\left[\begin{array}{cc}2 & 1 \\ -1 & 2\end{array}\right]\)	(I) 3
(B) \(\left[\begin{array}{ll}3 & 4 \\ 3 & 6\end{array}\right]\)	(II) 6
(C) \(\left[\begin{array}{cc}3 & 7 \\ -2 & -4\end{array}\right]\)	(III) 5
(D) \(\left[\begin{array}{ll}4 & 3 \\ 3 & 3\end{array}\right]\)	(IV) 2

Choose the correct answer from the options given below :

If \(A^2-A+I=0\), then \(A^{-1}\) is equal to :

A brown ring is formed in the ring test for \(NO_3^-\text{}\) ion. It is due to the formation of

Match List I with List - II.

List - I (Message Signal)	List - II (Band width)
(A) Speech	(I) 20 kHz
(B) TV Signal	(II) 2800 Hz
(C) Video for pictures	(III) 6 MHz
(D) Music	(IV) 4.2 MHz

Choose the correct answer from the options given below:

The first menstruation which begins at puberty is called :

If a person rides his motorbike \(x km\) at 30 km per hour, he has to spend ₹ 3 per kilometer on petrol; if he rides \(y km\) at a faster speed of 40 km per hour, the petrol cost increases to ₹ 4 per kilometer. If he has ₹ 100 to spend on petrol and wishes to find the maximum distance he can travel within one hour, then linear programming problem (LPP) formulation is:

Which of the following reactions is used to prepare Haloarenes?

Foetal ejection reflex triggers the release of: