The slope of the normal to the curve \(y=2 x^2-4\) at \(P(1,-2)\) is:

The area bounded by \(y^2=4 x\) and its latus rectum and \(x\)-axis in the first quadrant is:

The maximum value of a LPP \(z=3 x+4 y\) subject to the constraints: \(x+y \leq 6, x \geq 0, y \geq 0\) is:

If \(A\) and \(B\) are two invertible matrices, then which of the following statements are correct?
(A) \(\left|A^{-1}\right|=|A|^{-1}\)
(B) \(\operatorname{adj} A=|A| A^{-1}\)
(C) \((A B)^{-1}=A^{-1} B^{-1}\)
(D) \((A+B)^{-1}=A^{-1}+B^{-1}\)
Choose the correct answer from the options given below:

If \(\left|\begin{array}{ccc}-a^2 & a b & a c \\ a b & -b^2 & b c \\ a c & b c & -c^2\end{array}\right|=\lambda a^2 b^2 c^2\), then the value of \(\lambda\) is:

If the equation of a floor of a room is given by \(x+y-z+4=0\) and the equation of roof is given by \(x+y-z+5=0\). Then, the height of the room is :

Let the degree and order of the differential equation \(2 x^3 \frac{d y}{d x}-5\left(\frac{d^2 y}{d x^2}\right)^2=6\left(\frac{d y}{d x}\right)^3\) be \(m\) and \(n\) respectively. Then
(A) \(m=2\)
(B) \(n=3\)
(C) \(m=3\)
(D) \(m n=4\)

Match List-I with List-II

List-I	List-II
(A) Adenine	(I) Purine
(B) Thymine	(II) Pyrimidine
(C) Uracil	(III) DNA
(D) Deoxyribose	(IV) RNA

Choose the correct answer from the options given below:

If \(A=\left[\begin{array}{cc}3 & 2 a \\ 1 & 5\end{array}\right]\) and \(B=\left[\begin{array}{ll}2 & 3 \\ b & 5\end{array}\right]\) are singular matrices, then \(a+b\) is :

Choose the correct statements, when a cell of emf E and internal resistance r connected to external resistance R having current I flowing through the circuit is:
A. Potential difference across the terminals of the cell in a closed circuit having resistance R is always less than the emf.
B. For practical calculations, the internal resistance of the cells in the circuits may be neglected when the current I is such that E >> I.
C. Terminal potential difference in a closed circuit is always more than emf E.
D. Terminal potential difference versus current graph for a cell with closed circuit having resistance R is a straight line with a negative slope.
Choose the correct answer from the options given below:

The power of a combination of convex lens of focal length 40 cm and a concave lens of focal length 25 cm when placed in contact is :

Which disease is not the sexually transmitted infection?

Which of the following steps are included to make a healthy society?
(A) Aware the people to uncontrolled population growth
(B) Aware the people to social evil like sex abuse
(C) Aware the people to sex related crime
(D) The Peoples lead to increase the mortality rate of mother and infant
Choose the correct answer from the options given below: