Let \(A\) and \(B\) be \(3 \times 3\) matrices such that \(A \neq B\). If \(A^3=B^3\) and \(A^2 B=B^2 A\), then the determinant of \(A^2+B^2\) is :

If \(A=(2,3), B=(-1,0), C=(4,6)\) then the area of the parallelogram \(A B C D\) is:

The total cost \(C(x)\) in Rupees associated with the production of \(x\) units of an item is given by
\(C(x)=0.007 x^3+26 x^2+15 x+400\) 
The marginal cost when 10 items are produced is:

Which of the following statements are correct?
(A) If elements of a row (or column) of a determinant are multiplied with cofactors of any other row (or column), then their sum is zero.
(B) The value of determinant is equal to the sum of the product of elements of any row (or column) with their corresponding cofactors.
(C) If any two rows (or columns) of a determinant are interchanged, their sign of determinant does not change.
(D) The value of determinant remains unchanged if its rows and columns are interchanged.
(E) A square matrix A has inverse if and only if A is singular.
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There are 50 telephone lines in an exchange. The probability that any one of them will be busy is 0.1, then the probability that all the lines are busy?

Let A = \(\left[\begin{array}{ccc}152 & 105 & 3 \\ 149 & 25 & 35 \\ 2 & 1 & 0\end{array}\right]\) . If \(A_{i j}\) denotes the co-factor of an element \(a_{i j}\) of the matrix A, then the value of \(a_{11} A_{21}+a_{12} A_{22}+a_{13} A_{23}\) is equal to

The points of discontinuity of the function \(f\) defined by \(f(x)=\begin{cases} x + 2 & x \leq 1 \\x - 2 & 1 < x < 2\text { are: } \\0 & x \geq 2 \end{cases}\)

Which of the following statements are correct?
(A) The current under reverse bias is essentially voltage dependent on a critical reverse bias voltage.
(B) The diode gets destroyed due to overheating if the forward or reverse current exceeds the rated value.
(C) In forward bias measurement, we use a milliammeter since the expected current is large, while a microammeter is used in reverse bias to measure the current.
(D) The drift current is of the order of a few \( \mu \)A
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In RNAi genes are silenced by:

For the differential equation \(x \frac{d y}{d x}+3 y=x^2 \log _e x\) which of the following statements are TRUE?
(A) Product of order and degree is 1
(B) Integrating factor is \(x^3\)
(C) Integrating factor is \(3 x\)
(D) General solution is \(y=\frac{x^3}{36}\left(6 \log _e|x|-1\right)+C x^{-3}\), C is an arbitrary constant
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The order of increasing boiling point for the following compounds is
(A) \(CH_3CH_2CH_2CH_3\)
(B) \(CH_3CH_2CH_2CH_2OH\)
(C) \(C_2H_5OC_2H_5\)
(D) \(CH_3CH_2CH_2CHO\)
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Answer the question on basis of passage given below :
Vitamins represent a group of organic compounds which are needed in small amount for the healthy growth and maintenance of our body. These are not synthesized by the body and are supplied in the diet. The deficiency of vitamins can be supplemented with medicines.
Match List - I with List – II.

List - I	List - II
A. Vitamin A	I. Green leafy vegetables, spinach, cabbage.
B. Vitamin B12	II. Fish liver oil, carrots, butter and milk.
C. Vitamin C	III. Egg and curd.
D. Vitamin K	IV. Citrus fruits, amla and green leafy vegetables.

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An equiconvex lens has a focal length of 20 cm and its radius of curvature is 30 cm . Its refractive index is