The total cost \(C(x)\) associated with the production of \(x\) units of an item is given by
\(\ C(x)=0.001 x^3+0.06 x^2+20 x+500\).
The marginal cost when 10 units are produced is:

Under which of the following conditions the Poisson distribution is the limiting case of, binomial distribution :
(A) The number of trials is indefinitely large.
(B) The probability of success for each trial is indefinitely small.
(C) The product of the number of trials and the probability of success for each trial is finite.
(D) The probability of success for each trial is indefinitely large.
Choose the correct answer from the options given below :

Consider the LPP, Max Z = x + y subject to the conditions
\(x+y \leq 3, \quad x-y \geq 1, \quad x \geq 0, y \geq 0\),
then which of the following is not the corner point of the feasible region of above LPP.

If the matrix \(A=\left[\begin{array}{ccc}x & 2 & y \\ -2 & 0 & 3 \\ -1 & z & 0\end{array}\right]\) is skew-symmetric, then the value of \(2 x-3 y+5 z\) is equal to

If three points \(A \left(a_1, b_1\right), B \left(a_2, b_2\right)\) and \(C \left(a_3, b_3\right)\) are collinear and D is the determinant of their coordinates with a column of 1s, then:

Match List 1 with List 2.

List - 1 (Matrix)	List - 2 (Determinants)
(A) \(\operatorname{Matrix}(A)=\left[\begin{array}{cc}1 & 7 \\ -3 & 5\end{array}\right]\)	(I) 24
(B) \(\operatorname{Matrix}(B)=\left[\begin{array}{cc}-2 & 5 \\ -3 & -3\end{array}\right]\)	(II) 32
(C) \(\operatorname{Matrix}(C)=\left[\begin{array}{ll}-12 & 8 \\ -16 & 8\end{array}\right]\)	(III) 21
(D) \(\operatorname{Matrix}(C)=\left[\begin{array}{ll}-12 & 8 \\ -16 & 8\end{array}\right]\)	(IV) 26

Choose the correct answer from the options given below :

If a moneylender charges interest at the rate of 10 rupees per 100 rupees per half year, payable in advance, then the effective rate of interest per annum is :

A combination of progestogen-estrogen is used in:

Which one of the following is NOT the function of Leydig cells ?

The area of the region bounded by the curve \(y=\sin x\) and the \(x\)-axis between \(x=\pi / 2\) and \(x=3 \pi / 2\) is :

Match List-l with List-II:

List-I (Concepts)	List-II (Explanation)
(A) Standing state	(I) Available biomass for the consumption of heterotrophs
(B) Secondary productivity	(II) Rate of formation of organic matter by consumers
(C) Standing crop	(III) Mass of living matter in a trophic level at a given time
(D) Net primary productivity	(IV) Amount of mineral nutrients in the soil at a given time

Choose the correct answer from the options given below:

A motorbike costing Rs. 1, 25, 000 has a scrap value of Rs. 25, 000.
If the annual depreciation charge is Rs. 12, 500, then the useful life of the bike is (by using linear method):

MONOHYBRID CROSS
The inheritance of flower color in the dog flower (Snapdragon or Antirrhinum sp.) can be understood by crossbreeding between true-breeding red-flowered (RR) and true-breeding white-flowered plants (rr). When they were crossed, F₁ (Rr) was pink. When F₁ was self-pollinated, the F₂ results were Red, Pink and White. Here the genotype ratios were exactly as expected, but the phenotype ratios have been changed. What happened was that R was not completely dominant over r and this made it possible to distinguish Rr as pink from RR (Red) and rr (White).
What will be the genotypic ratio in F₂ generation when F₁ (Rr) was self-pollinated?