Let \(A=\left[a_{i j}\right]\) is given by \(A=\left[\begin{array}{ccc}1 & -1 & 2 \\ 3 & 4 & -5 \\ 2 & -1 & 3\end{array}\right]\). Then the matrix \(B=\left[b_{i j}\right]\), where \(b_{i j}\) = Minor of \(a_{i j}\) is:

A manufacturing unit makes two models, 'classic' and 'supreme' of the scooter.
Each piece of the classic model requires 9 labour hours for assembling and 1 labour hour for finishing.
Each piece of supreme model requires 12 labour hours for assembling and 3 labour hour for finishing.
Maximum labour hours available for assembling and finishing are 180 and 30 respectively.
Profit is Rs. 10000 on each classic piece and Rs. 15000 on each supreme piece.
Which option describes the LPP to maximize profit Z (where x and y are classic and supreme pieces)?

The area of the region enclosed between the two circles \(x^2+y^2=1\) and \((x-1)^2+y^2=1\) 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:

The area (in sq. units) of the region enclosed by the ellipse \(16 x^2+25 y^2=400\) is:

A tub contains \(60\) litres of milk. From this tub, \(6\) litres of milk was taken out and replaced with water. This whole process was repeated further two more times. How much milk is there in the tub now?

If \(X\) is normal distribution random variable with mean \(\mu=10\) and standard deviation \(\sigma=2, Z\) is standard normal variable and \(F(Z)\) is cumulative distribution function, then which of the following are true?
[Given that \(F(1.5)=0.9332, F(3)=0.9986, F(2.25)=0.9878\) and \(F(1)=0.8413\) ]
(A) \(P(X<13)=0.9332\)
(B) \(P(X>16)=0.9986\)
(C) \(P(12<X<14.5)=0.1465\)
(D) \(P(X>8)=0.8413\)
Choose the correct answer from the options given below:

Two identical point charges placed at a distance 'r' apart exert a force F on each other. If each charge is halved and the distance between them is doubled, then the new force acting on each charge would be

A 200 turns closely wound circular coil of radius 10 cm carries a current of 3.5 A. The magnetic moment of the coil is

Match List-I with List-II

List-I (Causes of biodiversity losses)	List-II ( Examples)
(A) Habitat loss and fragmentation	(I). Parthenium, Lantana and water hyacinth (Eichornia)
(B) Over-exploitation	(II). Co-evolved plant-pollinator mutualism
(C) Alien species invasion	(III). Deforestation for conversion of forest to grasslands
(D) Co-extinctions	(IV). Excessive fishing and over harvesting of certain fish populations

Choose the correct answer from the options given below:

Observe the illustration and answer the following question:

46 chromosomes are present in:

The enzyme used to treat a plant cell for isolation of DNA is:

Match List-l with List-ll

List-I (Terms)	List-II (Features)
(A) Spermatogenesis	(I) Nutrition to germ cells
(B) Acrosome	(II) Testicular hormones
(C) Leydig's cells	(III) Penetration of sperm
(D) Sertoli cells	(IV) Formation of sperms

Choose the correct answer from the options given below: