If \(A=\left[\begin{array}{ccc}2 & 1 & -1 \\ 0 & 1 & 2 \\ 2 & -1 & \lambda\end{array}\right]\) is a singular matrix, then the value of \(\lambda\) is:

An unbiased die is rolled. If the random variable \(X\) is defined as,
\(X=\left\{\begin{array}{ll}1 & \text { if the outcome is a number less than or equal to } 3 \\0 & \text { if the outcome is a number greater than } 3\end{array}\right.\)
Then the probability distribution of \(X\) is :

If matrices \(A=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]\) and \(B=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]\), then \(B A\) is equal to:

Match List-l with List-ll.Find the derivatives from List-I.

List-l	List-II
(A) \(y=\sqrt{\sin x+y}\)	(I) \(\frac{-\sin x}{1+\cos y}\)
(B)\(\sin y=x \sin (a+y)\)	(II) \(\frac{\cos x}{2 y-1}\)
(C) \(y+\sin y=\cos x\)	(III) \(\frac{-1}{\sin ^2(x+y)}\)
(D) \(y=\tan (x+y)\)	(IV) \(\frac{\sin ^2(a+y)}{\sin a}\)

Choose the correct answer from the options given below:

Let \(A=\left[\begin{array}{cc}3 & -1 \\ 2 & 4\end{array}\right]\), then \(\operatorname{adjoint}(A)\) is:

The cost of type 1 rice is Rs. 20 per kg and type 2 rice is Rs. 30 per kg. If both Type 1 and Type 2 are mixed in the ratio \(2: 3\), then the price per kg of the mixed variety is

If \(A, B\) are symmetric matrices of the same order, then \(A B-B A\) is a :

Maximum value of \(z=5 x+4 y\) subject to the constraints \(x-y \leq 0, x+y \leq 4, x \geq 0, y \geq 0\) occurs at the point \((a, b)\). Then \(4 a+5 b=\) \(\_\_\_\_\) ,

Read the paragraph given below and answer the question. Insulin used for diabetes was earlier extracted from slaughtered cattle and pigs. Insulin from an animal source, though caused some patients to develop allergy or other type of reactions. Insulin consists of two short polypeptide chains: chain A and chain B, that are linked bridges. In mammals, including human, insulin is synthesised as a pro-hormone. Patient with diabetes have:

A bag contains 8 blue and 12 green balls. Two balls are drawn in succession without replacement.
The probability that first is blue and second is green is

Read the passage carefully and answer the following questions
There are mainly four series of the transition metals, \(3 d\) series ( \(S c\) to Zn), \(4 d\) series (Y to Cd), \(5 d\) series (La and Hf to Hg ) and 6d series which has Ac and elements from Rf to Cn . The two series of the inner transition metals; \(4 f\) ( Ce to Lu ) and \(5 f\) (Th to Lr ) are known as lanthanoids and actinoids respectively. Their chemical properties are transitional between those of \(s\) and \(p\) block elements. The transition metals (with the exception of Zn, Cd and Hg) are very hard and have low volatility. Their melting and boiling points are high. Transition metals have incomplete d subshell either in neutral atom or in their ions. With partly filled d orbitals these elements exhibit certain characteristic properties such as display of a variety of oxidation states, formation of coloured ions and entering into complex formation with a variety of ligands. The transition metals and their compounds are known for their catalytic activity.
In general the electronic configuration of outer orbitals of transition metals is \((n - 1)d^{1-10}ns^{1-2}\) but Pd shows an exceptional electronic configuration as......

Once the BOD of sewage or waste water is reduced significantly, the effluent is then passed into a settling tank where the bacterial 'flocs' are allowed to sediment. This sediment is called as:

The values of \(b\) for which \(y=2 x^2-b x+2\) touches the \(x\)-axis are: