If \(\operatorname{det}\left(\begin{array}{cc}2 x & 5 \\ 8 & x\end{array}\right)=\operatorname{det}\left(\begin{array}{cc}6 & -2 \\ 1 & 1\end{array}\right)\), then the value of \(x\) is

If A and B are two matrices of order \(4 \times m\) and \(4 \times n\), respectively and \(m=n\),
then the order of matrix \((5 A-2 B)\) is:

Let \(f(x)=\left\{\begin{array}{ll}2 x-1, & x<1 \\ 1, & x=1 \\ x^2, & x>1\end{array}\right.\) then at \(x=1\)

Match List-I with List-II

List-I	List-II
(A) \(f ( x )=| x |\)	(I) Not differentiable at \(x=-2\) only
(B) \(f(x)=|x+2|\)	(II) Not differentiable at \(x=0\) only
(C) \(f(x)=\left|x^2-4\right|\)	(III) Not differentiable at \(x=2\) only
(D) \(f(x)=|x-2|\)	(IV) Not differentiable at \(x=2,-2\) only

Choose the correct answer from the options given below:

A vessel contains 56 litres of mixture of milk and water in the ratio \(5: 2\). How much water should be mixed with it so that the milk to water ratio becomes 4:5.

Let \(X\) and \(Y\) be any two invertible square matrices of order \(n\). Then which of the statements are true?
(A) \((A B)^{-1}=A^{-1} B^{-1}\)
(B) \((A B)^{-1}=B^{-1} A^{-1}\)
(C) \((A B)^T=A^T B^T\), where \(A^T\) denotes transpose of A
(D) \((A B)^T=B^T A^T\), where \(A^T\) denotes transpose of A
Choose the correct answer from the options given below :

The general solution of the differential equation \(\log _e\left(\frac{d y}{d x}\right)=a x+b y\) is

The corner points of the bounded feasible region for an LPP are : \((5,5),(15,15),(0,20)\) and \((0,10)\).
Let \(z=3 x+9 y\) be the objective function.
Then the value of maximum \((z)-\operatorname{minimum}(z)\) is :

For the given \(5\) values, \(15, 18, 21, 27, 39;\) the three year moving averages are:

Read the following paragraph and answer the given questions.
Cancer detection is based on biopsy and histopathological studies. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Do you know why mother's milk is considered very essential for the new-born infant? The yellowish fluid colostrum secreted by mother during the initial days of lactation has abundant antibodies (IgA) to protect the infant. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal. The exaggerated response of the immune system to certain antigens present in the environment is called allergy. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused. Morphine is a very effective sedative and painkiller, and is very useful in patients who have undergone surgery.
The drug, which is very effective sedative and painkiller and useful for patients who have undergone surgery is -

Which of the following is a fat soluble vitamin?

If an investment of Rs. \(12000\) becomes Rs. \(72000\) in \(4\) years, then the compound annual growth rate is:

Match List-I with List-II

Llst-I	Llst-(II)
(A) \(f(x)=[x]\)	(I) Continuous everywhere but not differentiable at \(x=-1\)
(B) \(f(x)=|x-1|\)	(II) Continuous everywhere except at all integral values
(C) \(f(x)=e^{|x|}\)	(III) Continuous everywhere but not differentiable at \(x=1\)
(D) \(f(x)=|x+1|\)	(IV) Continuous everywhere but not differentiable at \(x=0\)

Choose the correct answer from the options given below: