If \(A\) and \(B\) are independent events, then
A. not \(A\) and not \(B\) are independent
B. \(A\) and not \(B\) are independent
C. not \(A\) and \(B\) are not independent
D. \(P(A \cup B)=P(A)+P(B)\)
E. \(P(A \cap B)=P(A) P(B)\)
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The relation \(R\) on the set \(A=\{1,2,3,4,5\}\), given by \(R(a, b):|a-b|\) is even, is:

If A is a skew-symmetric matrix, then which of the following statements is NOT true?
(A) A is singular if order of A is odd
(B) A is non-singular
(C) \(A^{2025}\) is a skew-symmetric matrix
(D) \(A^{2025}\) is a symmetric matrix
(E) all diagonal elements of A are zeros
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The planes 2x - y + 4z = 5 and \(5 x-\frac{5}{2} y+10 z=6\) are

Choose the wrong statement.

Ravish rowed 40 km downstream in 2 hrs 30 min and returned to the starting point in 5 hrs . What is the speed of the current ?

If the minimum value of the objective function \(Z=a x+b y\) of an LPP occurs at two points \((3,5)\) and \((5,3)\), then

Identify the biodegradable polymer in the following :

Read the passage carefully and answer the questions
Carbohydrates are naturally formed organic compounds from various plants. The common chemical formula, \(C _x\left( H _2 O \right)_y\), was considered as hydrates of carbon to derive the various carbohydrates. For instance, the general formula for glucose ( \(C _6 H _{12} O _6\) ) easily fits into the above formula. Carbohydrates also called saccharides are classified on the basis of their behavior towards hydrolysis. Monosaccharides cannot be hydrolyzed further to simpler units of polyhydroxy aldehyde or ketones. About 20 monosaccharides are known to occur in nature. Carbohydrates that yield large number of monosaccharide units are called polysaccharides. Amino acids contain ( \(- NH _2\) ) and ( - COOH ), which can be classified in various forms. Proteins are polymers of alpha amino acids which are connected to each other by a peptide bond or peptide linkage. When a native protein is subjected to physical change, its globules unfold and helix get uncoiled and the protein loses its biological activity. The protein is said to be denaturated.
Which of the following statements is incorrect for Lactose ?

The value(s) of \(x\) for which the matrix \(A=\left[\begin{array}{ccc}x-1 & 1 & 1 \\ 1 & x-1 & 1 \\ 1 & 1 & x-1\end{array}\right]\) is singular, is/are :

The female reproductive system consists of :
(A) Ovaries
(B) External genitalia
(C) Cervix and vagina
(D) Oviducts and uterus
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Reaction of aniline with conc. \(HNO _3\) and conc. \(H _2 SO _4\) at 298 K will produce \(47 \%\) of:

Which of the following can be prepared from Sandmeyer's reaction?
(A) Chlorobenzene
(B) Bromobenzene
(C) lodobenzene
(D) Fluorobenzene
Choose the correct answer from the options given below: