The solution set of the inequation \(\frac{7+5 x}{4} \geq \frac{x}{3}-10, x \in R\) is :

If A and B are square matrix of order \(n \times n\), then \((A-B)^2\) is equal to
A. \(A^2-A B-B A+B^2\)
B. \(A^2-2 A B+B^2\)
C. \(A^2-2 B A+B^2\)
D. \(\quad A^2-B^2\)
E. \(A^2+2 A B+B^2\)
Choose the correct answer from the options given below:

The particular solution of the differential equation \(\left\{x \sin ^2\left(\frac{y}{x}\right)-y\right\} d x+x d y=0, y=\frac{\pi}{4}\) when \(x=1\) is

The coordinates of the point where the line \(\frac{x-3}{2}=\frac{y-4}{-3}=\frac{z-1}{5}\) crosses \(X Y\) plane is :

Consider the non-empty set consisting of children in a family and a relation R is defined as aRb if a is a brother of b. Then R is:

Match List - I with List - II. Match the integrating factors :

List - I (Differential Equation)	List - II (Integrating factor)
(A) \(\frac{d y}{d x}+3 y=e^{-2 x}\)	(I) \(\frac{1}{x}\)
(B) \(x \frac{d y}{d x}+y=3 x^2\)	(II) \(e^{-x}\)
(C) \(x \frac{d y}{d x}-y=3 x^2\)	(III) \(x\)
(D) \(\frac{d y}{d x}-y=x\)	(IV) \(e^{3 x}\)

Choose the correct answer from the options given below :

Match List I with List II

List - I	List - II
(A) \(\int x^2 e^{x^3} d x\)	(I) \(\frac{1}{2 a} \log \left|\frac{a+x}{a-x}\right|+C\)
(B) \(\int e^x\left(\tan ^{-1} x+\frac{1}{1+x^2}\right) d x\)	(II) \(\frac{1}{a} \tan ^{-1}\left(\frac{x}{a}\right)+C\)
(C) \(\int \frac{d x}{a^2-x^2}\)	(III) \(\frac{1}{3} e^{x^3}+C\)
(D) \(\int \frac{d x}{x^2+a^2}\)	(IV) \(e^x \tan ^{-1} x+C\)

If \(f: R \rightarrow R\) be given by \(f(x)=\left(3-x^3\right)^{\frac{1}{3}}\), then (fof) (x) is:

In coordinate compound \([Cr(NH_3)_6][Co(CN)_6]\)
what type of isomerism arises?

Read the passage carefully and answer the questions:
Optically active polyhydroxy aldehydes or ketones or molecules which provide such units on hydrolysis are called carbohydrates. They can be broadly classified as monosaccharides, disaccharides and polysaccharides depending on their behavior towards hydrolysis. They are also classified as reducing or non-reducing sugars. Another class of biomolecules is proteins which are polymers of twenty different amino acids linked by peptide bonds. Amino acids can be classified as acidic, basic or neutral depending on the relative number of amino and carboxyl groups in their
molecule. The essential amino acids cannot be synthesized by our body and hence must be provided through diet. Nucleic acids are the polymers of nucleotides which in turn consist of a base, pentose sugar and phosphate. There are two types of nucleic acids namely, DNA and RNA which differ in the composition of sugar and a base
The sugar moiety in DNA and RNA molecules, respectively, are

Which of the following vitamins are water soluble ?
(A) Thiamine
(B) Riboflavin
(C) Pyridoxine
(D) Ascorbic acid
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If the matrix \(A=\left[\begin{array}{ccc}0 & x+y & 1 \\ 3 & z & 2 \\ x-y & -2 & 0\end{array}\right]\) is skew-symmetric, then:

Arrange the following groups of plants in sequential order of their occurrence?
(A) Conifers
(B) Progymnosperms
(C) Ginkgos
(D) Angiosperms
Choose the correct answer from the options given below: