The non-negative remainder when \(7^{30}\) is divided by 5 is :

The sum of order and degree of the differential equation \(\frac{\left\{1+\left(\frac{d y}{d x}\right)^2\right\}^{\frac{5}{2}}}{\frac{d^2 y}{d x^2}}= p\) is :

If \(A=\left[\begin{array}{ccc}x+z & 2 & -3 \\ x & 0 & 4 \\ 3 & x-y & 0\end{array}\right]\) is a skew-symmetric matrix, then which of the following are true?
(A) \(y>z>x\)
(B) \(x>y\)
(C) \(x+y+z>0\)
(D) \(z>z\)
Choose the correct answer from the options given below :

Let \(f: R \rightarrow R\) defined by \(f(x)=2 x^3-7\) for \(x \in R\). Then :
(A) \(f\) is one-one function
(B) \(f\) is many to one function
(C) \(f\) is bijective function
(D) \(f\) is into function
Choose the correct answer from the options given below:

The value of \(x\) for which the slope of the curve \(y=-x^3+3 x^2+x^2+9 x-27\) is maximum, is:

The value of the determinant \(\left|\begin{array}{lll}a^2 & a & 1 \\ b^2 & b & 1 \\ c^2 & c & 1\end{array}\right|\) is:

The angle between the lines
\(l_1: \frac{x+1}{1}=\frac{2-y}{2}=\frac{z-1}{1}\) and \(l_2: \frac{x-1}{4}=\frac{2 y-4}{6}=\frac{z-1}{2}\), is:

Read the passage carefully and answer the Questions
Carbonyl compounds such as aldehydes, ketones, and carboxylic acids play an important role in the biochemical process of plants and animal kingdom. Many aldehydes and ketones find applications in dye, perfumery and other industries.
The carbonyl carbon atom is \(s p^2\)-hybridized forming three sigma and one pi-bond with oxygen.
C-O bonds are polar bond due to high electronegativity of oxygen than carbon.
Hence the carbonyl carbon behaves as an electrophilic center and oxygen as a nucleophilic centre.
Primary and secondary alcohols yield aldehydes and ketones respectively upon oxidation with variety of oxidixing agents.
The boiling points of aldehydes and ketones differ from hydrocarbons and ethers.
Aldehydes and ketones undergo nucleophilic addition reaction due to presence of electrophilic carbonyl carbon.
Nucleophile and a proton add across the carbon oxygen double bond.
In polar C-O bond in carbonyl compounds, the nature of carbon and oxygen atom is

If \(\cos y=x \cos (a+y)\), then \(\frac{d y}{d x}=\)

Which of the following statements are incorrect regarding food chain ?
(A) Primary carnivores are the tertiary consumers
(B) The flow of energy form the sun to producers and then to consumers is unidirectional
(C) The death of the organism is the initation of detritus food chain
(D) Plant are the primary consumers as they utilise the solar energy for making food
Choose the correct answer from the options given below:

Find the odd one out among the following structures?

The number of one - one functions from \(A=\{1,2,3,4\}\) to itself is:

Consider the function \(f: N \rightarrow N\) given by \(f(x)=\left\{\begin{array}{ll}x+1, & \text { if } x \text { is odd } \\ x-1, & \text { if } x \text { is even }\end{array}\right.\)