The value of \(3^{18}(\bmod 4)\) is equal to

If the lines \(\frac{x-1}{-3} = \frac{y-2}{2\lambda} = \frac{z-3}{2}\) and \(\frac{x-1}{3\lambda} = \frac{y-1}{2} = \frac{z-6}{-5}\) are perpendicular. Then the value of \(\lambda\) is:

If \(\left|\begin{array}{ccc}1 & \cos \theta & 0 \\ \sin \theta & 1 & \cos \theta \\ \cos \theta & 1 & -\sin \theta\end{array}\right|=A \sin \theta+B \cos \theta+C \sin \theta \cos \theta\) then :

If \(x^m y^n=(x+y)^{m+n}\), then \(\frac{d^2 y}{d x^2}\) is equal to:

\(\int_{-5 / 2}^{5 / 2}|x| d x\) is equal to :

If \((x+1) e^y=1\), then :

The unit's digit of \(2^{2025}\) is

The value of \(\int_0^1 \log _e\left(\frac{1}{x}-1\right) d x\) is :

Read the passage carefully and answer the questions
The carbonyl group of aldehydes and ketones is highly polar. The positively charged carbon is readily attacked by electron-rich nucleophile and the negatively charged oxygen atom is attacked by an electro-deficient electrophile. Aldehydes and ketones undergo nucleophilic addition reactions in the presence of acid or a base. The mechanism involves attack of a nucleophile on the electron deficient carbonyl carbon to form a tetrahedral intermediate. A new bond is formed between the carbon and oxygen. Protonation of the anion furnished by the reaction medium yields a neutral addition product. The addition product is same whether the reaction is catalyzed by acid or a base. For example in the presence of base aldehydes and ketones react with hydrogen cyanide to form cyanohydrin.
What is the product formed when an aldehyde other than formaldehyde is treated with Grignard reagent?

Derivative of \(x^x\) with respect to \(x\) \(log\) \(x\) is

Answer the question on the basis of passage given below:
Aldehydes are generally more reactive than ketones in nucleophilic addition reactions due to steric and electronic reasons. Sterically, the presence of two relatively large substituents in ketones hinders the approach of nucleophile to carbonyl carbon more than aldehydes having only one such substituent Electronically aldehydes are more reactive than ketones because two alkyl groups reduce the elctrophilicity of the carbonyl more effectively than in former.
For preparation of phenylethanoic acid from benzyl alcohol, reagents required are
A. HBr
B. \(CO _2\)
C. \(K C N\)
D. \(\Delta / H_3 O^{+}\)
E. \(AgNO _3\)
Choose the correct answer from the options given below:

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

Match List - I with List - II.

List - I	List - II
(A) Transgenic mice	(I) Hereditary disease
(B) PCR	(II) Safety of Polio vaccine
(C) Golden rice	(III) Molecular Diagnosis
(D) Gene Therapy	(IV) Enhanced nutritional value

Choose the correct answer from the options given below: