The order of a null matrix is:

If \(x=-4\) is a root of \(\left|\begin{array}{lll}x & 2 & 3 \\ 1 & x & 1 \\ 3 & 2 & x\end{array}\right|=0\) , then the sum of the other two roots is

A man rows a boat such that it covers a distance upstream in twice the time taken by him to cover the same distance downstream. If the speed of stream is 5 km/h, the speed of boat in still water is:

A car starts from a point \(P\) at time \(t=0\) seconds and stops at \(Q\).
The distance \(x\), in meters, covered by it in \(t\) seconds is given by \(x(t)=t^3\left(3-\frac{t^2}{5}\right)\).
The distance between \(P\) and \(Q\) is:

The area (sq. units) bounded by the curve \(y=\sin x, \pi \leq x \leq 2 \pi\) and the \(x\)-axis is

The function \(f(x)=\frac{x}{3}+\frac{3}{x}\) is increasing in the interval:

Match List-I with List-II

List-I	List-II
(A) A square matrix P is said to be non-singular if	(I) \(|P|=0\)
(B) A square matrix P is said to be singular if	(II) \(P P^T\) is symmetric
(C) If a matrix P is both symmetric and skew-symmetric, then	(III) \(|P| \neq 0\)
(D) If P is a square matrix, then	(IV) \(P\) is a null matrix

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Read the passage carefully and answer the Questions
Haloalkanes undergo nucelophilic substitution reactions owing to the polarity of CX bond. The nucleophile reacts with the haloalkane on the carbon possessing a partial positive charge holding the halogen atom. The halogen atom X is replaced by a nucleophile. Depending on the kinetics and mode of bond breaking, the mechanism can be either SN1 or SN2 reaction. The rate of SN1 reaction is governed by the stability of carbocation and in SN2 reaction, the rate of reaction is governed by steric factor. Chirality is the main factor in both SN1and SN2. In SN1 reaction, the chirality of alkyl halide is accompanied by racemization of the product, while in SN2 reaction, the product is characterized by inversion of configuration. The structure of alkyl halide and the nature of the solvent also governs the mechanism of the substitution.
Hydrolysis of 2-Chlorobutane will result in formation of

Which one of the following 1 molal aqueous solutions will show maximum freezing point depression?

The differential equation representing the family of curves \(y=A x+\frac{B}{x}, x \neq 0\), where A and B are arbitrary constants, is given by

Arrange the steps involved in creating pest-resistant transgenic plants
using RNA interference (RNAi).
(A) Binding of complementary RNAs to form double-stranded RNA
(dsRNA).
(B) Formation of sense and antisense RNA in the host cells.
(C) Silencing of specific mRNA of the nematode.
(D) Introduction of nematode-specific genes into the host plant using
Agrobacterium vectors.
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Match List-l with List-ll
Let \(A\) be any invertible square matrix. Then

List-l	List-ll
(A) \(A-A^T\)	(I) \(|A| A^{-1}\)
(B) \(A A^T\)	(II) Skew-symmetric
(C) \(\operatorname{det}\left(A^{-1}\right)\)	(III) Symmetric
(D) \(\operatorname{adj} A\)	(IV) \([\operatorname{det}(A)]^{-1}\)

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Arrange the trophic levels in an order from lowest to highest in a terrestrial food chain:
(A). Wolf
(B). Grass
(C). Cow
(D). Lion
Choose the correct answer from the options given below: