Let \(\vec{a}, \vec{b}\) be two vectors such that \(|\vec{a}|=2,|\vec{b}|=3, \vec{a} \cdot \vec{b}=4\). Then \(|\vec{a}-\vec{b}|\) is equal to :

A motorbike costing Rs. 1, 25, 000 has a scrap value of Rs. 25, 000.
If the annual depreciation charge is Rs. 12, 500, then the useful life of the bike is (by using linear method):

An objective function \(z=a x+b y\) is maximum at points \((15,15)\) and \((0,20)\). If \(a, b \geq 0\) and \(a b=27\), then the maximum value of the objective function is

Let \(A\) and \(B\) are square matrices of order 3 such that \(A+B=\left[\begin{array}{ccc}2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3\end{array}\right]\). If \(A\) is a symmetric matrix, then the value of \(|B|\) is:

If \(A=\left[\begin{array}{lll}a & a & a \\ 0 & a & a \\ 0 & 0 & a\end{array}\right]\), then |adj A| is equal to

If R and S are two equivalence relations on a set A, then

For the matrix \(A=\left[\begin{array}{ccc}2 & -1 & -1 \\ 0 & 2 & 3 \\ 1 & -2 & 1\end{array}\right]\), which of the following statements are correct?
(A) The order of the matrix is 3 × 3
(B) |A| = 21
(C) |adj A| = 225
(D) A is skew symmetric matrix
Choose the correct answer from the options given below:

Read the Passage carefully and answer the Questions
Kinetic studies not only help us to determine the rate of a chemical reaction but also describe the conditions by which the reaction rates can be altered.
The factors such as concentration, temperature, preasure and catalyst affect the rate of a reaction.
The speed of a reaction or the rate of a reaction can be defined as the change in concentration of a reactant or product in unit time.
Rate \(=k|A|^a[B]^y\)
Here \(k\) is the rate constant
\(x+y\) gives the overall order of a reaction, whereas \(x\) and \(y\) represent the order with respect to the reactants \(A\) and \(B\), respectively.
Table: Initial rate of formation of NO₂

S.No.	Initial [NO]/mol L-1	Initial [O2]/mol L-1	Initial rate of formation of [NO2]/mol L-1s-1
1.	0.30	0.30	0.096
2.	0.60	0.30	0.384
3.	0.30	0.60	0.192
4.	0.60	0.60	0.768

Based on the above observations, the rate of formation of NO₂ can be represented as

During gamete formation, the alleles of a gene do not show blending and both characters are recovered in F2 generation. This is called :-

When Tt x Tt are crossed, how many percent of the offsprings show a recessive phenotype?

If \(y=x \sin y\), then \(\frac{d y}{d x}\) is:

Select incorrect statements in reference to decomposition.
A. Decomposition rate is slower, if detritus is rich in nitrogen
B. Decomposition is largely an oxygen requiring process
C. Decomposition rate is faster if detritus is rich in lignin and chitin
D. Warm and moist environment favours decomposition
Choose the correct answer from the options given below:

The linear charge density of an infinite line charge producing a uniform electric field of \(9 \times 10^6 N / C\) at a distance of 2 cm is :
(Take permittivity of vacuum \(\epsilon_0=8.85 \times 10^{-12} C ^2 N^{-1} m^{-2}\) )