\(\int \frac{x}{x^2+x-12} d x\) is equal to

Approximate percentage increase in the volume of a sphere if its radius is increased by \(3 \%\) is:

The linear programming problem:
Maximize \(Z = x + y\),
subject to the constraints \(x-y \leq-1,-x+y \leq 0, x, y \geq 0\) has

If \(A=\left[\begin{array}{cc}2 & 1 \\ 1 & 4 \\ -1 & 6 \\ 0 & 7\end{array}\right]\) and \(B=\left[\begin{array}{cccc}1 & 2 & 3 & 0 \\ 2 & -1 & 6 & 7\end{array}\right]\), then

If \(A\) is a non-singular square matrix of order 3 such that \(A^3=4 A^2\), then the value of \(|A|\) is:

Consider the following statement regarding sample parameter and statistic; statistical inference and t-test:
A. There are only three types of probability sampling: stratified, simple and systematic.
B. Since a = probability of the Type-I error, then \((1-\alpha)\) is probability of not rejecting \(H_o\) when \(H_a\) is true.
C. t-value is represented as; \(t=\frac{\text { Mean - Comparison value }}{\text { Standard error }}\)
D. A sample of less than 30 is considered to be sufficient to hold Central Limit Theorem (CLT).
E. A confidence interval consists of three components: confidence level, sample statistic and margin of error.

Identify correctly:
A. \(\begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 5 \\ 3 & 5 & 6 \end{bmatrix}\) is a symmetric matrix
B. \(\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}\) is a null matrix
C. \(\begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{bmatrix}\) is an Identity matrix
D. \(\begin{bmatrix} 0 & 1 & 2 \\ -1 & 0 & 3 \\ -2 & -3 & 0 \end{bmatrix}\) is a skew symmetric matrix
E. \(\begin{bmatrix} \sqrt{3} & 0 & 0 \\ 0 & \sqrt{3} & 0 \\ 0 & 0 & \sqrt{3} \end{bmatrix}\) is a scalar matrix
Choose the correct answer from the options given below:

In a series LR circuit, the inductive reactance is equal to the resistance R of the circuit. An emf \( E = E_0 \cos \omega t \) is applied to the circuit. The average power dissipated in one cycle is :

Read the passage carefully and answer the Questions
The term vitamin was coined from the word vital +amine since the earlier identified compounds had amino groups. Later work showed that most of them didn't contain amino groups, so the letter "e" was dropped and ther term vitamin is used these days.
Vitamins are classified into two groups depending upon their solubility in water or fat. Fat soluble vitamins are soluble in fat and oils but insoluble in water. They are stored in liver and adipose (fat storing) tissues. Water-soluble vitamins are soluble in water. They must be supplied regularly in the diet as they are readily excreated in urine.
What are the sources of Vitamin B12?

Identify the correct statements with respect to Baculoviruses :
(A) They attack insects and other arthropods
(B) They have broad spectrum insecticidal applications
(C) They are species specific
(D) They show no negative impact on plants, mammals, birds, fishes and non-target insects
Choose the correct answer from the options given below:

Propionibacterium sharmanii is used in making which of the following food item

What amount of energy would be at the producer level if it is 50 KJ at third trophic level?

A long straight wire of radius 'a' carries a steady current 'I'. The current is uniformly distributed across its area of cross-section. The ratio of magnitude of magnetic fields \( B_1 \) at a distance a/2 and \( B_2 \) at a distance 2a from the axis of the wire is :