For the objective function \(Z = 3x + 5y\) subject to constraints \(x + 3y ≥ 3, x + y ≥ 2, x ≥ 0, y ≥ 0\):

Let \(\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=-\hat{i}+\hat{j}\).
Then a vector \(\vec{c}\) satisfying \(\vec{a} \times \vec{c}=\vec{b}\) and \(\vec{a} \cdot \vec{c}=8\) is equal to:

Kavya takes a personal loan of ₹ 10,00,000 at the rate of 12% per annum for 5 years, then the EMI by using flat rate method is:

If \(x=2 t^3\) and \(y=3 t^4\), then \(\frac{d^2 y}{d x^2}\) is equal to :

An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?

If \(x^2+2 x y+y^3=10\), then the value of \(\frac{d y}{d x}\) is:

If \(A\) and \(B\) are invertible matrices of same order, then which one of the following is NOT true?

A foetal genetic disorder can be studied by which of the following?

Match List-I with List-II

List-I (Matrix Product)	List-II (Order of resultant matrix)
(A) \(\left[a_{i j}\right]_{2 \times 3} \times\left[b_{i j}\right]_{3 \times 4}\)	(I) \(2 \times 4\)
(B) \(\left[a_{i j}\right]_{2 \times 1} \times\left[b_{i j}\right]_{1 \times 3}\)	(II) Not possible
(C) \(\left[a_{i j}\right]_{3 \times 2} \times\left[b_{i j}\right]_{3 \times 2}\)	(III) \(3 \times 3\)
(D) \(\left[a_{i j}\right]_{3 \times 3} \times\left[b_{i j}\right]_{3 \times 3}\)	(IV) \(2 \times 3\)

Choose the correct answer from the options given below :

In Young's Double Slit experiment, the intensities of two coherent monochromatic waves are I and 4I. The ratio of intensity at maxima to minima will be :

At room temperature (\(25.0^\circ C\)) the resistance of a heating element is \(100 \Omega\). The temperature of the element at which resistance becomes \(125.5 \Omega\) is : (Given that the temperature coefficient of the material of the resistor is \(1.70 \times 10^{-4} \text{ } ^\circ C^{-1}\))

The area (in sq. units) of the region bounded by the curve \(y=\cos x\) between \(x=-\frac{\pi}{2}, x=\frac{\pi}{2}\) and the \(x\)-axis 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 is Xerophthalmia disease?