Match List-I with List-II

List-I	List-II
(A) The degree of differential equation \(\frac{d^3 y}{d x^3}=e^{\frac{d y}{d x}}\)	(I) 2
(B) The order of differential equation \(\left(\frac{d y}{d x}\right)^2+\frac{d^3 y}{d x^3}=0\)	(II) 4
(C) The sum of order and degree of differential equation \(\frac{d}{d x}\left(\frac{d^2 y}{d x^2}\right)+\left(\frac{d y}{d x}\right)^5=x\)	(III) not defined
(D) The number of arbitrary constants in the general solution of a differential equation of order 2	(IV) 3

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Match List - I with List - II

List - I (Example)	List - II (Component of Time Series)
(A) Lockouts and strikes	(I) Secular trend
(B) Rise and fall of share market	(II) Seasonal trend
(C) Continuous decline in death rate	(III) Irregular trend
(D) The rise in prices before Diwali	(IV) Cyclical trend

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Consider the function \(f(x)=\sin x\) in the interval \([\pi, 2 \pi]\), then which of the following statements are correct?
(A) \(x=\frac{3 \pi}{2}\) is its stationary point.
(B) Its maximum value is 1
(C) Its minimum value is -1
(D) It attains its maximum value at \(\pi\) and \(2 \pi\)
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The corner points of the feasible region determined by the set of constraints (linear inequations) are P(0,5), Q(3, 5), R(5, 0) and S(4, 1) and the objective function z = ax + 2by where a, b > 0 The condition on a and b such that maximum z occurs at Q and S is :

Value of \(\int\left(\frac{1}{\log x}-\frac{1}{(\log x)^2}\right) d x\) is

A plane meets the coordinates axes at A, B and C such that centroid of \(\triangle A B C\) is at the point (2, 3, 1). If the equation of the plane is 3x + 2y + 6z = k, then k is:

For \(x \in[-2,2]\), let \(f(x)=x^2+2\).
A. \(f(x)\) is continuous in \([-2,2]\)
B. \(f(x)\) is differentiable in \((-2,2)\)
C. \(f(-2)=f(2)=6\)
D. \(f^{\prime}(1)=0\)
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A battery with potential V across it is connected to a combination of two identical resistors, and then has current i through it. What are the potential difference across and the current through either resistor if the resistors are connected in series ?

The non-negative remainder when \(7^{30}\) is divided by 5 is :

Calculate the lowering of vapour pressure caused by the addition of \(5 0 ~ g\) of sucrose (mol mass = \(3 4 2 ~ g / m o l\) ) to \(7 5 0 ~ g\) of water, if the vapour pressure of pure water at Ambient temperature is 23.8 mm Hg

Let \(A=\left[a_{i j}\right]\) be a square matrix of order 3 with \(|A|=2\) and let \(C=\left[C_{i j}\right]\), where \(C_{i j}\) is the cofactor of \(a_{i j}\) in \(A\). Then \(|C|\) is equal to :

Two resistance wires are of same material having length, l and 2l and area of cross-section, 4A and A respectively. When they are connected in parallel, their equivalent resistance can be expressed as

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. They are very essential for the body. They has to be taken various diet or in the form of medicines also.
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. These must be supplied regularly in diet because they are readily excreated in urine and cannot be stored in our body.
Deficiency of Scurvy disease leads to