A pair of dice is thrown, getting a total of 7 is considered a success. Then the probability of success in a single throw is:

The critical points of \(f(x)=x^3+x^2+x+1\) are

The differential equation whose solution is \(A x^2+B y^2=1\) where \(A\) and \(B\) are arbitrary constant is of:
(A) first order and first degree
(B) second order and first degree
(C) second order and second degree
(D) second order
Choose the correct answer from the options given below :

The area of the parallelogram determined by the vectors \(\hat{i}+2 \hat{j}+3 \hat{k}\) and \(3 \hat{i}-2 \hat{j}+\hat{k}\) is

Value of \(\frac{e^{\sin \left(\tan ^{-1} x+\cot ^{-1} x\right)}}{e^{\sin \left(\sin ^{-1} x+\cos ^{-1} x\right)}}, x \in[-1,1]\), is:

\(\int \frac{d x}{\left(1+5 \sin ^2 x\right)}\) is equal to

A machine costing Rs. \(2,00,000\) has a useful life of 5 years. The estimated scrap value is Rs. 20,000 . By using straight line method, the annual depreciation is

A voltage \( V = 200 \sin(400t) \) V AC source is connected to a series combination of an inductance 20 mH and resistance \( 6 \, \Omega \). The rms current in the AC circuit is:

Match List-I with List-II

List-I	List-II
(A) The equation of the line passing through the points \((-1,0,2)\) and \((3,4,6)\) is	(I) \(\vec{r}=(-\hat{i}+2 \hat{k})+\lambda(4 \hat{i}+4 \hat{j}+4 \hat{k})\)
(B) The vector equation of the line \(\frac{x-1}{2}=\frac{y+1}{3}=\frac{4-z}{5}\) is	(II) \(\vec{r}=(\hat{i}+3 \hat{j}+2 \hat{k})+\lambda(2 \hat{i}+\hat{j}+3 \hat{k})\)
(C) The equation of the line passing through \((1,3,2)\) and parallel to \(\frac{x+1}{2}=\frac{y-1}{1}=\frac{z+1}{3}\) is	(III) \(\vec{r}=(-\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(2 \hat{i}+\hat{j}+4 \hat{k})\)
(D) The equation of the line along \(2 \hat{i}+\hat{j}+4 \hat{k}\) and passing through \((-1,2,3)\) is	(IV) \(\vec{r}=(\hat{i}-\hat{j}+4 \hat{k})+\lambda(2 \hat{i}+3 \hat{j}-5 \hat{k})\)

where \(\lambda\) is an arbitrary constant.
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The hormone releasing IUDs function by-

According to Alexander Zaitsev the most preferred product for dehydrohalogenation of 2-Bromopentane will be :

Find the maximum value of the function sin x(1 + cos x) 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?