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If $I=\underset{0}{\overset{1}{\int }}\frac{dx}{\sqrt{1+x^4}}$, then

The set of solutions for $\frac{4x}{3}-\frac{9}{4}<x+\frac{3}{4}$ and $\frac{7x-1}{3}-\frac{7x+2}{6}>x$ is

x+200/50=10

Which of the following hold good? If n is a +ve integer, then

Mr. Numbers, a mathematician, has been challenged by a rival mathematician to find the sum of a series that is infinite. If the series progresses as given, calculate its sum.

${lim}_{x\to \frac{x}{3}}\frac{sin(\frac{x}{3}-x)}{2cosx-1}$ is equal to

Find
the inverse of each of the matrices, if it exists.

If $\int \sqrt{\frac{x^4}{a^6+x^6}}dx=g\left(x\right)+C,$ then $g\left(x\right)$ equals to (where $C$ is constant of integration)

If A, B are symmetric matrices of same order then the matrix AB-BA is a

If $a,b,c,d,e,f$ are A.M.'s between $2$ and $12$, then the value of $a+b+c+d+e+f$ is

If $a\to (b\wedge c)$ is false, then the truth values of $a,b$ and $c$ are

The real number $s$ lies in the interval

The equation of that diameter of the circle $x^2+y^2-6x+2y-8=0$ which passes through the origin is

A physical quantity A is related to four observable a, b, c and d as follows, $A=\frac{a^2{b}^3}{c\sqrt{d}}$, the percentage errors of measurement in a, b, c and d are $1\%,3\%,2\%$ and $2\%$ respectively. The maximum error in the quantity A is

The equation of the plane containing the straight line $\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$ and perpendicular to the plane containing the straight lines $\frac{x}{3}=\frac{y}{4}=\frac{z}{2}\text{and}\frac{x}{4}=\frac{y}{2}=\frac{z}{3}$is :

If $lo{g}_{30}3=c,lo{g}_{30}5$ then the value of $lo{g}_{30}8$

If $\underset{0}{\overset{1}{\int }}\frac{e^t}{1+t}dt=a,$ then $\underset{0}{\overset{1}{\int }}\frac{e^t}{(1+t{)}^2}$ is equal to

Four letters E, K, S and V, one in each, were purchased from a plastic warehouse. How many ordered pairs of letters, to be used as initials, can be formed from them?

The first of the two samples in a group has $100$ items with mean $15$ and standard deviation $3$. If the whole group has $250$ items with mean $15.6$ and standard deviation $\sqrt{13.44}$, then the standard deviation of the second sample is

A cricket club has $15$ members, of whom only $5$ can bowl. If the names of $15$ members are put into a box and $11$ are drawn at arandom, then the probability of getting an eleven containing at least $3$ bowlers is

The value of $\int \frac{dx}{{\cos }^{2}x(4+\tan x{)}^4}$ is

$Theinverseoff\left(x\right)={(5-{(x-8)}^5)}^{\frac{1}{3}}is$

Which of the following statements is correct about a null matrix?

Three children are selected at random from a group of 6 boys and 4 girls. It is known that in this group exactly one girl and one boy belong to same parents. The probability that the selected group of children have no blood relations, is equal to :

The sum of the $n$ terms of the series $3+8+22+72+266+1036+\cdots$

If $P=\left[\begin{array}{cc}\sqrt{3}/2& 1/2\\ -1/2& \sqrt{3}/2\end{array}\right],A=\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right]\text{and}Q=PA{P}^T,\text{then}{P}^T{Q}^{2005}P\text{is}$

A man arranges to pay off a debt of Rs. 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one - third of the debt unpaid, find the value of the first instalment.

The angle at which the circles $(x-1{)}^2+y^2=10and{x}^2+(y-2{)}^2=5$ intersect is

If the Cartesian coordinates of a point are $(-3,-\sqrt{3})$, then the polar coordinates are

If $x^x+x^y+y^x=a^b$ , then find $\frac{dy}{dx}$.