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The sum of all natural numbers ${}^{\prime }{n}^{\prime }$ such that $100<n<200$ and H.C.F. $(91,n)>1$ is:

The sum of all natural numbers ${}^{\prime }{n}^{\prime }$ such that $100<n<200$ and H.C.F. $(91,n)>1$ is:

The asymptotes of the curve $y=\frac{x^2+2x-1}{x}$ are

The value of the quantity $P$ where $P={\int }_0^{1}x{e}^{x}dx,$ is equal to

x log 2x

Let f(x) be a continuous function of x defined on [0, a] such that f(a - x) = f(x). Then, ${\int }_0^{a}xf\left(x\right)dx$ is equal to

$f:R\to R$ defined by $f\left(x\right)=1+x^2$. Is it one one , onto or bijective?

If $2\cos 3B+3\cos 4A=3$ and $2\sin 3B-3\sin 4A=0$, where $2A$ and $2B$ are positive acute angles. If $2A+3B=\frac{\pi }{J}$, then the value of $J$ is

How many triangles can be formed by joining four points on a circle

The differential equation of the family of curves represented by the equation $x^2+y^2=a^2$ is

If the tangent to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a>b$ at the point $P(a\cos \theta ,b\sin \theta )$ meets the auxiliary circle at $A$ and $B$ such that the chord $AB$ subtends a right angle at the centre of the circle, then

$($Here, $e$ represents the eccentricity of ellipse$)$

Choose the correct pair of equal sets.

If $f:[1,\infty )\to B$ defined by the function $f\left(x\right)=x^2-2x+6$ is a surjection, then $B$ is equal to

If $Z$ is the set of all Integers, $W$ is the set of Whole Numbers, $N$ is the set of Natural Numbers, then which of the following is/are correct?

Let $m$ and $M$ be respectively the minimum and maximum values of

$\left|\begin{array}{ccc}{\cos }^{2}x& 1+{\sin }^{2}x& \sin 2x\\ 1+{\cos }^{2}x& {\sin }^{2}x& \sin 2x\\ {\cos }^{2}x& {\sin }^{2}x& 1+\sin 2x\end{array}\right|$

Then the ordered pair $(m,M)$ is equal to:

The ratio of the coefficient of $x^{15}$ to the term independent of $x$ in the expansion of ${(x^2+\frac{2}{x})}^{15}$ is

A committee of $5$ members is to be formed from $6$ boys and $5$ girls. The number of ways in which the committee can be formed so that the committee must contain at least one boy and one girl having majority of boys is

So long as the degree of consolidation (U) does not exceed 60% , its value after a time t is determined by the equation

If $\overrightarrow{x}$ and $\overrightarrow{y}$ are two non-collinear vectors such that $(9a-3b)\overrightarrow{x}+(8b-6c)\overrightarrow{y}+(8c-16a)(\overrightarrow{x}\times \overrightarrow{y})=\overrightarrow{0},$ then which of the following is/are correct ?

Evaluate $\underset{0}{\overset{7}{\int }}\text{sgn}(x+\frac{1}{x}-1)dx$

If $f\left(x\right)=\underset{-1}{\overset{x}{\int }}|t|dt$, then for any $x\ge 0,f\left(x\right)$ is equal to

k = $\underset{x\to \infty }{lim}\left(\frac{\sum _{k=1}^{1000}(x+k{)}^m}{x^m+{10}^{1000}}\right)$ is (m > 101)