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The negation of the statement $(p\vee \sim q)\wedge q$ is

If $x>3$ and $y=3x+4$, then

Standard deviation about mean $\left(\overline{x}\right)$ for a given discrete frequency distribution $x_1,x_2,x_3,.....x_n$ with frequencies $f_1,f_2,f_3,...f_n$ is

Find the value of ${\sin }^n{1890}^{\circ }+{\text{cosec}}^n{1890}^{\circ }$. Where $n\in N$

Derivative of $f\left(x\right)=\sin (x^3+2x+1)$ is

Which one of the following can be classified as a Bronsted base

Find the value of tan A + 2 tan2A + 4 tan4A + 8 cot 8A

Which of the following are correct?

(1) cot(A+B) = $\frac{cotAcotB-1}{cotA+cotB}$

(2) cot(A-B) = $\frac{cotAcotB-1}{cotA-cotB}$

(3) tan(A+B) = $\frac{tanA+tanB}{1-tanAtanB}$

(4) tan(A-B) = $\frac{tanA-tanB}{1-tanAtanB}$

The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.

$\text{Let}f\left(x\right)=e^x,g=si{n}^{-1}xandh\left(x\right)=f\left(g\right(x\left)\right),then\frac{h^{\prime }\left(x\right)}{h\left(x\right)}$

Find the general solution for the following equation:

$se{c}^2$ 2x = 1 - tan 2x

Find the sum of first n terms of the series $3+7+13+21+31+....$

Or

If a b and c are in GP and x,y are the arithmetic means of a,b and b,c respectively. prove that $\frac{a}{x}+\frac{c}{y}=2and\frac{1}{x}+\frac{1}{y}=\frac{2}{b}$.

If a, b and c are three positive real numbers, then the minimum value of the expression $\frac{b+c}{a}+\frac{c+a}{b}+\frac{a+b}{c}$ is

If set A has p element and set B has q element number of element in set (A $\times$ B) is _____.

How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?

The sum of series $4-9x+16x^2-25x^3+36x^4-49x^5+\dots +\infty$ is

The value of ${\sum }_{k=1}^{13}\frac{1}{sin(\frac{\pi }{4}+\frac{(k-1)\pi )}{6})sin(\frac{\pi }{4}+\frac{k\pi }{6})}$ is equal to

The sum of the first four terms of an AP is 56 and the sum of the last four terms is 112. If its first term is 11, then find the number of terms.

Point R(h, k) divides a line segment between the axis in the ratio 1: 2. Find equation of the line.

The middle term in the expansion of ${(\frac{b\sqrt{a}}{5}-\frac{5}{a\sqrt{b}})}^{12}$ is:

Explain the conditions of consumer's equilibrium using indifference curve analysis.

If the points (k,2-2k), (1-k, 2k) and (-k-4, 6-2k) are collinear, possible values of k are ..............

Find the general solution of $co{s}^{2}x-1=0$

The centre and radius of the circle $x^2+y^2+2gx+2yf+c=0$ are and respectively.

If p: Arjun is the fastest q: Azad is the captain. Then which of the following denotes the compound statement: "Arjun is the fastest OR Azad is not the captain”

Find the total number of terms in the expansion of $(x+a{)}^{100}+(x-a{)}^{100}$

In $\Delta ABC,ifa=3,b=4,c=5,thensin2B=$

Find the coordinates of the point which divides the join of $P(2,-1,4)$ and $Q(4,3,2)$ in the ratio $2:3$ (i) internally (ii) externally.

The Derivative of $e^x$

The number lock of a suitcase has 4 wheels, each labelled with ten digits i.e., from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a
person getting the right sequence to open the suitcase?

How many numbers are there between 100 and 1000 such that every digit is either 2 or 9?

If every pair among the equations $x^2+px+qr=0,x^2+qx+rp=0$ and $x^2+rx+pq=0$ have a common root, then $\frac{\left(sumofroots\right)}{\left(productofroots\right)}$ =

If f(x) =$\frac{1}{x}$, g(x) = $x^2$ and h(x) =$x^3$ find f[g(hf(x))].

Solve for $-2x+5\le 10$

$\sqrt{3}+i=(a+ib)(c+id),then{\tan }^{-1}\frac{b}{a}+{\tan }^{-1}\frac{d}{c}$

has the value

mmen and n women are to be seated in a row so that no two women sit together. If m > n, then the number of ways in which they can be seated is

If the mean and standard deviation of 75 observations is 40 and 8 respectively, find the new mean and standard deviation if

(i) Each observation is multiplied by 5.

(ii) 7 is added to each observation.

There was a survey in a city about number of people reading newspaper A, B and C. There are 42% of people read newspaper A; 51% of people read newspaper B and 68% of people read paper C. 30% of people read both newspaper A and B. 28% reads B and C and 36% read C and A. 8% do not read any newspaper. Find the percentage of people who read all the three newspapers.

Find the quotient of the identity function by the reciprocal function.

(i) If $f\left(x\right)=\{\begin{array}{cc}\frac{x-\left|x\right|}{x}& ifx\ne 0\\ 2& ifx=0\end{array}$, show that $\underset{x\to 0}{lim}f\left(x\right)$ does not exist.

(ii) Evaluate $\underset{x\to 0}{lim}\frac{sinx-2xin3x+sin5x}{x}.$

Or

(i) Find the derivative of $\frac{(x-1)(x-2)}{(x-3)(x-4)}.$

(ii) Differentiate $x{e}^x$ by using first principle.

$\text{Let f (x)be a twice differentiable function and f"(0)=5, then}\underset{x\to 0}{lim}\frac{3f\left(x\right)-4f\left(3x\right)+f\left(9x\right)}{x^2}\text{is equal to:}$

Find the range of each of the following functions:

(i) $f\left(x\right)=2-3x,xϵR$ and $x>0$

(ii) $g\left(x\right)=x^2+2,xϵR$

If $\alpha ,\beta$ are the roots of equation $a(x^2-1)+2bx=0$, then the equation whose roots are 2 $\alpha -\frac{1}{\beta }and2\beta -\frac{1}{\alpha }$ is

If AM between two numbers exceeds their GM by $\frac{5}{2}$ and the GM exceeds their HM by 2, the ratio of numbers is

Match the following for ellipse, $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a>b$, with eccentricity $e.$