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Calculate standard deviation by step-deviation method:

$\begin{array}{cccccc}\text{Class Interval}& 10-20& 20-30& 30-50& 50-70& 70-80\\ \text{Frequency}& 5& 8& 16& 8& 3\end{array}$

As $\%s$ - character of a hybrid orbital increases

The vertices of the Ellipse

Let p : Kiran passed the examination,
q : Kiran is sad
The symbolic form of a statement "It is not true that Kiran passed therefore he is sad' is

If the standard deviation of $0,1,2,\mathrm{3...9}$ is $K$, then the standard deviation of $10,11,12,\mathrm{13...19}$ is

A line perpendicular to the line segment joining the points (1, 0) and (2, 3) divides it in the ratio 1 : n. Find the equation of the line.

The sum of 10 values is 100 and the sum of their squares is 1090. Find the coefficient of variation.

A parabolic reflector is 9 cm deep and its diameter is 24 cm. How far is its focus from the vertex?

The origin is shifted to (m,2) and the axes are rotated through an angle of ${90}^{\circ }$ anti clockwise. The new co-ordinates of P(3,5) is (3,-2) . Find the value of m.

Find the centre and radius of the circles.
$(x+5{)}^2+(y-3{)}^2=36$

Find the derivative of:

(i) 2x - $\frac{3}{4}$
(ii) $(5x^3+3x-1)$ (x-1)

(iii) $x^{-3}$ (5+3x)
(iv) $x^5(3-6x^{-9})$

(v) $x^{-4}(3-4x^{-5})$
(vi) $\frac{2}{x+1}-\frac{x^2}{3x-1}$

$$\begin{array}{cc}coloumn1& coloumn2\\ a& p)\frac{1}{x}\\ b& q)\frac{1}{x^2}\\ c& r)\frac{1}{x^3}\\ d& s)\frac{1}{x^4}\end{array}$$

A box $B_1$ contains $1$ white ball, $3$ red balls, and $2$ black balls. Another box $B_2$ contains $2$ white balls, $3$ red balls, and $4$ black balls. A third box $B_3$ contains $3$ white balls, $4$ red balls, and $5$ black balls.
If 1 ball is drawn from each of the boxes $B_1,B_2$ and $B_3$ the probability that all $3$ drawn balls are of the same colour is

If $A$ = $\{x:x^2-3x+2=0\}$, and R is a universal relation on A, then R is

Mean of five observations is $4.4$ and variance is $8.24$. If three of the observations are $1,2$ and $6$, then the other two observations are

If the domain of the function $f\left(x\right)={\log }_e\left({\log }_{|\cos x|}\right(x^2-7x+26)-\frac{4}{{\log }_2|\cos x|})$ is set $A,$ then $A$ contains the interval(s)

The domain of the function $f\left(x\right)=x^{1/\ln x}$ is

If $|\sin x+\cos x|=|\sin x|+|\cos x|$, where $\sin x\ne 0,\cos x\ne 0$, then in which quadrant does $x$ lie?

Let a, b, and c be distinct real numbers which are in G.P. If x $\in$ R is such that a+ x, b+x, and c+x are in H.P., then x equals

A natural number is chosen at random from among the first 500. What is the probability that the number so chosen is divisible by 3 or 5 ?

If the chord of the hyperbola $x^2-y^2=a^2$ touch the parabola $y^2=4ax,$ then the locus of the middle point of these chord is _____

If |z+7| ≤ 9, for z ∈ C, the greatest value of |Z+2| is __

|$Z_1$ + $Z_2$| ≤ |$Z_1$| + |$Z_2$|

If 3-4 i is a root of $x^2$-px+q=0 ,where p,q $ϵ$ R then the value of $\frac{2p-q}{p+q}$ is

$x=1+a+a^2+...\infty (a<1)$
$y=1+b+b^2+...\infty (b<1)$
Then the value of $1+ab+a^2{b}^2+.....\infty$ is
[MNR 1980; MP PET 1985]

Given that $f\left(x\right)=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+...$ up to infinite terms.

The derivative of $f\left(x\right)$ is .

$sin{20}^{\circ }sin{40}^{\circ }sin{60}^{\circ }sin{80}^{\circ }$=

[MNR 1976, 81]

For a frequency distribution consisting of 18 observations, the mean and the standard deviation were found to be 7 and 4 respectively. But on comparison with the original data, it was found that a figure 12 was miscopied as 21 in calculations. Find the correct mean and standard deviation.___

Let $S=\left\{xϵ\right(-\pi ,\pi ):x\ne 0,\pm \frac{\pi }{2}\}$. The sum of all distinct solutions of the equation $\sqrt{3}secx+cosecx+2(tanx-cotx)=0$ in the set S is equal to

Which of these can most likely be $3\hat{i}+6\hat{j}$

The relation R ={(x,$\sqrt{x}$):x is a natural number less than 100}. Write the relation in roster form. All the elements of Relation are integers.

If x is very large compared to y, then the value of k if $\sqrt{\frac{x}{x+y}}\sqrt{\frac{x}{x-y}}$ = $1+\frac{y^2}{k{x}^2}$

Find the value of ${}^{n+1}{C}_1$ - ${}^{n+1}{C}_2$ + ${}^{n+1}{C}_3$ ..................$(-1{)}^{n+1}$ ${}^{n+1}{C}_{n+1}$

If the equation $x^4-p{x}^2+3x+5=0$ has 2 as a one root. Find the value of p.

1, $\omega$, ${\omega }^2$ are the cube roots of unity then the roots of $(x-1{)}^3+8=0$

If $e^{sinx}-e^{-sinx}=a$ has alteast one real solution, then

In a ${\Delta }^{le}ABC,tan\frac{A}{2},Tan\frac{B}{2}Tan\frac{C}{2}$ are in H.P. then the value of cot $\left(\frac{A}{2}\right).cot\left(\frac{C}{2}\right)=$

$(\frac{a}{a+x}{)}^{\frac{1}{2}}$ + $(\frac{a}{a-x}{)}^{\frac{1}{2}}$ =

The value of ${}^{12}{C}_2{+}^{13}{C}_3{+}^{14}{C}_4+........{+}^{999}{C}_{989}$ is

y = $\frac{si{n}^2{1500}^{\circ }+4si{n}^4{750}^{\circ }-4si{n}^2{750}^{\circ }co{s}^2{750}^{\circ }}{4-si{n}^2{1500}^{\circ }+4si{n}^2{750}^{\circ }}$ Find the value of 9y.

If the coefficient of $x^{7}in{(a{x}^2-\frac{1}{bx})}^{11}$ is equal to the coefficient of $x^{-7}in{(ax-\frac{1}{b{x}^2})}^{11}$ then ab =

Let T = $\{x|\frac{x+5}{x-7}-5=\frac{4x-40}{13-x}\}$. Is T an empty set ? Justify your answer.

The solution set of $x^4-8x^2-9\le 0$ is

The value of $x$, if ${\log }_{\sqrt{2}}\left({\log }_2\right({\log }_4(x-15)\left)\right)=0$