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Calculate mean deviation from the median of the following data :

$\begin{array}{cccccc}\text{Class Interval :}& 0-6& 6-12& 12-18& 18-24& 24-30\\ \text{Frequency :}& 4& 5& 3& 6& 2\end{array}$

The expression ${[x+\sqrt{x^3-1}]}^5$+
${[x-\sqrt{x^3-1}]}^5$ is a Polynomial of degree

A determinant is chosen at random from the set of determinants of order 2 with elements 0 and 1. What is the probability that the determinant chosen has the value non-negative?

If the chord $y=mx+1$ of the circle $x^2+y^2=1$, subtends an angle of $\frac{\pi }{4}$ at the major segment of the circle, then $m=$

Three coins are tossed together. Find the probability of getting:

(i) exactly two heads

(ii) at least two heads

(iii) at least one head and one tail.

We know that the sum of the interior angles of a triangle is ${180}^{\circ }$. Show that the sums of the interior angles of polygons with 3, 4, 5, 6, …. sides form an arithmetic progression. Find the sum of the interior angles for a 21 sided polygon.

If $z_1,z_2\text{and}{z}_3,z_4$ are two pairs of conjugate complex numbers, prove that $arg\left(\frac{z_1}{z_4}\right)+arg\left(\frac{z_2}{z_3}\right)=0.$

$If\sqrt{3}cos\theta +sin\theta =\sqrt{2},thengeneralvalueof\theta is$

Let $A$ be a matrix such that $A\cdot \left[\begin{array}{cc}1& 2\\ 0& 3\end{array}\right]$ is a scalar matrix and $|3A|=108$. Then $A^2$ equals :

If $\frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in A.P., prove that:
(i) $\frac{b+c}{a},\frac{c+a}{b},\frac{a+b}{c}$ are in A.P.
(ii) $a(b+c),b(c+a),c(a+b)$ are in A.P.

Let A and B be two sets such that n (A) = 16, n(B) = 14, $n(A\cup B)$= 25. Then, $n(A\cap B)$ is equal to .

The solution of differential equation $sin\left(x\frac{dy}{dx}\right)cosy=\frac{dy}{dx}+sinycos\left(x\frac{dy}{dx}\right)$ is

If $\frac{sinx}{siny}=\frac{1}{2},\frac{cosx}{cosy}=\frac{3}{2},xyϵ(0,\frac{\pi }{2})$, then tan (x+y)=___

If two dice are thrown simultaneously, then the probability that the sum of the numbers which come up on the dice to be more than 5 is ________

The number of seven-digit natural numbers in which only $2$ and $3$ are present as digits and no two $2^{\prime }s$ are consecutive in any number, is

The value of $2\cos \frac{\pi }{13}\cos \frac{9\pi }{13}+\cos \frac{3\pi }{13}+\cos \frac{5\pi }{13}$ is

A polygon has $35$ diagonals. The number of sides of polygon is

$f\left(x\right)=\left|\begin{array}{ccc}3& 1& 2\\ a^3& 2a& a^2\\ 3x^2& 2& 2x\end{array}\right|then{\int }_0^{a}f\left(x\right)is$ ___

The angle between the normals to the parabola $y^2=24x$ at points $(6,12)$ and $(6,-12)$ is :

The parametric representation of a parabola is x=3+t² , y=2t-1. Its focus is at

Show that $\int \frac{2x-1}{2x+3}dx=x-log|(2x+3{)}^2|$ + C

Find the least value of a such that the function f given by $f\left(x\right)=x^2+ax+1$ is strictly increasing on (1,2).

How many times would digit 2 be written, if you wrote down all the whole numbers from 1 to 100?

$tan(si{n}^{-1}\frac{3}{5}+co{t}^{-1}\frac{3}{2})$

If $\alpha ,\beta ,\gamma$ are the roots of $x^3+3x^2+2=0$ then find the equation whose roots are $\frac{\alpha }{\beta +\gamma },\frac{\beta }{\gamma +\alpha },\frac{\gamma }{\alpha +\beta }$

Refer to question 1 above. If the die were fair, determine whether or not the events A and B are independent.

Show that the general solution of the differential equation $\frac{dy}{dx}+\frac{y^2+y+1}{x^2+x+1}=0$ is given by $(x+y+1)=A(1-x-y-2xy)$, where A is a parameter.

How should I solve the proving questions in trigonometry? Pls help.

Like for example:-

sinA(1+tanA) + cosA( 1+cotA) = secA + cosecA.

I am facing problems in these kinds of questions. How should I proceed when I get these questions. (I can solve this particular question but don’t know how to tackle other questions of the same kind)

In a circle 2 chords PQ and RS intersects at O, which of the following is correct.

If $\tan A=\text{cosec}{5}^{\circ }-\cot 5^{\circ }$, where $A$ is an acute angle, then the value of $\tan 24A+\tan 12A+\tan 6A$ is

If a is any real number the number of roots of cot x-tanx=ain the first quadrant is

Let n = 1! + 4! + 7! +......+ 400! then tens digit of n is

Bag A contains 4 green and 3 red balls and bag B contains 4 red and 3 green balls. One bag is taken at random and a ball is drawn and noted it is green. The probability that it comes from bag B is

The point $(-2m,m+1)$ is an interior point of the smaller region bounded by the circle $x^2+y^2=4$ and the parabola $y^2=4x$, then $m$ lies in the interval

In how many ways can the letters of the word JUPITER be arranged in a row so that the vowels appear in alphabetic order?

The equation of a hyperbola , conjugate to the hyperbola $x^2+3xy+2y^2+2x+3y=0is$

Select a personal pronoun for the blank.

___ kept her brother’s laptop in his black haversack bag.

The distance between the foci of the Ellipse x=5cos$\theta$, y=4sin$\theta$ is

Let $\alpha ,\beta$ be the roots of the equation $x^2-px+r=0$ and $\frac{\alpha }{2},2\beta$ be the roots of the equation $x^2-qx+r=0$. Then the value of r is: