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Find the mean and variance for the following frequency
distribution.

Find the squar root of

(5+ 71/5)×0.169/1.6

A manufacturer of radio sets produced 600 units in the third year and 700 units in the seventh year. Assuming that the product increases uniformly be a fixed number every year, find

(i) the production in the first year

(ii) the total product in 7 years and

(iii) the product in the 10^th year.

Direction ratios of the line represented by the equation x = ay + b, z = cy + d are

Let S be the area bounded by $y=e^{|\cos 4x|},$ $x=0,y=0$ and $x=\pi$, then

If $n\in N$, then ${11}^{n+2}+{12}^{2n+1}$ is divisible by:

(use principle of mathematical induction)

If $si{n}^{2}4x+co{s}^{2}x=2sin4x.co{s}^{4}x$ then number of values of x satisfying, if $x\in [-2\pi ,2\pi ]$ is

If $x>1$, then the least value of the expression $2{\log }_{10}x-{\log }_{x}0.01$ is

If $\int \frac{dx}{(x^2+1)(x^2+4)}=Kta{n}^{-1}x+Lta{n}^{-1}\frac{x}{2}+c$ where c is arbitrary constant, then K + L =

Let a matrix $A=\left[\begin{array}{cc}3& 2\\ 1& 1\end{array}\right],$ such that $A^2+aA+bI=O$. Then $(a,b)$ is

Find the general solution of the equation

P,Q and R were partners in a firm sharing profits in the ratio of 3:2:1. They admitted S as a new partner for 1/8th share which be acquired from the partners in their old ratio. Find out new ratio.

If Cos A + sin A= 2 cos A show that Cos A-sinA= 2 Sin A.

If the expression $f\left(x\right)=x^2+6x+k$ is non negative $\forall x\in R$, then the interval in which $k$ lies is

The sum of intercepts of any tangent on the curve $\sqrt{x}+\sqrt{y}=2$ is

If $f\left(x\right)=\{\begin{array}{cc}ax,& x<2\\ a{x}^2-bx+3,& x\ge 2\end{array}$ is differentiable for all real values of $x,$ then

Write the coordinates of the following points:

1. M 2. E 3. G 4. C

If the equation $p{x}^2+(2-q)xy+3y^2-6qx+30y+6q=0$ represents a circle, then which of the following is/are correct?

For two sets $A$ and $B$, $(A\cup B)\cap (A^{\prime }\cup B^{\prime })=$

The equation of the plane passing through $(2,-3,1)$ and is normal to the line joining the points $(3,4,-1)$ and $(2,-1,5)$ is given by

Let $U_1\text{and}{U}_2$ be two urns such that $U_1$ contains 3 white and 2 red balls, and $U_2$ contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from $U_1$ and put into $U_2$. However, if tail appears then 2 balls are drawn at random from $U_1$ and put into $U_2$. Now 1 ball is drawn at random from $U_2$.



Given that the drawn ball from $U_2$ is white, the probability that head appeared on the coin is

The value of m for which the area of the triangle included between the axes and any tangent to the curve $x^{m}y=b^m$ is constant is

Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs. 60 per kg and food Q costs Rs. 80 per kg. Food P contains 3 units per kg of vitamin A and 5 units per kg of vitamin B while food Q contains 4 units per kg of vitamin A and 2 units per kg of vitamin B. Determine the minimum cost of the mixture.

If the equation ${\cot }^{4}x-2{\text{cosec}}^{2}x+a^2=0$ has at least one real solution in $x$, then the number of possible integral values of $a$ is

The given combination represents the following gate

The general solution of $\frac{d^{2}y}{d{x}^2}+y=0$ is