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A conical and a hemispherical solid of the same height and radius are to be attached at both ends of a solid cylindrical metallic block whose radius is the same as that of the other solids. The height of the new solid so formed is ³/₂ times the height of the cylindrical block. is the radius of the hemisphere.

What is the difference between the total surface areas of the new solid and the cylindrical block?

Find the median of: 7, 12, 15, 6, 20, 8, 4 and 10

Find all the common zeroes of the polynomials $x^3+5x^2-9x-45$ and $x^3+8x^2+15x$.

In the given figure, $△ABC$ is an isosceles triangle with $AB=AC$ and $O$ is the centre of the circle. If $\angle AOB=\alpha$ and $\angle AOC=\beta$, then which of the following is true?

The value of $\frac{2(sin2\theta +2co{s}^2\theta -1)}{cos\theta -sin\theta -cos3\theta +sin3\theta }$ is

In the following, determine whether the given quadratic equations have real roots and if so, find the roots. [3 MARKS]

$6x^2+x-2=0$

The quadratic equation whose roots are real and equal is:

In the adjoining figure, DE || BC.
(i) If AD=3.4 cm, AB=8.5 cm and AC=13.5 cm, find AE.
(ii) If $\frac{AD}{DB}=\frac{3}{5}$ and AC=9.6 cm, find AE.

Given below is the concentration of SO₂ in air (in ppm = parts per million) in 30 localities:
$\begin{array}{cc}S{O}_2\text{concentration (in ppm)}& \text{Number of localities}\\ 0.00-0.04& 4\\ 0.04-0.08& 9\\ 0.08-0.12& 9\\ 0.12-0.16& 2\\ 0.16-0.20& 4\\ 0.20-0.24& 2\end{array}$
Find the mean of $S{O}_2$ concentration using assumed - mean method.

The supply of commodity refers to

H.C.F of $x^3{y}^4{z}^2$ and $x^6{y}^8{z}^4$ is 'a' and H.C.F of $x^5{y}^6{z}^3$ and $x^6{y}^7{z}^4$ is 'b'. What is $\frac{a}{b}$

A circle has a radius of 7 cm. What is the nature of its circumference?

1. 24

In the given figure, $\angle ABC={90}^o$. and $BD\perp AC$. If AB = 5.7 cm, BD = 3.8 cm and CD = 5.4 cm, find BC.

Evaluate $3\left[\begin{array}{cc}1& -1\\ -2& 0\\ 1& -2\end{array}\right]-\left[\begin{array}{cc}-5& 2\\ -1& 3\\ 4& -4\end{array}\right]$

If the arms of one angle are respectively parallel to the arms of another angle, then the two angles are :

1. 3

What is the maximum length of equal pieces of cardboard that Nirmala can get, if she breaks two bars of cardboard 84 cm and 156 cm long?

Find the common difference and write the next four terms of each of the following arithmetic progressions:
(i) $1,-2,-5,-8,\dots$
(ii) $0,-3,-6,-9,\dots$
(iii) $-1,\frac{1}{4},\frac{3}{2},\dots$
(iv) $-1,-\frac{5}{6},-\frac{2}{3},\dots$

One card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of getting

a) a king of red colour

b) the jack of hearts

If the line $2x+y=k$ passes through the point which divides the line segment joining the points $(1,1)$ and $(2,4)$ in the ratio $3:2,$ then $k$ equals

Sandeep deposited Rs. 5000 in his saving account. His amount increases by 1/10 times of itself after every two years. What are the maturity amounts (in Rs.) of investment after $2^{nd}$, $4^{th}$, $6^{th}$ and $8^{th}$ years respectively? Are the maturity amounts (in Rs.) after $2^{nd}$, $4^{th}$, $6^{th}$ and $8^{th}$ years the terms of an AP?

Which of the following correctly explains distributive law?