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A cylindrical road roller made of iron is 1m long.Its internal diameter is 54 cm and the thickness of the iron sheet used in making the roller is 9 cm.Find the mass of the roller, if 1 $c{m}^3$ of iron has 7.8 gm mass.$(Use\pi =3.14)$

You have studied in class 10 that a median of triangle divides in two triangle of equal area . verify this result for triangle ABC whose vertices are A(4,-6) B(3,-2) C(5,2)

The variance of the number obtained on a throw of an unbiased die is:

An equilateral triangle has two vertices at the points (3, 4) and (-2, 3), find the coordinates of the third vertex.

Make a crossword puzzle on real numbers.

A 1.5 m tall boy is standing at some distance from a 31.5 m tall building. If he walks 'd' m towards the building the angle of elevation of the top of the building changes from ${30}^{\circ }$ to ${60}^{\circ }$. Find the length d. (Take $\sqrt{3}$ = 1.73)

If ABC is a triangle right angled at B, then the hypotenuse will be _____.

In the given figure, if a = 9 cm and b = 12 cm, then c = ___

$\frac{1}{1+ta{n}^2\theta }+\frac{1}{1+co{t}^2\theta }=$

Solve each of the following systems of eqautions by the method of cross-multiplication:

$x+ay=b$

$ax-by=c$

O is the centre of the circle as shown in the figure, $\angle ORP={35}^{\circ }$ and the distance between P and Q through 'O' is 4 cm. What is the measure of $\angle ROQ$ ?

Range of the function defined by $9^x+3^{f\left(x\right)}=3$ is :

Are all three at the same point on the road?

The value of

$5\frac{4}{7}÷1\frac{3}{10}=$

A television was sold at a loss of $5\%.$ If it was sold for $Rs.2000$ more the profit would have been $5\%.$ What is the cost price of the television

One leg of a right angled triangle exceeds the other leg by 4 inches. The hypotenuse is 20 inches. Find the length of the shorter leg of the triangle.

In an election contested between A and B, A obtained was equal to twice the number of persons on the electoral roll who did not cast their votes and this later number was equal to twice his majority over B. If there were 18000 persons on the electoral roll, how many voted for B?

1. 2

Question 104

Solve the following:

Denominator of a number is 4 less than its numerator. If 6 is added to the numerator, it becomes thrice the denominator. Find the fraction.

The following table given the frequency distribution of the percentage of marks obtained by 2300 students in a competitive examination.

$$\begin{array}{cccccccc}Marksobtained& 11-20& 21-30& 31-40& 41-50& 51-60& 61-70& 71-80\\ \left(inpercent\right)& & & & & & & \\ Numberof& 141& 221& 439& 529& 495& 322& 153\\ students& & & & & & & \end{array}$$

(a) Convert the given frequencty distribution into the continuous form.

(b) Find the median class and write its class mark.

(c) Find the modal class and write its cumulative frequency.

Which of the following would be the Inverse of the matrix A found using Elementary Row Transformations where

A =$\left|\begin{array}{ccc}1& 3& 1\\ 0& 1& 1\\ 3& 6& 1\end{array}\right|$

An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11 km/h more than that of the passenger train, find the average speed of the express train.

The first and the last terms of an AP are 5 and 45 respectively. If the sum of all its terms is 40, find the common difference and the number of terms.

Find the value of $\frac{\cos \theta }{1-\tan \theta }+\frac{\sin \theta }{1-\cot \theta }$

Calculate the length of the median through the vertex A of ∆ ABC with vertices A (7, -3), B(5 , 3) & C (3 , -1).

Construct a $\Delta$ ABC, in which BC = 6 cm, AB = 9 cm and $\angle$ABC = 60${}^{\circ }$

i. Construct the locus of all points inside $\Delta$ ABC, which are equidistant from B and C.

ii. Construct the locus of the vertices of the triangle with BC as base, which are equal in area to triangle ABC.

iii. Mark the point Q in your construction, which would make $\Delta$ QBC equal in area to $\Delta$ ABC, and isosceles.

iv. Measure and record the length of CQ.

Factorise :

$x^2+3x+2+ax+2a$

If a tower casts a shadow 200 [sq root (3)] m on the ground when the sun's elevation is 60°, then the height of the tower is ___ m.

If $x^2+y^2+z^2=2(x+z-1),$ then what is the value of $x^3+y^3+z^3=?$

Question 6

In the following figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.