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In the given figure, $AB||DEandBD||EF.Then,D{C}^2=?$

The integral value of $k$ for which the equation $(k-12)x^2+2(k-12)x+2=0$ possesses no real solutions is :

The number of arcs to be made to divide a line segment in the ratio 5 : 7 using a single ray is ____.

When any natural number is divided by 10 what is the sum of all possible remainders

Question 2

Theinner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm.The length of the pipe is 35 cm. Find the mass of the pipe, if $1c{m}^3$ of wood has a mass of 0.6 g.

$[Assume\pi =\frac{22}{7}]$

Match the object in Column A to the formulae in Column B. Choose the option with correct matches.

$$\begin{array}{cc}A:& B:\\ 1.VolumeofCone& 1.\pi r^{2}h\\ 2.VolumeofSphere& 2.\frac{4}{3}\pi r^3\\ 3.VolumeofCylinder& 3.\frac{\pi r^{2}h}{3}\end{array}$$

Draw the graph with (i) four-4 nodes (ii) two-2 nodes.

Which of the following is a solution of the quadratic equation x² – b² = a (2x – a )

Question 1
Two line segments AB and AC include an angle of ${60}^{\circ }$, where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that $AP=\frac{3}{4}AB$ and $AQ=\frac{1}{4}AC$ .Join P and Q measure the length PQ.
Thinking Process
(i) Firstly we find the ratio of AB in which P divides, it with the help of the relation $AP=\frac{3}{4}AB$
(ii) Secondly, we find the ratio of AC in which Q divides. It with the help of the relation $AQ=\frac{1}{4}AC$.
(iii) Now, construct the line segment AB and AC in which P and Q respectively divide it in the ratio from step (i) and (ii) respectively.
(iv) Finally get the point P and Q. After that join PQ and get the required measurement of PQ.

What is the ratio whose terms differ by $40$ and the measure of which is $\frac{2}{7}$?

A right circular cylinder of radius r and height h (h > 2r) just encloses a sphere of diameter

(a) r (b) 2r (c) h (d) 2h

A large number of water drops, each of radius $r$, combine to form a drop of radius $R$. If the surface tension is $T$ and the mechanical equivalent of heat is $J$, the rise in heat energy per unit volume will be :

A number x is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3, the probability that |x| < 2 is

Given that the LCM of 306 and 657 is 22338, what is the LCM of 102, 306 and 657

A man rowing a boat away from a lighthouse which is 100 m high takes 2 mins to change the angle of elevation of the lighthouse from ${60}^{\circ }$ to ${45}^{\circ }$. The speed of the boat is:

Find the ${12}^{th}$, ${24}^{th}$ and $n^{th}$ term of the A.P. given by 9, 13, 17, 21, 25, .........

In a function Madhu wished to give Rs.21 toeach person present and found fell short of Rs.4. So she distributed Rs.20 to each and found that Rs.1 were left over.How much money does he have and how many persons were there.

In Fig. 7.146, we have AB ||CE||EF. If AB=6 cm, CD=x cm, EF= 10 cm, BD=4 cm and DE - y cm, calculate the values of x and y.

If the sum of the first $n$ terms of an AP is $5n-n^2$, the common difference is ______

The condition that the point (x,y) may lie on the line joining (3,4) and (-5,-6) is

If $S_n$ is the sum of the first n even natural numbers, then which of the following leave no remainder on dividing $S_n$ ?

The corresponding sides of two similar triangles are in the ratio of $2:3$. If the area of the smaller triangle is $48c{m}^2$, find the area of the larger triangle.

Find out the missing number in the series given below :

$6,13,28,59,?,249$

Twenty-seven spherical solid metallic balls are melted to form some cylindrical rods. The radii of the rods are the same as those of the spherical balls.

If the height of a rod is twice its radius, then how many cylindrical metallic rods can be made from the spherical balls?