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In the given triangle, find $sec{60}^{\circ }$ , if $\frac{AC}{BC}=2$

In the diagram, a square is drawn such that the diagonally opposite corners touch the Centre and the circumference of a circle whose radius is r. Find the area of the square.

Statement I: A line segment can be extended indefinitely in both the directions.

Statement II: Two lines are parallel if they do not intersect each other.

Pick the correct option

The circumference of the front wheel of a cart is $3m$ long and that of the back wheel is $4m$ long. What is the distance traveled by the cart, when the front wheel makes five more revolutions than the rear wheel?

The polynomial $a{x}^3+b{x}^2+x–6$ has $(x+2)$ as a factor and leaves a remainder 4 when divided by $(x–2)$. Find $a$ and $b$.

Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42 cm.

The construction of a $\Delta PQR$, given that QR = 7 cm, $\angle PQR={45}^{\circ }$ is not possible when difference of PQ and PR is equal to

Consider a rectangle of area one square metre. What is the relation between the length and the breadth of the rectangle in terms of proportion?

The sides of a triangle are 35 cm, 54 cm and 61 cm. The length of its longest altitude is

Pavan built a conical flask using $550m^2$ of aluminium sheet. If the radius of the flask is $7m,$ then how much water can he fill into the flask (in litres)?
(The bottom of flask was made out of some other material.)

Find the solution of the given system of equations.

$\frac{x+y-8}{2}=\frac{x+2y-14}{8}=\frac{3x+y-12}{11}$

A right triangle is formed by connecting the 3 coordinates A, B and C. Find the area of the $\Delta ABC$, if AB and BC are parallel to the coordinate axes as shown in the figure.

Find the measure of $\angle ADC$ in the given figure.

factorize: 8x³-125y³+180xy+216

What is the inradius of a regular hexagon of sides 6 cm?

ABCD is a trapezium in which AB || CD and AD = BC (see the given figure). From the figure, which of the following can be deduced?

If twice the age of son is added to the age of father, the sum is 56. But if twice the age of the father is added to the age of son, the sum is 82. Find the ages of father and son.

If the radius of a sphere is reduced by a factor of 3. Its volume is

The volume of a cylinder of altitude 15 cm is 1200 cm³. The area of its base is

In a parallelogram ABCD, AB = 2 BC. If the length of the altitude corresponding to AB is 10 cm, what is the length of the altitude corresponding to BC?

If 2^x.5^y.7^z= 98 x 10³, then x+y+z is equal to

Find the difference between the compound interest and the simple interest on a sum of Rs.1500 for 2 years at the rate of 10% per annum.

Find the area of the given polygon:

If x = 2z, then x is ________

$cos{36}^{\circ }cos{42}^{\circ }cos{60}^{\circ }cos{78}^{\circ }=\frac{1}{16}$

A cube whose volume is $1/8$ cubic centimetre is placed on top of a cube whose volume is 1 $c{m}^3.$ The two cubes are then placed on top of a third cube whose volume is 8 $c{m}^3.$ The height of the stacked cubes is

In the figure, sides AD and AB of cyclic quadrilateral ABCD are produced to E and F respectively. If $\angle CBF={130}^{\circ }and\angle CDE=x^{\circ },$ find the value of $x$.

Question 75

If Naresh walks 250 steps to cover a distance fo 200 metres, find the distance travelled in 350 steps.

The curved surface area of a cone is $308c{m}^2$ and its slant height is 14 cm. Find the radius of the base and total surface area of the cone.

Factorise:
$18x^2+3x-10$

Of the three angles of a triangle, one is twice the smallest and another is thrice the smallest. The angles of the triangle will be

In the given figure, ABCD is a cyclic quadrilateral in which AB||DC and $\angle BAD={100}^{\circ }.Then,\angle ABC=?$

(a) ${80}^{\circ }$

(b) ${100}^{\circ }$

(c) ${50}^{\circ }$

(d) ${40}^{\circ }$

In the given figure, E is any point on median AD of a ΔABC. What is ar (ABE) ?

A conical pit is dug into the earth upto the depth of 12 m .It is then closed with lid of diameter 7m which exactly fitted on it. The volume of petrol that can be filled in it is

Evaluate :

1. 4/(216) to the power of -2/3 + 1/(256) to the power of -3/4 + 2/(243) to the power of -1/5.

Find the range from the marks obtained by 10 students in a class.

95, 67 , 28 , 32 , 65 , 65 , 69 , 33 , 98 , 96

The value of $tan\theta$ in given $△$ ABC in terms of a, b and c is

If the altitude drawn from the vertices of ABC to the opposite sides are equal, prove that the triangle is equilateral.

Which of the following are true?

Which of the following is a hexagonal prism ?

Find four rational numbers between $\frac{3}{7}$ and $\frac{5}{7}$

What are terminating and recurring decimals?

What are the signs of the abscissa and the ordinate of a point in the third quadrant, respectively?

Find and explain the condition when x+ a can be a factor of x raise to power n + a raise to power n