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Locate the COM of a uniform hemisherical solid with respect to 0 as shown in figure. (Radius = r)

In the following figure, if O is the centre of the circle then $\angle DOE$ equals

Two towers A and B are standing at some distance apart. From the top of tower A, the angle of depression of the foot of tower B is found to be ${30}^{\circ }$. From the top of tower B, the angle of depression of the foot of tower A is found to be ${60}^{\circ }$. If the height of tower B is ‘h’ m then the height of tower A in terms of ‘h’ is _____ m

In the parallelogram, D is the mid point of side PQ. Which of the following options is NOT true?

Mid point theorem is NOT a special case of which of the following theorems ?

Which of the following has all its angles equal to ${90}^{\circ }$?

If the sum of 2 numbers is 11 and the sum of their cubes is 737.

Find the sum of their squares

For two figures to be on the same base and between the same parallels, they must have a common base and

How much is 10% of Rs. 10000?

The sum of the measures of angles of a quadrilateral and that of a triangle is _______ .

What are the values of a, b and c if $-2x+\frac{3}{2}y-4=0$ is represented in the form of ax + by + c = 0?

If the value of $\sqrt{2}$ and $\sqrt{3}$ is 1.4 and 1.7 respectively, find the value of $\frac{\sqrt{3}+\sqrt{2}}{3\sqrt{3}}$

4,7 and a are the measure of sides of a triangle. Find the range of values of a.

A point O is taken inside an equilateral $\Delta ABC$. If $OM\perp AC$, $OL\perp BC$ and $ON\perp AB$ such that OL = 14 cm, OM = 10 cm and ON = 6 cm, find the area of $\Delta ABC$.

In the given figure,ABCD is a ||gm in which diagonals AC and BD intersect at O.If ar(||gm ABCD) is 52 $c{m}^2$ then the ar$\left(△AOB\right)$=?

(a) $26c{m}^2$

(b) $18.5c{m}^2$

(c) $39c{m}^2$

(d) $13c{m}^2$

Draw the graph of the equation y = 3x.

From your graph, find the value of y when (i) x = 2 (ii) x = -2

The following table shows the blood groups of 40 students of a class.

$\begin{array}{ccccc}\text{Blood group}& A& B& O& AB\\ \text{Number of students}& 11& 9& 14& 6\end{array}$

One student of the class is chosen at random. What is the probability that the chosen studet has blood group (i) O? (ii) AB?

Factorize $1029-3x^3$

Draw the graph of each of the equations given below. Also, find the coordinates of the points where the graph cuts the coordinate axes:

$\left(i\right)6x-3y=12$ $\left(ii\right)-x+4y=8$ $\left(iii\right)2x+y=6$ $\left(iv\right)3x+2y+6=0$

The pillars of an apartment are made in the cylindrical shape. If each pillar has a circular base of radius 40 cm and height 20 m, then how much concrete would be required to build 7 such pillars?

In the given figure AB is the side of a regular hexagon and BC is the side of a regular pentagon. Find $\angle$ OAC.

An umbrella is made by stitching 12 triangular pieces of cloth, each measuring $(50cm\times 20cm\times 50cm.)$ Find the area of the cloth used in it.

An angle which measures more than ${180}^{\circ }$ but less than ${360}^{\circ }$, is called

(a) an acute angle

(b) an obtuse angle

(c) a straight angle

(d) a reflex angle

Which of the following expressions is a polynomial ?
(a) $\sqrt{x}-1$
(b) $\frac{x-1}{x+1}$
(c) $x^2-\frac{2}{x^2}+5$
(d) $x^2+\frac{2x^{\frac{3}{2}}}{\sqrt{x}}+6$

Show that there is no value of n for which ($2^n\times 5^n$) ends in 5.

(a-1)x^2+a^2xy+(a+1)y^2

ans (x+ay+y)(ax-x+y)

Question 39

The loss per cent on selling 140 geometry boxes at the loss of SP of 10 geometry boxes is equal to ___.

Using the information given in the figure, the values of x and y are __

Which of the following equation/s is/are correct?

$i\left)\right(a+b+c{)}^2=a^2+b^2+c^2-2(ab+bc+ca)$
$ii\left)\right(a+b{)}^3=a^3+b^3+3ab(a-b)$
$iii\left)\right(a-b{)}^3=a^3-b^3-3ab(a+b)$
$iv)a^2-b^2=(a+b\left)\right(a-b)$

The mode of the given data 7, 9, 11, 13, 9 13, 9, 9, 7, 8 is

AD and BE and CF are altitudes of ∆ABC .If AD =,BE= CF prove ABC is equilateral triangle

Which of the following should be the SECOND sentence after rearrangement?

If ∪ = {2, 4, 6, 8, 10, 12, 14, 17}, where ∪ is Universal set

and some set A = {1, 4, 6, 9, 11, 12}

The set A^C is

Question 3(d)
Fill in the blanks:
- 87 $÷$ ___ = 87

Question 4
The radius of a spherical balloon increases from 7 cm to14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

Question 8
ABCD is a cyclic quadrilateral finds the angles of the cyclic quadrilateral.

If A and B are symmetric matrices of the same order and X = AB + BA and Y = AB - BA, then $(XY{)}^T$ is equal to

Adjacent angles of a parallelogram are:

How many secants can be drawn to a circle from a point outside the circle?

The perimeter of rectangular field is 50 m. If the length of the field is 13 m. Find the area of the field.

If the point A(2,-4) is equidistant from P(3,8) and Q(-10,y), then find the value of y.

Question 1 (iii)
Express 3825 as the product of its prime factors.