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In the given figure, if $\angle AOC$ and $\angle BOC$ are in ratio 2 : 3, find $\angle AOC$, $\angle COB$, $\angle BOD$ and $\angle AOD$.

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in $(A\cup B)$

Question 7

A kite in the shape of a square with a diagonal 32cm and an isosceles triangles of base 8cm and sides 6cm each is to be made of three different shades as shown in the given figure. How much paper of each shade has been used in it?

Which numbers cannot be represented by points on the number line?

Given that ACBD is a kite. By which congruency property are the triangles ACB and ADB congruent?

In ∠ABC shown below, the length of AB is 6 centimetres and the length of AC is 5 centimetres. The length of AP is 4 centimetres. The line PQ is parallel to BC.

Find the lengths of AQ and QC.

In the figure, O is the centre of the circle and the measure of arc ABC is 100^o. The measure of angle ABC will be

The histogram below represents marks of students in a Mathematics exam with passing marks as 30. How many students failed in the exam?

Which of the following is a quadratic polynomial ?
(a) $x+4$
(b) $x^3+x$
(c) $x^3+2x+6$
(d) $x^2+5x+4$

Question 73

A bicycle wheel makes 500 revolutions in moving 1 km. Find the diameter of the wheel.

ABCD is a rhombus, EABF is a straight line such that EA = AB = BF. Prove that ED and FC when produced meet at right angles.

In a ___ triangle the median, altitude and angular bisector from one vertex coincides.

$\text{A box made of sheet metal costs Rs6480 at Rs120 per square metre. If the box is 5m long and 3 m wide, find, its height.}$

In a quadrilateral ABCD, $\angle A={90}^{\circ },\angle B=3x,\angle C=3x+5,\angle D=8x-15$. Then the value of $\angle D$ is

In the given figure, If AB || CD, EF ⊥ CD and ∠GED = 126º, find ∠AGE, ∠GEF and ∠FGE.

In the figure given below, lines RS and PQ intersect each other at point O.

$\text{If}\angle POR:\angle ROQ=11:13,$

find $\angle SOQ$.

The mean of 5 numbers is 18. If one number is excluded, their mean is 16. Find the excluded number.

A teacher wanted to analyse the performance of two sections of students in a mathematics test of 100 marks. Looking at their performances, she found that a few students got under 20 marks and a few got 70 marks or above. So she decided to group them into intervals of varying sizes as follows: 0 − 20, 20 − 30… 60 − 70, 70 − 100. Then she formed the following table:

(i) Find the probability that a student obtained less than 20 % in the mathematics test.

(ii) Find the probability that a student obtained marks 60 or above.

The point of intersection of lines $3x+6y=9$ and $7x–15y=2$ is

After three years, a man’s age will be five times his son’s age. If the man's current age is represented by 'x' and his son's age by 'y', which among the following options is a linear equation in two variables representing this statement?

The polygon formed in the front side of the figure is called as a ___.

Factorise: $x^3-2x^2-5x+6$

Bisectors of angles A, B and C of a triangle ABC intersect its circumcircle at D, E and F respectively. Prove that the angles of the triangle DEF are 90° .

Two dice are thrown. The events A, B and C are as follows:
A: getting an even number on the first die
B: getting an odd number on the first die
C: getting the sum of the numbers on the dice $\le$ 5
Describe the events
(i) A'
(ii) not B
(iii) A or B
(iv) A and B
(v) A but not C
(vi) B or C
(vii) B and C
(viii) $A\cap B^{\prime }\cap C^{\prime }$