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Which of the following concepts play an important role in the construction of ${60}^{\circ }$angle?

The bisectors of any two adjacent angles of a parallelogram intersect at

(a) ${30}^{\circ }$

(b) ${45}^{\circ }$

(c) ${60}^{\circ }$

(d) ${90}^{\circ }$

An equilateral triangle ABC is inscribed in a circle centered at O and of radius 4 cm, as shown below. OD is a radius such that it is perpendicular to BC and cuts BC at point E. Then the length of OE is

In quadrilateral ACBD, AC = AD and AB bisects ∠A (See the given figure). Show that ΔABC ≅ ΔABD. What can you say about BC and BD?

Does representing equation y =x+3 pass through original?why or why not ?

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If $x^2=11+2\sqrt{30}$, then $x$ = ______

Question 6

The product of $\frac{11}{13}$ and 4 is

(a) $3\frac{5}{13}$
(b) $5\frac{3}{13}$
(c) $13\frac{3}{5}$
(d) $13\frac{5}{3}$

Prove that we get a right angled triangle by joining the points (2, 1), (3, 4), (−3, 6).

The figure given below, shows a circle with centre O.

Given : $\angle$ AOC = a and $\angle$ ABC = b.

(i) Find the relationship between a and b.

(ii) Find the measure fo angle OAB, if OABC is a parallelogram.

In a quadrilateral PQRS, the angles P, Q, R and S are in the ratio 2 : 3 : 5 : 5. The measures of each angle are:

1. 560

A bag contains 3 red balls, 5 black balls and 4 white balls. A ball is drawn at random from the bag. What is the probability of not getting a black ball?

If AD is median of $△ABC$ and P is a point on AC such that $ar\left(△ADP\right):ar\left(△ABD\right)=2:3$, then $ar\left(△PDC\right):ar\left(△ABC\right)$ is

The volume of cuboid is given by the expression x³ + 2x³ – x - 2 . The dimension of the cuboid for x = 5 is:

A typist types 45 words in 15 minutes and takes a 5-minute break to align the paper. How many words will he type in one and half hours? [3 MARKS]

Question 13

Find the missing number in the box in each of the proportions:

$\frac{8}{\square }=\frac{3.2}{4}$

Which instrument would you use to draw an arc?

PQ and RS are two parallel chords of a circle whose centre is O and radius is 10 cm. If PQ = 16 cm and RS = 12 cm, find the distance between PQ and RS, if they lie.
(i) on the same side of the centre O.

(ii) on opposite of the centre O.

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The area of the triangle formed by the points P (0,1), Q(0,5) and R(3,4) is

In the figure, ABCD is a parallelogram. Sides AB and BC are equal to 15 cm and 6 cm, respectively. If DF = 4 cm, what is the value of BE?

Express 12470000000000 in the standard form.

Question 12
Taking 0.5 cm as 1 unit, plot the following points on the graph paper.
A(1, 3), B(-3, -1), C(1, -4), D(-2, 3), E(0, -8) and F(1, 0)

A rectangular block has 5 metres,6 metres and 7 metres as length, width and height respectively. If the sides of the block are extended by the same measure, 8 metres, what is the volume of the new rectangular block?

Question 14

P and Q are points on opposite sides AD and BC of a parallelogram ABCD such that PQ passes through the point of intersection O is its diagonals AC and BD. Show that PQ is bisected at 0.



Thinking Process



Firstly, prove that $\Delta ODPand\Delta OBQ$ are congruent by ASA rule. Further show the required result by CPCT rule.

Write the equation of a line passing through the point (0, 4) and parallel to x-axis.

The frequency polygon which represents the following given data is

$$\begin{array}{cc}Weight\left(kg\right)& NumberOfStudents\\ 35.5-40.5& 5\\ 40.5-45.5& 2\\ 45.5-50.5& 12\\ 50.5-55.5& 2\\ 55.5-60.5& 45\end{array}$$