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In the given figure, BOC is a diameter of a circle with centre O. If AB and CD are two chords such that AB||CD and AB = 10 cm then CD = ?

(a) 5 cm

(b) 12.5 cm

(c) 15 cm

(d) 10 cm

$\text{The surface area of a sphere is 1386}c{m}^2.\text{Its volume is}\left(a\right)1617c{m}^3\left(b\right)3234c{m}^3\left(c\right)4851c{m}^3\left(d\right)9702c{m}^3$

In the figure X and Y are the mid points of AC and AB respectively, QP || BC and CYQ and BXP are straight lines. Prove that $ar\left(△ABP\right)=ar\left(△ACQ\right).$

Find the value of k if y+4 is a factor of 3y²+ky+6

Find the value of $a+b+c+d$ in the following figure.

Write each of the following statements in the form "if-then".

(i) You get a job implies that your credentials are good.

(ii) The Banana tree will bloom if it stays warm for a month.

(iii) A quadrilateral is a parallelogram if its diagonals bisect each other.

(iv) To get an $A^{+}$ in the class it is necessary that you do all the exercises of the book.

Find the volume and surface ara of a sphere whose radius is :

(i) 3.5 cm (ii) 4.2 cm (iii) 5 m

find the missing term

4,10,(.........),82,244,730

If $x^2+\left(\frac{1}{x^2}\right)=27,$ find the value of $x+\left(\frac{1}{x}\right).$

In a trapezium ABCD,AB||DC and M is the midpoint of BC.Through M,a line PQ||AD has been drawn which meets AB in P and DC produced in Q,as shown in the adjoining figure. Prove that ar(ABCD)=ar(APQD).

The mean weight of a class of 34 students is 46.5 kg. If the weight of the teacher is included, the mean rises by 500 g.
Find the weight of the teacher.

Look at the given numbers :

4 , 7 , 8 , 9 , x , 12 , 3 , 4 and 5.

If the Mean of these numbers is 7, find x

$\text{If O is a point within}\Delta ABC,\text{show that}\text{(i) AB + AC}>OB+OC\text{(ii) AB + BC + CA}>OA+OB+OC\text{(iii) OA + OB + OC}>\frac{1}{2}(AB+BC+CA.)$

If $\sqrt{2}=1.414then\sqrt{\frac{(\sqrt{2}-1)}{(\sqrt{2}+1)}}=?$

(a) 0.207 (b) 2.414 (c) 0.414 (d) 0.621

The difference between the maximum value and minimum value of the given data is called ___

The diameter of the base of a cylinder is 6 cm and its height is 14 cm. The volume of the cylinder is

$\left(a\right)198c{m}^3\left(b\right)396c{m}^3\left(c\right)495c{m}^3\left(d\right)297c{m}^3$

Select the correct option about the numbers given below.

(i) √27

(ii) √256

(iii) 0.3796

(iv) 7.478478...

(v) 1.101001000100001...

Points A(0,0), B(4,0), C(6,6) and D(2,6) are joined to form a figure. What is the figure ABCD called?

If Tanya burns 7 calories for every meter she walks. How many times should she complete the entire track so that she burns 448 calories? (All dimensions are in m and $\pi$ = 22/7)

ABCD is a trapezium with AB $\parallel$ CD. A line parallel to DB intersects CD at X and BC at Y. If area($△$BDY) = 5 $c{m}^2$,
then ar($△$ADX) is

Each side of an equilateral triangle measures 8 cm. Find (i) the area of the triangle, correct to 2 places of decimal and (ii) the height of the triangle, correct to 2 places of decimal. $(Take\sqrt{3}=\mathrm{1.732.})$

Two coins are tossed simultaneously. Find the probability of getting
(i) exactly 1 head (ii) at most 1 head (iii) at least 1 head.

The sum of a two digit number and the number obtained by reversing its digits is 121. The two digits differ by 3. Find the number.

As observed from the top of a lighthouse, 100 m above sea level, the angle of depression of a ship, sailing directly towards it, changes from ${30}^{\circ }to{60}^{\circ }$. Determine the distance travelled by the ship during the period of observation. [Take $\sqrt{3}=\mathrm{1.732.}$]

Which of the following is equal to $(2x+3y{)}^2$?

Define major and minor segment of a circle. [2 MARKS]

A tent is in the form of a right circular cylinder surmounted by a cone.The diameter of cylinder is 24 m.The height of the cylindrical portion is 11 m while the vertex of the cone is 16 m above the ground.Find the area of the canvas required for the tent.

The given figure shows two circles with centres A and B; and radii 5 cm and 3 cm respectively, touching each other internally. If the perpendicular bisector of AB meets the bigger circle in P and Q, find the length of PQ.

Question 101

State whether the statement is True or False.

$a-b=b-a$

The straight line x = a (where a is a constant) is parallel to the ___ - axis.

P is any point on base BC of $△ABC$ and D is teh mid point of BC. De is drawn parallel to PA to meet AC at E. If ar $\left(△ABC\right)=12c{m}^2,$ then find area of $△EPC$

$\text{In the given figure, OA = OB and OP = OQ.}\text{Prove that (i) PX = QX, (ii) AX = BX.}$

1. 13

Remainder theorem states that

Find the area of the parallelogram ABCD.

Given, BC = 5 cm and the corresponding altitude AP = 8 cm.

​​​​​​find the factor of x³ - x + 6

If ray OC stands on line AB such that Angle AOC = Angle BOC then show that
Angle BOC= 90˚

If the linear equation y = 7x - 4 is written in the standard form ax +by +c =0, then what are the values of a, b and c?

Question 73

A hedge boundary needs to be planted around a rectangular lawn of size $72m\times 18$ m. If 3 shrubs can be planted in a metre of hedge, how many shrubs will be planted in all?

Question 14

A circular flower garden has an area of 314 $m^2$. A sprinkler at the center of the garden can cover an area that has a radius of 12 m. Will the sprinkler water the entire garden?
$(Take\pi =3.14)$

(a) Draw an angle of measure ${115}^{\circ }$ and construct its bisector.
(b) Suppose an angle (whose measure we do not know) is given and you have to make a copy of this angle. How will you do it? [4 MARKS]

Find the value of the polynomial $5x-4x^2+3$ at
(i) $x=0$
(ii) $x=-1$
(iii) $x=2$

The radius of a circle is 2.5 cm. AB and CD are two parallel chords 2.7 cm apart. If the length of the chord AB is 4.8 cm, then find the length of chord CD.