\(\frac{5}{6}\div\frac{6}{2}\) is 

(a)

\(\frac{5}{2}\)

(b)

\(\frac{2}{5}\)

(c)

\(\frac{5}{18}\)

(d)

\(\frac{30}{12}\)

\(\frac { 1 }{ 2 } \times \left( \frac { 2 }{ 3 } +\frac { 6 }{ 4 } \right) =\left( \frac { 1 }{ 2 } +\frac { 2 }{ 3 } \right) +\left( \frac { 1 }{ 2 } \times \_ \_ \right) \)

(a)

\(\frac{1}{2}\)

(b)

\(\frac{2}{3}\)

(c)

\(\frac{4}{6}\)

(d)

0

Multiplicative identity is _______.

(a)

1

(b)

0

(c)

the given number itself

(d)

reciprocal of the given number

In  if the faces shows the area in the net, then the shape mentioned is

(a)

pyramid

(b)

Cube

(c)

cuboid

(d)

prism

If V = 6, E = 12 then the faces of the polyhedron is

(a)

6

(b)

7

(c)

8

(d)

9

A part of the circumference of a circle is called

(a)

circular arc

(b)

segment

(c)

sector

(d)

chord

Perimeter of a sector is

(a)

\(\frac{lr}{2}\)

(b)

\(\frac{l+r}{2}\)

(c)

l+2r

(d)

\(\pi\)+2

A closed plane figure formed by three or more sides is called a

(a)

quadrilateral

(b)

pentagon

(c)

triangle

(d)

polygon

Volume of the rectangle 1 = 2ab, b = 3ac and h = 2ac is _________.

(a)

12a²bc²

(b)

12a²bc

(c)

12a² bc

(d)

2ab + 3ac + 2 ac

Product of 6a² - 7b + ab and 2ab is __________.

(a)

12a³b - 14ab² + 10 ab

(b)

12a³b - 14ab² + 10 a²b²

(c)

6a²b - 7b² + 7 ab

(d)

12a²b -7ab² + 10 ab

Square of (3x - 4y) is _______.

(a)

9x²-16y²

(b)

6x²-8y²

(c)

9x²+ 16y² + 24xy

(d)

9x² + 16y²-24xy

On dividing 57p² qr by 114 pq we get __________.

(a)

\(\frac{1}{4}\)pr

(b)

\(\frac{3}{4}\)pr

(c)

\(\frac{1}{2}\)pr

(d)

2pr

Common factor of 3ab and 2pq is _________.

(a)

1

(b)

-1

(c)

a

(d)

c

(a) \(\frac { x }{ 2 } \) = 10     (i) x = 4
(b) 20 = 6x – 4   (ii) x = 1
(c) 2x – 5 = 3 – x  (iii) x = 20
(d) 7x – 4 – 8x = 20  (iv) x = \(\frac { 8 }{ 3 } \)
(e) \(\frac { 4 }{ 11 } \)- x = \(\frac { -7 }{ 11 } \)   (v) x = –24

(a)

(i), (ii), (iv), (iii), (v)

(b)

(iii), (iv), (i), (ii), (v)

(c)

(iii), (i), (iv), (v), (ii)

(d)

(iii), (i), (v), (iv), (ii)

The additive inverse of -2 is __________.

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+2

Addition of rational numbers commutative, so a + b =_______.

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b+a

If the difference between the circumference and radius of a circle is 37cm then find the circumference of the circle.

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44

If a wire is bent to the shape of a square, the area of the square is 81cm². If it is bent to a semi-circle then find the area of the semicircle?

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77 cm²

The radius of a wheel is 0.25m, how many revolutions are needed to travel a distance of 11 km?

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7000

The circumference of a circle is 100 cm. Find the side of the square inscribed in the circle.

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\(\frac{50\sqrt2}{\pi}\)

Find the area of the larger triangle that can be inscribed in a semi circle of radius 'r' cm.

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r²

The area of the circle is 220 cm². What is the area of the square inscribed in it?

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140 cm²

On simplificaiton  \(\frac{3x+3}{3}\) = ________.

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x+1

The factorization of 2x + 4y is ________.

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2(x+2y)

Factorisation of 18 mn + 10 mnp is = ___________.

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2mn(9+5p)

\(\frac { 5 }{ 6 } -\frac { 11 }{ 12 } =\frac { -1 }{ 12 } \)

(a) True

(b) False

\(\frac { 4 }{ 3 } \times \frac { 3 }{ 11 } =\frac { 12 }{ 11 }\)

(a) True

(b) False

(a + b)² = a² + b²

(a) True

(b) False

Product of two negative terms is a negative term

(a) True

(b) False

p²q + q² r + r² is a binomial

(a) True

(b) False

(a+b)(a-b) = a² - b²

(a) True

(b) False

Common factor of 12a²b²+ 4ab² - 32 is 4.

(a) True

(b) False

Add \(\frac{3}{5}\) and \(\frac{13}{5}\)

Add \(\frac{7}{9}\) and \(\frac{-12}{9}\)

Subtract \(\frac{3}{4}\) and \(\frac{7}{4}\)

Subtract \(\frac{6}{17}\) and \(\frac{7}{4}17\)

Divide 1 by \(\frac{1}{2}\)

Divide \(\frac{2}{3}\) by \(\frac{-7}{12}\) 

Verify addition of rational numbers is closed using \(\frac{1}{4}\) and \(\frac{2}{3}\).

Is subtraction is commutative for rational numbers. Give an example,

Add \(\frac{31}{-4}\)and \(\frac{-5}{8}\)

\(\frac { 5 }{ 9 } +\frac { -11 }{ 6 } \).

Subtract \(\frac{-2}{3}\)from \(\frac{5}{6}\)

Evaluate \(\frac { -6 }{ 13 } -\frac { -7 }{ 13 } \)

Multiply \(\frac{-11}{13}\)by\(\frac{-21}{7}\)

What should we multiply with \(\frac{-1}{6}\)to get \(\frac{-23}{9}?\)

What should we multiply with \(\frac{-15}{28}\)to get \(\frac{-5}{7}?\)

The given circular figure is divided into six equal parts. Can we call the parts as sectors? Why?

Fill the central angle of the shaded sector (each circle is divided into equal sectors)

If the radius of a circle is doubled, what will the area of the new circle so formed?

All the sides of a rhombus are equal. Is it a regular polygon?

In the above example split the given mat as into two trapeziums and verify your answer

If π = \(\frac{22}{7}\) show that the area of the unshaded part of a square of side 'a' units is approximately \(\frac{3}{7}\) a² sq. units and that of the shaded part is approximately \(\frac47\) a² sq. units for the given figure.

List out atleast three objects in each category which are in the shape of cube, cuboid, cylinder, cone and sphere.

Tabulate the number of faces(F), vertices (V) and edges(E) for the following polyhedron. Also find F + V - E

Find the area of the given nets.

Find the length of arc if the perimeter of a sector is 65 cm and radius is 20 cm.

Find the area of the sector whose arc length is 20 cm and radius is 7 cm

What is the least number of planes that can enclose a solid? What is the name of the solid? 

Find the product of the following: (x,y)

Find the product of the following.
(10x, 5y)

Find the product of the following
(2x², 5y²)

Find the product of the following
(4a, 3a²)

Find the product of the following
(3mn, 4np) 

Divide:12x³y³ by 3x²y

Divide. -15a² bc³ by 3ab

Divide :25x³y² by -15x²y

Divide. -72x²yz by -12yz

Divide 6x³y²z² by 3x²yz

Evaluate:
(2x+3y)²

Evaluate:
(2x-3y)²

Evaluate :
(2x+3y)(2x-3y)

Factorize:7(2x + 5) + 3 (2x + 5)

Factorize :12x³y⁴+16x²y⁵-4x⁵y²

Factorize:x²+xy+8x+8y

Factorize:9a² -16b²

Multiply (p + 6), (q - 7).

Multiply (pz - 2r) (pq - 2r)

Simplify (ab - q)²+ 2abc

Expand (xy +yx)²

(7x - 5)² Expand

Expand 9a² - 16b²

Evaluate 99² using identity

Factorize 6 ab + 12 bc

Factorize - xy - ay

Factorize 6x³ - 9² + 3x

Simplify (pq - qr)² + 4pq²r

(x²- 4) + (x² + 4) + 16. Simplify

Simplify (-2x - 2y - 10) + (x +Y + 5)

Identify the pairs of figures which are similar and congruent and write the letter pairs.

Match the following by their congruence

S.No.	A		B
1.		(i)	RHS
2.		(ii)	SSS
3.		(iii)	SAS
4.		(iv)	ASA

In the figure, DA = DC and BA = BC. Are the triangles DBA and DBC congruent? Why?

Is it possible to construct a quadrilateral PQRS with PQ = 5 cm, QR = 3 cm, RS = 6 cm, PS = 7 cm and PR = 10 cm. If not, why?

In the given figure if \(\frac { AO }{ OC } =\frac { BO }{ OD } =\frac { 1 }{ 2 } \) and AB=5cm. Find the value of DC.

In the given figure if \(\angle \)A =\(\angle \)C then prove that \(\triangle \)AOB ~\(\triangle \)COD

In the figure AB\(\bot \) BC and DE\(\bot \)AC prove that \(\triangle \)ABC ~\(\triangle \)AED.

In the given figure if \(\angle \)P =\(\angle \)RTS, prove that \(\triangle \)RPQ ~\(\triangle \) RTS.

A fast food restaurant has a meal special Rs.50 for a drink, sandwich, side item and dessert. The choices are Sandwich : Grilled chicken, AU beef patty, Vegeburger and Fill filet.
Side: Regular fries, cheese fries, potato fries
Dessert: Chocolate chip cookie or Apple pie.
Drink: Fanta, Dr. Pepper, Coke, Diet coke and sprite.
How may meal combos are possible?

A company puts a code on each different product they sell. The code is made up of 3 numbers and 2 letters. How many different codes are possible?

Add \(\frac{4}{-3}\) and \(\frac{8}{15}\)

What number should be subtracted from \(\frac{7}{3}\) to get \(\frac{5}{4}?\)

The product of two rational numbers is \(\frac{-28}{81}\). If one of the number is \(\frac{14}{27}\). find the other number.

Add and simplify in mixed fraction \(\frac{-12}{5}\)and \(\frac{43}{10}\)

Simplify 1+\(\frac{-4}{5}\)

Simplify \(\frac { 2 }{ 5 } +\frac { 8 }{ 3 } +\frac { -11 }{ 15 } +\frac { 4 }{ 5 } +\frac { -2 }{ 3 } \)

What number should be subtracted from \(\frac{-5}{3}\) to get \(\frac{5}{6}\)?

Simplify \(\left( \frac { 13 }{ 7 } \times \frac { 11 }{ 26 } \right) -\left( \frac { -4 }{ 3 } \times \frac { 5 }{ 6 } \right) \)

Find the length of arc whose radius is 42 cm and central angle is 60⁰

Verify Euler's formula for a pyramid.

Verify Eulers formula for a triangular prism

Find the length of an arc if the radius of the circle is 14 cm and area of the circle is 63 cm².

A circular arc whose radius is 12 cm makes an angle 30° at the center. Find the perimeter of the sector formed (ㅠ = 3.14)

Find r₁ + r₂ if the sum of the areas of two circles with radii r₁ and r₂ is equal to the area of a circle of radius r.

If the perimeter of a semicircle is 36 cm find its diameter.

Find the product of the following
3ab²c³ by 5a³b²c

Find the product of the following
\({ 4x }^{ 2 }yzby\cfrac { 3 }{ 2 } { x }^{ 2 }{ yz }^{ 2 }\)

Find the product of the following.
\(\cfrac { -8 }{ 5 } { x }^{ 2 }{ yz }^{ 2 }by-\cfrac { 3 }{ 4 } { xy }^{ 2 }z\)

Find the product of the following
\(\cfrac { 3 }{ 14 } { x }^{ 2 }yby\cfrac { 7 }{ 2 } { x }^{ 4 }y\)

Find the product of the following.
2.1 a²bc by 4ab²

Divide 15m²n³ by 5m²n²

Divide 24a³b³ by -8ab

Divide -21abc² by 7abc

Divide 72xyz²  by-9xz

Divide -72a⁴b⁵c⁸ by -9a²b²c³

Divide 16m³y by 4m²y

Divide 32m²n³p² by 4mnp

Evaluate the following (2x-3)(2x+5)

Evaluate the following (y-7)(y+3)

Evaluate the following
107\(\times\)103

Evaluate the following
56X48

Evaluate the following 95 x 97

Factorize
81a²-121b²

Factorize
x²+8x+16

Factorize
4a² - 4a + 1

Factorize
4x²-4xy+y²-9z²

Find the length of breadth of a rectangle with area x²- 3x + 2.

Divide 76x 5y³ z³ \(\div\)19x²y²

Divide (3x⁴ - 1875) \(\div\) by (3x²-75)

Divide -121p⁴ q²r² \(\div\) (-11pqr)

Factorize r² - 12x + 20

Factorize x² -7x- 8

Factorize x² -6x- 8

D is a point on the side BC. Such that \(\angle \)ADC = \(\angle \)BAC. Prove that \(\frac { CA }{ CD } =\frac { CB }{ CA } \) or CA² = CBXCD.

In the figure with respect to \(\triangle \)BEP and \(\triangle \)CPD prove that BP x PD = EP x PC.

Two triangles BAC and BDC right angled at A and D respectively are drawn on the same base BC and on the same side of BC. If AC and DB intersect at P. Prove that AP x PC = DP x PB.

Colour the graph with minimum number of colours and no two adjacent vertices should have the same colour.

Simplify \(=\frac { -12 }{ 10 } +\left( \frac { -90 }{ 15 } \right) -\left( \frac { 3 }{ 8 } \right) \)

Simplify \(\left( \frac { -7 }{ 18 } \times \frac { 15 }{ -7 } \right) -\left( 1\times \frac { 1 }{ 4 } \right) +\left( \frac { 1 }{ 2 } \times \frac { 1 }{ 4 } \right) \)

Verify associative property for addition of rational numbers for \(a=\frac{5}{6}, b=\frac{-3}{4},c=\frac{4}{7}\)

Rearrange suitably and apply the properties to simplify \(\left( \frac { 6 }{ 7 } \times \frac { 2 }{ 3 } \right) +\left( \frac { 9 }{ 11 } +\frac { 2 }{ 3 } \right) +\left( \frac { 2 }{ 3 } \times \frac { 4 }{ 9 } \right) \)

Find three rational numbers between -2 and 5 by average method.

Divide the sum of \(\frac{-13}{5}\) and \(\frac{12}{7}\) by the product of \(\frac{-31}{7}\) and \(\frac{-1}{2}\).

The cost of 2\(\frac{1}{3}\)metres of cloth is 275 \(\frac{1}{4}\). Find the cost cloth meter.

A sector is cut from a circle of radius 21 cm. The angle of the sector is 150°. Find the length of its arc and area of the sector.

An arc of a circle is of length 5π cm and the sector it bounds has an area of 20π cm² Find the radius of the circle.

PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal semi-circles drawn on PQ and QS as diameters. Find the perimeter and area of the shaded region

In the figure AOBCA represents a quadrant of a circle of radius 3.5cm D with center 'O' calculate the area of the shaded portion \(\left( \pi =\frac { 22 }{ 7 } \right) \)

Find the area of the shaded region in the figure.

An athletic track 14 m wide consists of two straight sections 120 m long joining semicircular ends whose inner radius is 35 m. Calculate the area of the shaded region.

Find the area of the shaded portion.

Find the area of the shaded region.

Simplify (3x-2)(x-1)(3x+5).

Simplify (5 -x) (3 - 2x) (4 - 3x).

Divide.9m⁵+12m⁴-6m² by 3m²

Divide 24x³y+20x²y²-4xy by 2xy

Divide.6x²yz-3xy³z+8x²yz⁴ by 2xyz

Divide
\(\cfrac { 2 }{ 3 } { a }^{ 2 }{ b }^{ 2 }{ c }^{ 2 }+\cfrac { 4 }{ 3 } { ab }^{ 2 }{ c }^{ 3 }-\cfrac { 1 }{ 5 } { ab }^{ 3 }{ { c }^{ 2 } }by\cfrac { 1 }{ 2 } abc\)

If x+y=12 and xy=14 find x²+y²

If 3x + 2y = 12 and xy = 6 find the value of 9x²+4y²

Factorize
x²+2xy+y²-a²+2ab-b

Factorize
9-a⁶+2a³-b⁶

Factorize 
x¹⁶-y¹⁶+x⁸+y⁸

Factorize
(p + q)² - (a - b)² + P + q - a + b

Factorize
100 (x +y)² - 81 (a + b)²

Factorize 
(x+1)²-(x-2)²

The area of a square is 4x²- + 12xy + 9y²-. Find its side.

If p + q = 12 and pq = 22 find p² + q²

If a + b = 25, a²+ b² = 225 find ab

If (x +y) = 13 and xy = 28, find x²+y²

If m - n = 16 and m² + n² = 400 find mn.

P and Q are points on sides AB and AC respectively of \(\triangle \)ABC. If AP = 3 cm PB = 6cm, AQ = 5 cm and QC = 10 cm, show that BC = 3 PQ.

In the given figure if \(\frac { QT }{ PR } =\frac { QR }{ QS } \) and \(\angle \)1 = \(\angle \)2.Prove that \(\triangle \)PQS ~\(\triangle \)TQR.