81279 + Interview Questions in Mathematics QA in Mathematics

1.	How many square tiles of side 40 cm are needed to buildthe floor of a room of length 16 m and breadth 10 m?
Answer»

Discussion

2.	3 m 40 cm.Find the volume of a cube with side 1 m 60 cmboid nhose length is 1
Answer» 1m = 100 cm So, 1 cm = 1/100 m 60 cm = 60/100 = 0.6 m So, 1 m 60 cm = 1.6 m Volume of cube is side³ = (1.6 m)³ = 4.096 m³

2.

3 m 40 cm.Find the volume of a cube with side 1 m 60 cmboid nhose length is 1

Answer»

1m = 100 cm

So, 1 cm = 1/100 m

60 cm = 60/100 = 0.6 m

So, 1 m 60 cm = 1.6 m

Volume of cube is side³

= (1.6 m)³

= 4.096 m³

Discussion

3.	The fraction 5/8 is found between which pair of fractions on a number line ? (a) 8/16 and 21/32 (b) 9/16 and 19/32
Answer» ( b ) 9/16 and 19/32 b. 9/16 & 19/32 it is the correct answer. 9/16 n 19/32is your answer 9/17and 19/32 is answer

3.

The fraction 5/8 is found between which pair of fractions on a number line ? (a) 8/16 and 21/32 (b) 9/16 and 19/32

Answer»

( b ) 9/16 and 19/32

b. 9/16 & 19/32 it is the correct answer.

9/16 n 19/32is your answer

9/17and 19/32 is answer

Discussion

4.	U)hnpele (a) Fรกrad(vi) The torque acting on an electric dipole of dipole moment P placedparallel to electric field E will be:(a) PE(b) P/E(c) Zero(d) E/Pii) The distance to whi
Answer» Torque experienced by the dipole in uniform electric fieldτ=PEsinθτ=PEsin⁡θ (i) For minimum torqueθ=0∘θ=0∘ τmin=pEsinθ∘τmin=pEsin⁡θ∘ =0=0 (ii) For maximum torqueθ=90∘θ=90∘ τmax=PEsin90∘τmax=PEsin⁡90∘ =PE

4.

U)hnpele (a) Fรกrad(vi) The torque acting on an electric dipole of dipole moment P placedparallel to electric field E will be:(a) PE(b) P/E(c) Zero(d) E/Pii) The distance to whi

Answer»

Torque experienced by the dipole in uniform electric fieldτ=PEsinθτ=PEsin⁡θ

(i) For minimum torqueθ=0∘θ=0∘

τmin=pEsinθ∘τmin=pEsin⁡θ∘

=0=0

(ii) For maximum torqueθ=90∘θ=90∘

τmax=PEsin90∘τmax=PEsin⁡90∘

=PE

Discussion

5.	A. +a1. (0)2. 0 1
Answer» 2 multy 3 -0 multi -4=6-0=6

Discussion

6.	iv) p(x) 2011173Find reminder when x + 3x2 + 3x + 1 is divided by (x +1).ditided by ( ĐĽ-
Answer»

Discussion

7.	(1) PyramidThe number of prime factor for 2016 is1) 8(2) Sphere(3) Prism(2) 3(3) 4(4) 7
Answer» 2016= 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7 Thus, 2016 has 3 different prime factors=> 2,3 and 7 Hence, option (2) is correct.

7.

(1) PyramidThe number of prime factor for 2016 is1) 8(2) Sphere(3) Prism(2) 3(3) 4(4) 7

Answer»

2016= 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7

Thus, 2016 has 3 different prime factors=> 2,3 and 7

Hence, option (2) is correct.

Discussion

8.	व न, RO o —y s(i) (sec A +tanA) (1 -sin A)=
Answer» (secA + tanA)(1 - sinA) = (1/cosA + sinA/cosA)(1 - sinA) = (1 + sinA)(1 - sinA)/cosA = (1 - sinAsinA)/cosA = cosAcosA/cosA = cosA

Discussion

9.	4 \operatorname { cos } ^ { 2 } \theta + \sqrt { 3 } = 2 ( \sqrt { 3 } + 1 ) \operatorname { cos } \theta ( UP 2011 )
Answer» thanks

Discussion

10.	1 Factorise x+4y'.se this to prove that 2011 64 is a compo sitenumber.
Answer» That's the sum of two squares. But we can only factor the difference of two squares, so we see if it is possible to change it to the difference of two squares by adding and subtracting a square, like this x⁴ + ___ + 4y⁴ - ___ We ask ourselves this question: What term would have to be placed in those blanks so that the first three terms would factor as the square of the sum of their square roots, x² and 2y²? To find out we multiply out the square of the sum of their square roots: (x² + 2y²)² = x⁴ + 4x²y² + 4y⁴ We see that the term that must be placed in the two blanks would be 4x²y², which does happen to be a square. So we place 4x²y² in the two blanks: x⁴ + 4x²y² + 4y⁴ - 4x²y² Then we factor the first three terms: (x²+2y²)² - 4x²y² and that is the difference of two squares, and factors as [(x²+2y²) - 2xy][(x+2y²) + 2xy] Removing the parentheses inside the brackets: [x² + 2y² - 2xy][x² + 2y² + 2xy] Then we can change the brackets to parentheses and rearrange the trinomials in descending order of x and ascending order of y: (x² - 2xy + 2y²)(x² + 2xy + 2y²)

10.

1 Factorise x+4y'.se this to prove that 2011 64 is a compo sitenumber.

Answer»

That's the sum of two squares. But we can only factor the difference of two squares, so we see if it is possible to change it to the difference of two squares by adding and subtracting a square, like this

x⁴ + ___ + 4y⁴ - ___

We ask ourselves this question: What term would have to be placed in those blanks so that the first three terms would factor as the square of the sum of their square roots, x² and 2y²?

To find out we multiply out the square of the sum of their square roots: (x² + 2y²)² = x⁴ + 4x²y² + 4y⁴

We see that the term that must be placed in the two blanks would be 4x²y², which does happen to be a square.

So we place 4x²y² in the two blanks: x⁴ + 4x²y² + 4y⁴ - 4x²y²

Then we factor the first three terms: (x²+2y²)² - 4x²y² and that is the difference of two squares, and factors as

[(x²+2y²) - 2xy][(x+2y²) + 2xy]

Removing the parentheses inside the brackets: [x² + 2y² - 2xy][x² + 2y² + 2xy]

Then we can change the brackets to parentheses and rearrange the trinomials in descending order of x and ascending order of y:

(x² - 2xy + 2y²)(x² + 2xy + 2y²)

Discussion

11.	1. Find the largest number that divides 2623 and 2011 and leavesemainders 5 and 9 respectively. (154)
Answer»

Discussion

12.	Construct an L of ro andits supplementary anle.bisect.1A
Answer»

Discussion

13.	[-144 + (~14+2)] + 72 + (4+8))
Answer» [-144 ÷ (- 14 + 2)] ÷ 72 ÷ (4+8)= [-144 ÷ (-12)] ÷ 72 ÷ 12= (12) ÷ 6= 12/6= 6

Discussion

14.	Independent PracticeEstimate by rounding. Show how you estimatee4 687Âˇ79 Ă 56
Answer» 68/7=9.71428572437956=4424 687 = 476 79*56 = 4424

14.

Independent PracticeEstimate by rounding. Show how you estimatee4 687Âˇ79 Ă 56

Answer»

68/7=9.714285724379*56=4424

68*7 = 476

79*56 = 4424

Discussion

15.	(b) The mean of the following numbers is 68. Find the value of x45, 52, 60, Ń, 69, 70, 26, 81, 94Hence, estimate the median.
Answer» Mean = (45+52+60+x+69+70+26+81+94)/9 => 68*9 = 497+x=> 612= 497+x=> x = 115.

Discussion

16.	\cos 2 A \cos 4 A \ldots \ldots \cos 2^{n-1} A=\frac{\sin 2^{n} A}{2^{n} \sin 2 A}\sin ^{4} \frac{\pi}{8}+\sin ^{4} \frac{3 \pi}{8}+\sin ^{4} \frac{5 \pi}{8}+\sin ^{4} \frac{1 \pi}{8}
Answer» sin⁴(π/8) + sin⁴(3π/8) + sin⁴(5π/8) + sin⁴(7π/8) = [sin²(π/8)]² + [sin²(3π/8)]² + [sin²(5π/8)]² + [sin²(7π/8)]² = [{1 - cos(π/4)}/2]² + [{1 - cos(3π/4)}/2]² + [{1 - cos(5π/4)}/2]² + [{1 - cos(7π/4)}/2]² = [{1 - √2/2 }/2]² + [{1 + √2/2 }/2]² + [{1 + √2/2}/2]² + [{1 - √2/2}/2]² = 2[{1 - √2/2 }/2]² + 2[{1 + √2/2 }/2]² = 2[{2 - √2}/4]² + 2[{2 + √2}/4]² = (1/8)(2 - √2)² + (1/8)(2 + √2)² = (1/8)[(4 - 4√2 + 2) + (4 + 4√2 + 2)] = 12/8 = 3/2

16.

\cos 2 A \cos 4 A \ldots \ldots \cos 2^{n-1} A=\frac{\sin 2^{n} A}{2^{n} \sin 2 A}\sin ^{4} \frac{\pi}{8}+\sin ^{4} \frac{3 \pi}{8}+\sin ^{4} \frac{5 \pi}{8}+\sin ^{4} \frac{1 \pi}{8}

Answer»

sin⁴(π/8) + sin⁴(3π/8) + sin⁴(5π/8) + sin⁴(7π/8)

= [sin²(π/8)]² + [sin²(3π/8)]² + [sin²(5π/8)]² + [sin²(7π/8)]²

= [{1 - cos(π/4)}/2]² + [{1 - cos(3π/4)}/2]² + [{1 - cos(5π/4)}/2]² + [{1 - cos(7π/4)}/2]²

= [{1 - √2/2 }/2]² + [{1 + √2/2 }/2]² + [{1 + √2/2}/2]² + [{1 - √2/2}/2]²

= 2[{1 - √2/2 }/2]² + 2[{1 + √2/2 }/2]²

= 2[{2 - √2}/4]² + 2[{2 + √2}/4]²

= (1/8)(2 - √2)² + (1/8)(2 + √2)²

= (1/8)[(4 - 4√2 + 2) + (4 + 4√2 + 2)]

= 12/8 = 3/2

Discussion

17.	1. Estimate each of the following products by PoUhalng u(b) 42 x 75(a) 28 x 532. Estimate each of the following products by rounding off(c)54 x 47
Answer» a) 3050 = 1500 b) 4080 = 3200 c) 50*50 = 2500

17.

1. Estimate each of the following products by PoUhalng u(b) 42 x 75(a) 28 x 532. Estimate each of the following products by rounding off(c)54 x 47

Answer»

a) 30*50 = 1500

b) 40*80 = 3200

c) 50*50 = 2500

Discussion

18.	68, Prove that Cot cos A cosecA168. Prove that cot A cos A-cosec A+ 1 .cot. A- cos A cosec A-1IGRSE 2011
Answer» Lhs = (cotA - cosA)/(cotA+cosA)=(cosA/sinA - cosA)/(cosA/sinA + cosA) =cosA(1/sinA - 1)/cosA(1/sinA + 1) = (1/sinA -1)/(1/sinA+1)=(cosecA-1)/(cosecA+1) since 1/sinA= cosecA=rhs

18.

68, Prove that Cot cos A cosecA168. Prove that cot A cos A-cosec A+ 1 .cot. A- cos A cosec A-1IGRSE 2011

Answer»

Lhs = (cotA - cosA)/(cotA+cosA)=(cosA/sinA - cosA)/(cosA/sinA + cosA)

=cosA(1/sinA - 1)/cosA(1/sinA + 1)

= (1/sinA -1)/(1/sinA+1)=(cosecA-1)/(cosecA+1) since 1/sinA= cosecA=rhs

Discussion

19.	Solve the proportion.
Answer» Given:s/12 = 15/18s=(15/18)×12s=10

Discussion

20.	EXERCISE 7.3Estimate the cube ro1. 138245. 795079. 729LET'S RECALL
Answer» 1. cube root of 13824 = 24.2. cube root of 79507 = 43.3. cube root of 729 = 9. Please hit the like button if this helped you

20.

EXERCISE 7.3Estimate the cube ro1. 138245. 795079. 729LET'S RECALL

Answer»

1. cube root of 13824 = 24.2. cube root of 79507 = 43.3. cube root of 729 = 9.

Please hit the like button if this helped you

Discussion

21.	(4/3)(1/(8((2/4))))
Answer» 1/8 ÷ 2 1/4 * 4 1/3 = 1/8 ÷ 9/4 * 13/3 = 1/8 * 4/9 * 13/3 = 1/18 * 13/3 = 13/54

21.

(4/3)(1/(8((2/4))))

Answer»

1/8 ÷ 2 1/4 * 4 1/3

= 1/8 ÷ 9/4 * 13/3

= 1/8 * 4/9 * 13/3

= 1/18 * 13/3

= 13/54

Discussion

22.	8+12-24+8-1(b)(20 + 8) + (4-2)
Answer» (20+8)÷(4-2) = 28÷2 = 14 Like my answer if you find it useful!

22.

8+12-24+8-1(b)(20 + 8) + (4-2)

Answer»

(20+8)÷(4-2)

= 28÷2

= 14

Like my answer if you find it useful!

Discussion

23.	पृ नजe ok
Answer» Given : x + y = 17 .....(1) x - y = 1 ........(2) Eliminating y by adding (1) and (2) 2x = 18 x = 9 So, y = 17 - 9 = 8

23.

पृ नजe ok

Answer»

Given :

x + y = 17 .....(1)

x - y = 1 ........(2)

Eliminating y by adding (1) and (2)

2x = 18

x = 9

So, y = 17 - 9 = 8

Discussion

24.	108. If tan 0+= 2, then the value of tand+-tan 8।tan’o is :यदि tan8+1=2 हो, तो tan 0+tan १ .(1) 4(2) 16tan-8का मान होगा :2(4)(3)8
Answer» Let theta = x Given,tan x + 1/tan x = 2 Squaring both sides(tan x + 1/tan x)^2 = 4 tan^2 x + 1/tan^2 x + 2tan x1/tan x = 4 tan^2 x + 1/tan^2 x = 4 - 2 tan^2 x + 1/tan^2 x = 2 (3) is correct option esaka answer hoga 08 ka 1. 4 =4-2=2.options (3) is correct

24.

108. If tan 0+= 2, then the value of tand+-tan 8।tan’o is :यदि tan8+1=2 हो, तो tan 0+tan १ .(1) 4(2) 16tan-8का मान होगा :2(4)(3)8

Answer»

Let theta = x

Given,tan x + 1/tan x = 2

Squaring both sides(tan x + 1/tan x)^2 = 4

tan^2 x + 1/tan^2 x + 2*tan x*1/tan x = 4

tan^2 x + 1/tan^2 x = 4 - 2

tan^2 x + 1/tan^2 x = 2

(3) is correct option

esaka answer hoga 08 ka 1. 4

=4-2=2.options (3) is correct

Discussion

25.	1. 289 xo20 -- 22. Гоо ха7. 43. 399 x 470 - 3y. ST) 4 x 47- 4292 x 4 - 2297 x 10т 1-217 28 x 472-8. 29 x 69-29,SCIox 8 10 - 1
Answer» (1) 29478(2) 48494(3) 337557(4) 50337(5) 278614(6) 288720(7) 278962(8) 203253(9) 413099 it is answer

Discussion

26.	यदि 8 - ० न 4 और 90 न 45, तो (8+0)* का मूल्य क्या है?96146156196
Answer»

Discussion

27.	(1) 576(2) 144344. The least number such that when it divided byremainder 7. 17. 27 and 37 respectively, is(1) 1575(2) 1557(3) 1576ch that when it divided by 15. 25. 35 and 45. it leaves) 1567(3) 15764
Answer» 15-7=825-17=835-27=845-37=8LCM=1575The required number =1575-8=1567

Discussion

28.	1Lomif Q=30 - 6=130H-10
Answer»

Discussion

29.	14What is the value of the expression below?32- 16+4+2
Answer» using bodies,9-16/6 = -7/6

Discussion

30.	Find the simple interest on the following:(i) 2000 for 6 years at 7 %
Answer»

Discussion

31.	leet org ginal rÃ¡ke ber megre32-16 20(2-4)= Valsnty finds112 erat
Answer» Vx^2-16 -( x-4)=Vx^2-5x+4; -16-x+4=-5x+4; -16-x=-5x; -16=-x+5x; 16=-x+5x; 16=-x+5x; 16=4x; 16÷4=x=4

Discussion

32.	Which of the following are in proportion?(a) 16, 4, 32, 8
Answer»

Discussion

33.	5+3{-34--16-14}÷3[17+(-3)×4-2×(-7)]
Answer»

Discussion

34.	Q.7 Find the median of the following dataClasses 10-10 10-20 20-30 \| 30-40 40-50Frequency \| 8 16 \| 36 \| 34 16
Answer» answer is 43.22 median of the following data

Discussion

35.	10. What is the cost of c kg of sugar at sh63.50 per kg and m kg of sugar at shsy per kg
Answer» Cost of c kg of sugar at sh 63.50 per kg= 63.50c Cost of m kg of sugar at shs y per kg = my Therefore,Total Cost of Sugar= shs 63.05c + my

35.

10. What is the cost of c kg of sugar at sh63.50 per kg and m kg of sugar at shsy per kg

Answer»

Cost of c kg of sugar at sh 63.50 per kg= 63.50c

Cost of m kg of sugar at shs y per kg = my

Therefore,Total Cost of Sugar= shs 63.05c + my

Discussion

36.	Find any ten rational numbers between
Answer» To find 10 rational numbers between - 2/5 and 1/2. Multiply a divide first rational number by 4 and second rational number by 10 Then,-2/5 = - 24/54 = - 8/201/2 = 110/210 = 10/20 Therefore,Ten rational numbers between - 2/5 and 1/2 are - 7/20, - 6/20,-5/20, - 4/20, - 3/20, - 2/20, - 1/20, 1/20, 2/20, 3/20

36.

Find any ten rational numbers between

Answer»

To find 10 rational numbers between - 2/5 and 1/2. Multiply a divide first rational number by 4 and second rational number by 10

Then,-2/5 = - 2*4/5*4 = - 8/201/2 = 1*10/2*10 = 10/20

Therefore,Ten rational numbers between - 2/5 and 1/2 are - 7/20, - 6/20,-5/20, - 4/20, - 3/20, - 2/20, - 1/20, 1/20, 2/20, 3/20

Discussion

37.	"Vouu lomd3provethatit coso] =(coseo coto]1- Coro
Answer»

Discussion

38.	- TUJ2000 VOU7. Find the smallest 5 digit number which is divisible by 18, 24, and 32.
Answer» 2 I 18, 24, 32 L________ 3 I 9, 12, 16 L________ 3 I 3, 4, 16 L________ 2 I 1, 4, 16 L________ 2 I 1 , 2, 8 L________ 2 I 1 , 1, 4 L________ 2 I 1, 1, 2 L________ I 1, 1, 1 LCM= 2^{5} x 3^{2}=32x9=288 By using EUCLID DIVISION LEMMA,We get, a=bq+r 100,000=288(347)+64 100,000 - 64 = 99,936∴The largest 5-digit number that is divisible by 18,24 and 32 is 99,936 HOPE IT HELPS..! Read more on Brainly.in - https://brainly.in/question/2793943#readmore

38.

- TUJ2000 VOU7. Find the smallest 5 digit number which is divisible by 18, 24, and 32.

Answer»

2 I 18, 24, 32 L________ 3 I 9, 12, 16 L________ 3 I 3, 4, 16 L________ 2 I 1, 4, 16 L________ 2 I 1 , 2, 8 L________ 2 I 1 , 1, 4 L________ 2 I 1, 1, 2 L________ I 1, 1, 1

LCM= 2^{5} x 3^{2}=32x9=288

By using EUCLID DIVISION LEMMA,We get, a=bq+r 100,000=288(347)+64 100,000 - 64 = 99,936∴The largest 5-digit number that is divisible by 18,24 and 32 is 99,936

HOPE IT HELPS..!

Read more on Brainly.in - https://brainly.in/question/2793943#readmore

Discussion

39.	3.5883.5893.5885 .ss91.983.sya3.58833.5887Step4し,A3.5888EXERCISE 1.3ísualise 2.874 on the number line, using successive magnificaticVisualilse 5,28 on the number line, upto 3 decimal places.OPERATIONS ON REAL NUMBERS
Answer»

Discussion

40.	REAL NUMBERSEXERCISE 1.11.Use Euclid's division algorithm to find the HCF of:(i)135 and 225(ii)196 and 38220
Answer» we can also do this by division

Discussion

41.	REAL NUMBERSEXERCISE 1.11. Use Euclid's division algorithm to find the HCF of:(i) 135 and 225(ii) 196 and 38220bitie odd intemer is of the form 60 +1+ 3
Answer»

Discussion

42.	EXERCISEfind the mean variance1. 6,7, 10, 12, 13, 4, 8, 12pirst n natural numbersand variance for each of the data in Exercies 1 to 5.152
Answer»

Discussion

43.	10. A map is drawn to a scale of 1:30000000. The distance between two towns is 7 cm on the map.What is the actual distance between the two towns in kilometres?tottles ofcold drink are served for a hatch fh erHow many bottles would
Answer» how to determine the actual distance on the map:The actual distance = the distance on a map x scale = 7 x 30000000 = 210000000 cm = 2100 km direct and inverse variations ma

43.

10. A map is drawn to a scale of 1:30000000. The distance between two towns is 7 cm on the map.What is the actual distance between the two towns in kilometres?tottles ofcold drink are served for a hatch fh erHow many bottles would

Answer»

how to determine the actual distance on the map:The actual distance = the distance on a map x scale = 7 x 30000000 = 210000000 cm = 2100 km

direct and inverse variations ma

Discussion

44.	Find 12 rational numbers between-1 and 2.
Answer»

Discussion

45.	4 The product of two rational numbers is -9. If one of the numbers is -12, find the other
Answer»

Discussion

46.	12) Find any ten rational numbers betweenno
Answer» - 0.6 , - 0.5 ,-0.4 ,-0.3,-0.2,-0.1,0, 0.1,0.2,0.3,0.4,0.5,0.6=5/8

Discussion

47.	4. The product of two rational numbers is -9. If one of the numbers is -12, find the other.
Answer»

Discussion

48.	D. Tuy \|\|C. Cyioplusu8 How are bacteria able to attach to otherbacteria?9 Why are protozoa known as heterotrophs?
Answer» Bacteria usually live in species-rich communities and frequently exchange nutrients and other metabolites. Until now, it was unclear whether microorganisms exchange metabolites exclusively by releasing them into the surrounding environment or whether they also use direct connections betweencellsfor this purpose.

Discussion

49.	18. A student was asked to multiply a given number by sy mistake he codegiven number by His answer was 36 more than the correct answer who was thegiven number?Hint. Let the number be, then
Answer» 80 is the answer of this question

Discussion

50.	s. A machine fills 420 bottles in 3 hours. How many bottles will it fill in 5 hours?(a) 252(b) 700(c) 504(d) 300
Answer» thank u so much how many primes to 420 with do not exed 420

50.

s. A machine fills 420 bottles in 3 hours. How many bottles will it fill in 5 hours?(a) 252(b) 700(c) 504(d) 300

Answer»

thank u so much

how many primes to 420 with do not exed 420

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

How many square tiles of side 40 cm are needed to buildthe floor of a room of length 16 m and breadth 10 m?

3 m 40 cm.Find the volume of a cube with side 1 m 60 cmboid nhose length is 1

The fraction 5/8 is found between which pair of fractions on a number line ? (a) 8/16 and 21/32 (b) 9/16 and 19/32

U)hnpele (a) Fรกrad(vi) The torque acting on an electric dipole of dipole moment P placedparallel to electric field E will be:(a) PE(b) P/E(c) Zero(d) E/Pii) The distance to whi

A. +a1. (0)2. 0 1

iv) p(x) 2011173Find reminder when x + 3x2 + 3x + 1 is divided by (x +1).ditided by ( ĐĽ-

(1) PyramidThe number of prime factor for 2016 is1) 8(2) Sphere(3) Prism(2) 3(3) 4(4) 7

व न, RO o —y s(i) (sec A +tanA) (1 -sin A)=

4 \operatorname { cos } ^ { 2 } \theta + \sqrt { 3 } = 2 ( \sqrt { 3 } + 1 ) \operatorname { cos } \theta ( UP 2011 )

1 Factorise x+4y'.se this to prove that 2011 64 is a compo sitenumber.

1. Find the largest number that divides 2623 and 2011 and leavesemainders 5 and 9 respectively. (154)

Construct an L of ro andits supplementary anle.bisect.1A

[-144 + (~14+2)] + 72 + (4+8))

Independent PracticeEstimate by rounding. Show how you estimatee4 687Âˇ79 Ă 56

(b) The mean of the following numbers is 68. Find the value of x45, 52, 60, Ń , 69, 70, 26, 81, 94Hence, estimate the median.

\cos 2 A \cos 4 A \ldots \ldots \cos 2^{n-1} A=\frac{\sin 2^{n} A}{2^{n} \sin 2 A}\sin ^{4} \frac{\pi}{8}+\sin ^{4} \frac{3 \pi}{8}+\sin ^{4} \frac{5 \pi}{8}+\sin ^{4} \frac{1 \pi}{8}

1. Estimate each of the following products by PoUhalng u(b) 42 x 75(a) 28 x 532. Estimate each of the following products by rounding off(c)54 x 47

68, Prove that Cot cos A cosecA168. Prove that cot A cos A-cosec A+ 1 .cot. A- cos A cosec A-1IGRSE 2011

Solve the proportion.

EXERCISE 7.3Estimate the cube ro1. 138245. 795079. 729LET'S RECALL

(4/3)*(1/(8*((2/4))))

8+12-24+8-1(b)(20 + 8) + (4-2)

पृ नजe ok

108. If tan 0+= 2, then the value of tand+-tan 8।tan’o is :यदि tan8+1=2 हो, तो tan 0+tan १ .(1) 4(2) 16tan-8का मान होगा :2(4)(3)8

1. 289 xo20 -- 22. Гоо ха7. 43. 399 x 470 - 3y. ST) 4 x 47- 4292 x 4 - 2297 x 10т 1-217 28 x 472-8. 29 x 69-29,SCIox 8 10 - 1

यदि 8 - ० न 4 और 90 न 45, तो (8+0)* का मूल्य क्या है?96146156196

(1) 576(2) 144344. The least number such that when it divided byremainder 7. 17. 27 and 37 respectively, is(1) 1575(2) 1557(3) 1576ch that when it divided by 15. 25. 35 and 45. it leaves) 1567(3) 15764

1Lomif Q=30 - 6=130H-10

14What is the value of the expression below?32- 16+4+2

Find the simple interest on the following:(i) 2000 for 6 years at 7 %

leet org ginal rÃ¡ke ber megre32-16 20(2-4)= Valsnty finds112 erat

Which of the following are in proportion?(a) 16, 4, 32, 8

5+3{-34--16-14}÷3[17+(-3)×4-2×(-7)]

Q.7 Find the median of the following dataClasses 10-10 10-20 20-30 | 30-40 40-50Frequency | 8 16 | 36 | 34 16

10. What is the cost of c kg of sugar at sh63.50 per kg and m kg of sugar at shsy per kg

Find any ten rational numbers between

"Vouu lomd3provethatit coso] =(coseo coto]1- Coro

- TUJ2000 VOU7. Find the smallest 5 digit number which is divisible by 18, 24, and 32.

3.5883.5893.5885 .ss91.983.sya3.58833.5887Step4し,A3.5888EXERCISE 1.3ísualise 2.874 on the number line, using successive magnificaticVisualilse 5,28 on the number line, upto 3 decimal places.OPERATIONS ON REAL NUMBERS

REAL NUMBERSEXERCISE 1.11.Use Euclid's division algorithm to find the HCF of:(i)135 and 225(ii)196 and 38220

REAL NUMBERSEXERCISE 1.11. Use Euclid's division algorithm to find the HCF of:(i) 135 and 225(ii) 196 and 38220bitie odd intemer is of the form 60 +1+ 3

EXERCISEfind the mean variance1. 6,7, 10, 12, 13, 4, 8, 12pirst n natural numbersand variance for each of the data in Exercies 1 to 5.152

10. A map is drawn to a scale of 1:30000000. The distance between two towns is 7 cm on the map.What is the actual distance between the two towns in kilometres?tottles ofcold drink are served for a hatch fh erHow many bottles would

Find 12 rational numbers between-1 and 2.

4 The product of two rational numbers is -9. If one of the numbers is -12, find the other

12) Find any ten rational numbers betweenno

4. The product of two rational numbers is -9. If one of the numbers is -12, find the other.

D. Tuy ||C. Cyioplusu8 How are bacteria able to attach to otherbacteria?9 Why are protozoa known as heterotrophs?

18. A student was asked to multiply a given number by sy mistake he codegiven number by His answer was 36 more than the correct answer who was thegiven number?Hint. Let the number be, then

s. A machine fills 420 bottles in 3 hours. How many bottles will it fill in 5 hours?(a) 252(b) 700(c) 504(d) 300

Independent PracticeEstimate by rounding. Show how you estimatee4 687Âˇ79 Ă 56

(b) The mean of the following numbers is 68. Find the value of x45, 52, 60, Ń, 69, 70, 26, 81, 94Hence, estimate the median.

(4/3)(1/(8((2/4))))