81279 + Interview Questions in Mathematics QA in Mathematics

1.	Why did various classes and groups of Indiansparticipate in the Civil DisobedienceMovement?
Answer» Various classes and different social groups of Indians participated in the Civil Disobedience Movement led by Gandhiji in 1930. All of them joined this movement on account of their own needs, aspirations and limited understanding. In the rural areas, rich farmers and peasant communities such as Patidars (Gujarat) and Jats in Uttar Pradesh were very hard hit by the trade depression and decreasing costs of their commercial crops. They found themselves unable to pay the government’s revenue due to the disappearance of their cash income. For them the fight was a struggle against high revenue. So, the rich peasants participated in the Civil Disobedience Movement and supported the boycott programmes. The poorer peasants were not in favour of Iowering of the revenue demand. Many of them were small tenants who used to cultivate rented land taken from landlords. As the depression continued, cash income dwindled and so the tenants were unable to pay their land-rent. They demanded that their dues of rent should be remitted. The business classes participated in the movement to oppose the colonial polices that restricted business activities. They wanted protection against: imports of foreign goods, and a rupee-sterling foreign exchange ratio that would discourage imports. A few of them attacked colonial control over the Indian Economy and supported the Civil Disobedience Movement. Besides it they supported the movement financially and boycotted the trading of foreign goods. The industrial working classes stayed away from this movement leaving the Nagpur region as industrialists came closer to the congress. Women took part in this movement. They began to see service to the nation as a sacred duty of women.

1.

Why did various classes and groups of Indiansparticipate in the Civil DisobedienceMovement?

Answer»

Various classes and different social groups of Indians participated in the Civil Disobedience Movement led by Gandhiji in 1930. All of them joined this movement on account of their own needs, aspirations and limited understanding.

In the rural areas, rich farmers and peasant communities such as Patidars (Gujarat) and Jats in Uttar Pradesh were very hard hit by the trade depression and decreasing costs of their commercial crops. They found themselves unable to pay the government’s revenue due to the disappearance of their cash income. For them the fight was a struggle against high revenue. So, the rich peasants participated in the Civil Disobedience Movement and supported the boycott programmes.

The poorer peasants were not in favour of Iowering of the revenue demand. Many of them were small tenants who used to cultivate rented land taken from landlords. As the depression continued, cash income dwindled and so the tenants were unable to pay their land-rent. They demanded that their dues of rent should be remitted.

The business classes participated in the movement to oppose the colonial polices that restricted business activities. They wanted protection against: imports of foreign goods, and a rupee-sterling foreign exchange ratio that would discourage imports. A few of them attacked colonial control over the Indian Economy and supported the Civil Disobedience Movement. Besides it they supported the movement financially and boycotted the trading of foreign goods.

The industrial working classes stayed away from this movement leaving the Nagpur region as industrialists came closer to the congress. Women took part in this movement. They began to see service to the nation as a sacred duty of women.

2.	\operatorname { tan } ^ { - 1 } \frac { 1 } { 2 } + \operatorname { tan } ^ { - 1 } \frac { 1 } { 5 } + \operatorname { tan } ^ { - 1 } \frac { 1 } { 8 } = \frac { \pi } { 4 }
Answer» Tq

5.	4. In an election, 1785436 persons has casted their votes for different parties, but 19209 voteout of them were found invalid. Find the number of valid votes
Answer» to find the number of valid votes1785436-19209=1766227

7.	ceasing meaning
Answer» put an end to a state or an activity

8.	\tan ^ { - 1 } \left( \frac { 1 } { 5 } \right) + \tan ^ { - 1 } \left( \frac { 1 } { 7 } \right) + \tan ^ { - 1 } \left( \frac { 1 } { 3 } \right) + \tan ^ { - 1 } \left( \frac { 1 } { 8 } \right) = \frac { \pi } { 4 }
Answer» tan^(-1)((1/5+1/7)/(1-1/35))+tan^(-1)((1/3+1/8)/(1-1/24))=tan^(-1)(12/34)+tan^(-1)(11/23)=tan^(-1)(6/17)+tan^(-1)(11/23)=tan^(-1)((6/17+11/23)/(1-66/(17*23))=tan^(-1)(((138+187)/(23×17))/(325/(23+17))=tan^(-1)(325/325)=tan^(-1)(1)=pie/4

9.	7. If the point (a, a -2) lies on the graph of the equation3x + 5y = 30. find the value of a.
Answer»

10.	8. Find the equation of straight lines which are perpendicular to the line12x+5y = 17 and at a distance of 2 units from the point (-4,1)
Answer»

11.	\left. \begin{array} { l } { \operatorname { tan } ^ { - 1 } ( \frac { 1 } { 1 + 1.2 } ) + \operatorname { tan } ^ { - 1 } ( \frac { 1 } { 1 + 2.3 } ) + } \\ { + \operatorname { tan } ^ { - 1 } ( \frac { 1 } { 1 + n \cdot ( n + 1 ) } ) = \operatorname { tan } ^ { - 1 } \theta } \end{array} \right.
Answer»

13.	9. Candidates of four schools appear in a mathematics test. The data were as follows:No. of Candidates6048Not available40SchoolsAverage Score7580IV50If the average score of the candidates of all the four schools is 66, find the number ofcandidates that appeared from school III.
Answer» Thanks teacher your solution is correct....

14.	15. In an election. 4.98,656 votes were found valid, 6768 votes were found invalid and83,865 persons did not cast their votes. How many votes were registered in all?
Answer» Total number of votes registered in all=498656+6768+83865=589289

15.	r andy from a lincar pair lf 0, then find the ml984. In the given figure, state if AB is parallel to CD. Give reason for your answer.98ăĄ
Answer» No not parallel as parallel line should have corresponding angle equal considering thay we 98 is not equal 82 .

12.	tan^-1(x+1)+tan^-1(x-1)=tan^-1 8/31
Answer»

16.	1. In the figure alongside, ZPOR and 00R area lincarpair. f xso find the values of x and y
Answer» As x and y are linear pair sox+y = 180and given x-y = 80so we get2x = 260x = 130therefore y is 50

19.	cos-1虱丽すUat 큠cos6
Answer»

20.	Example 4. A party of 15 persons sit at a round table. Findthe odds against two specified individuals sitting next to eachother.
Answer» n(E)=(n-2)!2!n(s)=(n-1)! as circular arrngmntnwP(E)=(n-2)!2!/(n-1)!=2/(n-1)P(E)'=(1-(2/n-1))=(n-3)/(n-1)now ATQodd against:P(E)'/P(E)=(n-3)/2=(n-3)/2put n =15hence15-3/2=12/2=6 chances

18.	3. The graph of a lincar equation 25y - 10 is the line which meets the y -axis. Find the poind
Answer»

22.	(1024) x (81)(243)"X (128)Ä°plify2
Answer» (1024×1024×1024×81×81×81×81)/(243×243×128×128×128×128) = (4×4×4×81×81)/(3×3) = 4×4×4×9×81 = 46656

23.	\lim _{x \rightarrow 2} \frac{x^{10}-1024}{x-2}
Answer» thank u very much

24.	ar+x- 1805r= 180°ZBAC 2x 72x= 36"Hence ProvedExercise 7A1. Which of the following pairs of triangles are congruent? Alsostate the condition of congruency ineach case:65Date: "Page No.55°60°
Answer» i) both triangle are congurent by SAS rule

26.	ŕ¤ŕ¤A Hence Proved. \|). 13. Prove that :(1-sin 0 + cos 9)* = 2(1 + cos ) (1 - sin o)e 2 pum
Answer» Consider the LHS:(1-sinA+cosA)^2= [(1-sinA) + cosA]^2= (1-sinA)^2+ cos^2A+ 2(1-sinA)cosA= 1 + sin^2A− 2sinA+ cos^2A+ 2(1-sinA)cosA= 1 + (sin^2A+ cos^2A)− 2sinA+ 2(1-sinA)cosA= 1 + 1− 2sinA+ 2(1-sinA)cosA [Since,sin^2A+ cos^2A =1]= 2− 2sinA+ 2(1-sinA)cosA= 2(1− sinA) + 2(1-sinA)cosA= 2(1− sinA)(1 +cosA)= RHS

28.	Hence Proved.ample 9. In the given figure, AD is perpendicular to BC and EFBC, if < EABFAC,show that triangles ABD and ACD are congruent.Also, find the values of x and y if AB-2r+3, ACBD,and DC =y+1.3y+1,
Answer» Where is the figure?

29.	2. ABC is an isosceles triangle in which ABAC. Using RHS property, prove that <B-2C.[Hint: Draw AD丄BC. Prove ΔΑΙΒ兰AADC by RHS congruence]
Answer» thanks

33.	tihe followin4 cm4 cm4 cm2 cm
Answer» If you find this solution helpful, Please like it.

34.	l tihe argles so obtained.3. Using your protractor, drawan angle of measure 108°. With this angle as given,draw an angle of 540
Answer»

37.	If a, b, c, d are in G.P., prove that:(i) (a2- b2), (b2 - c2), (c2 -d2) are in G.P.2a. b' b2 + c2 , c2+d2 are in GP
Answer»

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Why did various classes and groups of Indiansparticipate in the Civil DisobedienceMovement?

\operatorname { tan } ^ { - 1 } \frac { 1 } { 2 } + \operatorname { tan } ^ { - 1 } \frac { 1 } { 5 } + \operatorname { tan } ^ { - 1 } \frac { 1 } { 8 } = \frac { \pi } { 4 }

\tan ^{-1}\left(\frac{1}{2}\right)+\tan ^{-1}\left(\frac{1}{5}\right)+\tan ^{-1}\left(\frac{1}{8}\right)=\frac{\pi}{4}

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4. In an election, 1785436 persons has casted their votes for different parties, but 19209 voteout of them were found invalid. Find the number of valid votes

d die sum ot odd integers from 1 to 2001.d the sun of all naturalnumbers lying betwn10 aud 1000 h

ceasing meaning

\tan ^ { - 1 } \left( \frac { 1 } { 5 } \right) + \tan ^ { - 1 } \left( \frac { 1 } { 7 } \right) + \tan ^ { - 1 } \left( \frac { 1 } { 3 } \right) + \tan ^ { - 1 } \left( \frac { 1 } { 8 } \right) = \frac { \pi } { 4 }

7. If the point (a, a -2) lies on the graph of the equation3x + 5y = 30. find the value of a.

8. Find the equation of straight lines which are perpendicular to the line12x+5y = 17 and at a distance of 2 units from the point (-4,1)

\left. \begin{array} { l } { \operatorname { tan } ^ { - 1 } ( \frac { 1 } { 1 + 1.2 } ) + \operatorname { tan } ^ { - 1 } ( \frac { 1 } { 1 + 2.3 } ) + } \\ { + \operatorname { tan } ^ { - 1 } ( \frac { 1 } { 1 + n \cdot ( n + 1 ) } ) = \operatorname { tan } ^ { - 1 } \theta } \end{array} \right.

tan^-1(x+1)+tan^-1(x-1)=tan^-1 8/31

9. Candidates of four schools appear in a mathematics test. The data were as follows:No. of Candidates6048Not available40SchoolsAverage Score7580IV50If the average score of the candidates of all the four schools is 66, find the number ofcandidates that appeared from school III.

15. In an election. 4.98,656 votes were found valid, 6768 votes were found invalid and83,865 persons did not cast their votes. How many votes were registered in all?

r andy from a lincar pair lf 0, then find the ml984. In the given figure, state if AB is parallel to CD. Give reason for your answer.98ăĄ

1. In the figure alongside, ZPOR and 00R area lincarpair. f xso find the values of x and y

N 4X o © न ि.न्फेउ हक न कि ८5 = 2 Moo -

3. The graph of a lincar equation 25y - 10 is the line which meets the y -axis. Find the poind

cos-1虱丽すUat 큠cos6

Example 4. A party of 15 persons sit at a round table. Findthe odds against two specified individuals sitting next to eachother.

2 x^{2}=\sqrt{1024} x=?

(1024) x (81)(243)"X (128)Ä°plify2

\lim _{x \rightarrow 2} \frac{x^{10}-1024}{x-2}

ar+x- 1805r= 180°ZBAC 2x 72x= 36"Hence ProvedExercise 7A1. Which of the following pairs of triangles are congruent? Alsostate the condition of congruency ineach case:65Date: "Page No.55°60°

he graph of the lincar equstion x 2y- Atwhich point s) does the graph cut the

ŕ¤ŕ¤A Hence Proved. |). 13. Prove that :(1-sin 0 + cos 9)* = 2(1 + cos ) (1 - sin o)e 2 pum

Hence Proved.ample 9. In the given figure, AD is perpendicular to BC and EFBC, if &lt; EABFAC,show that triangles ABD and ACD are congruent.Also, find the values of x and y if AB-2r+3, ACBD,and DC =y+1.3y+1,

2. ABC is an isosceles triangle in which ABAC. Using RHS property, prove that &lt;B-2C.[Hint: Draw AD丄BC. Prove ΔΑΙΒ兰AADC by RHS congruence]

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[Hint: Simplify LHS and RHS separately]

tihe followin4 cm4 cm4 cm2 cm

l tihe argles so obtained.3. Using your protractor, drawan angle of measure 108°. With this angle as given,draw an angle of 540

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Vertfy the Tndentrty f046 -0+206+bgeome tri colly b ag 2nits, 6ihg d2 unië Units |

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ŕ¤ŕ¤A Hence Proved. |). 13. Prove that :(1-sin 0 + cos 9)* = 2(1 + cos ) (1 - sin o)e 2 pum

Hence Proved.ample 9. In the given figure, AD is perpendicular to BC and EFBC, if < EABFAC,show that triangles ABD and ACD are congruent.Also, find the values of x and y if AB-2r+3, ACBD,and DC =y+1.3y+1,

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Vertfy the Tndentrty f046 -0+206+bgeome tri colly b ag 2nits, 6ihg d2 uniëUnits |

Pumpe timberuers show that the square of any positive odd integer inof the form 4q4i an and ag for some integer &Set

41.	Axioms or postulates are the assumptions which are obvious universal truths. Tproved.
Answer» Axiomsandpostulatesare the basicassumptionsunderlying a given body of deductive knowledge. They are accepted without demonstration. All other assertions (theorems, if we are talking about mathematics) must be proven with the aid of these basicassumptions.

46.	ofAttempt any four questions from this section,)Question 5.2(a) If-cos θ +ysin θ = 1 and a sin θ-b1, then prove that _ + 3-2cos θrth30 The
Answer» Thanxx..