81279 + Interview Questions in Mathematics QA in Mathematics

1.	The angle of elevation of cloud from point ‘h’ m above surface of lake is θ and the angle of depression of its reflection in lake is ɸ. Prove that height of cloud from lake is h[(tanɸ + tanθ)/(tanɸ-tanθ)]
Answer»

Discussion

2.	yS0o -y s07O R ARGV uisz-yusपश्पा ग*०्य्त LT
Answer» (sinθ- 2 sin^3θ)/(2cos^3θ-cosθ) =sinθ(1-2sin^2θ)/cosθ(2cos^2 θ-1) = sin θ [1- 2(1- cos^2 θ)/cos θ(2cos ^2 θ -1) = sin θ [1-2+ 2cos ^2 θ]/ cos θ (2 cos^2θ -1) = sin θ(2cos^2 θ -1)/ cos θ(2 cos ^2θ-1) = sin θ/ cos θ = tanθ

2.

yS0o -y s07O R ARGV uisz-yusपश्पा ग*०्य्त LT

Answer»

(sinθ- 2 sin^3θ)/(2cos^3θ-cosθ)

=sinθ(1-2sin^2θ)/cosθ(2cos^2 θ-1)

= sin θ [1- 2(1- cos^2 θ)/cos θ(2cos ^2 θ -1)

= sin θ [1-2+ 2cos ^2 θ]/ cos θ (2 cos^2θ -1)

= sin θ(2cos^2 θ -1)/ cos θ(2 cos ^2θ-1)

= sin θ/ cos θ

= tanθ

Discussion

3.	ⓒ Compare the(リ3.anel
Answer» 35/45 and 44/54=15/20 and 16/20=hence 16/20>15/20

Discussion

4.	4 सु e penie) BRE 2 0 QSR धन T
Answer» कालीबंगा राजस्थान के हनुमानगढ़ ज़िले में घग्घर नदी के बाएं तट पर स्थित है। खुदाई 1953 में 'बी.बी. लाल' एवं 'बी. के. थापड़' द्वारा करायी गयी। यहाँ पर प्राक् हड़प्पा एवं हड़प्पाकालीन संस्कृति के अवशेष मिले हैं। यह प्राचीन समय में चूडियों के लिए प्रसिद्ध था। ये चूडियाँ पत्‍थरों की बनी होती थी

Discussion

5.	12.8 cm28. From a cubical piece of wood of side 21 cm, a hemisphere is carved ouin such a way that the diameter of the hemisphere is equal to the side othe cubical piece. Find the surface area and volume of the remainingpiece.20 A
Answer» Cubical volume =212121=9261cm3cubical surface area =62121=2646cm2diameter = side of cubical piece radius =diameter/2r=21/2=10.5cmvolume of new side =10.510.510.5=1157.625cm3surface area of new side =610.510.5=661.5cm2 volume of remaining piece =9261-1157.625=8103.375cm2surface area remaining piece 2646-661.5=1984.5cm2

Discussion

6.	An article was purchased for Rs.1239 including GST of 18%. Find the price of the article before added the GST.
Answer» Cost with gst included = rupees 1239 Cost with out gst = x rupees gst = 18% If we take this into equation - x + ( ( 18 ÷ 100 ) × x ) = 1239 cost before gst + gst = cost with gst x + ( 9x ÷ 50 ) = 1239 ( 50x + 9x ) ÷ 50 = 1239 59x ÷ 50 = 1239 59x = 1239 × 50 59x = 61950 x = 61950 ÷ 59 x = 1050 Price before GST = 1050 rupees

6.

An article was purchased for Rs.1239 including GST of 18%. Find the price of the article before added the GST.

Answer»

Cost with gst included = rupees 1239

Cost with out gst = x rupees

gst = 18%

If we take this into equation -

x + ( ( 18 ÷ 100 ) × x ) = 1239

cost before gst + gst = cost with gst

x + ( 9x ÷ 50 ) = 1239

( 50x + 9x ) ÷ 50 = 1239

59x ÷ 50 = 1239

59x = 1239 × 50

59x = 61950

x = 61950 ÷ 59

x = 1050

Price before GST = 1050 rupees

Discussion

7.	EXERCISE 1B1. Represent each of the following numbers on the number line:(iii) 15
Answer» plz explain carefully

Discussion

8.	EXERCISE 1B1. Represent each of the following numbers on the number line:(iii) 1 -(iv) 2(v) 3(vi) 5(vii) 4(viii) 8
Answer» eska ans ky hoga

Discussion

9.	cimal7. Rahul attempted in of the total numberof questions in an examination. If of theanswers were wrong, what fraction of theattempted questions did he answer correctly?
Answer» He attempted 9/10100= 90 percentagequestionnowwrngt answers = 3/8100300/8= 150/4= 75/2= 37.5 percentageso remainin= 90-37.552.5 percentage he attempted right he attempted 9/10100=90percentagequestionnowwrngt answer=3/8100300/8=150/4=75/2=37.5percentageso remain=90-37.552.5percentage he attempted right

9.

cimal7. Rahul attempted in of the total numberof questions in an examination. If of theanswers were wrong, what fraction of theattempted questions did he answer correctly?

Answer»

He attempted 9/10*100= 90 percentagequestionnowwrngt answers = 3/8*100300/8= 150/4= 75/2= 37.5 percentageso remainin= 90-37.552.5 percentage he attempted right

he attempted 9/10*100=90percentagequestionnowwrngt answer=3/8*100300/8=150/4=75/2=37.5percentageso remain=90-37.552.5percentage he attempted right

Discussion

10.	51. 8963-5413-2869=?(1) 861 (2) 663(5) इनमें से कोई नहीं(3) 681(4) 654
Answer» 8963-5413-2869=8963-(5413+2869)=8963-8282=681Therefore option 3 is the correct answer. 8963-5413-2869= 8963-(5413+2869= 8963-8282=681c is correct

10.

51. 8963-5413-2869=?(1) 861 (2) 663(5) इनमें से कोई नहीं(3) 681(4) 654

Answer»

8963-5413-2869=8963-(5413+2869)=8963-8282=681Therefore option 3 is the correct answer.

8963-5413-2869= 8963-(5413+2869= 8963-8282=681c is correct

Discussion

11.	b61 The solution of differential equationdy-ex-y + x²e-Y isdx36813Y+C
Answer»

Discussion

12.	vatives so that the order of difterentiation is immaterial.10.Prove that dicurlA=0,i.ะต.,โฝ-(TXA)-2-Romhav 681
Answer» Part 1 Part 2

12.

vatives so that the order of difterentiation is immaterial.10.Prove that dicurlA=0,i.ะต.,โฝ-(TXA)-2-Romhav 681

Answer»

Part 1

Part 2

Discussion

13.	7. What is an earthquake?
Answer» Anearthquake(also known as aquake,tremorortemblor) is the shaking of the surface of the Earth, resulting from the sudden release of energy in theEarth'slithospherethat createsseismic waves. Earthquakes can range in size from those that are so weak that they cannot be felt to those violent enough to toss people around and destroy whole cities. Theseismicity, orseismic activity,of an area is the frequency, type and size of earthquakes experienced over a period of time. The wordtremoris also used fornon-earthquake seismic rumbling.

Discussion

14.	Which visual fraction model correctly shows the shaded region for theexpression?
Answer»

Discussion

15.	3Saran is 4 times as old as his bon.After 16 years, he will be twice as oldas his son find his son's present age.
Answer» let son age =x yearsfather age = 4x16 years after son age = x+16father age= 4x +16A/S4x+16=2(x+16)4x+16= 2x+324x-2x= 32 -162x= 16x= 16/2=8so son present age= 8 yearsfather present age= 4x= 4×8=32 years

Discussion

16.	Evaluate:cosec? (90° - 0) न tanzﬁ-o4(cos? 48° + cos? 42°)2 tan? 30°.sec* 52°.sin” 38sec? 70° — cot~ 20°
Answer»

Discussion

17.	42. If sin θ2x and x cos θ-2, 0°< θ < 90°, then the value of 2 \| x2 +-11 is :
Answer»

Discussion

18.	EXERCISE 8.1t.) The angles of quadrilateral are in the ratio 3 5: 9 13. Find all the angles ofquadrilateral.bon how tbat it is a rectang
Answer»

Discussion

19.	If 0 < S 90°, solve for 'e' wherecos? - 3 cos + 2 = 2 sin? O.A)60°B)45°C)90°D)30°
Answer» option C ) 90° is correct answer

Discussion

20.	(a)40(6)10(c)9044. यदि 3:436 :: है, तो . का क्या मान होगा -
Answer» x= 8 is the correct answer of the given question 3/4=6/x3x=6×43x=24x=8 3/4=6/x3x=6×43x=24x=8answer correct answer for this question is 8 8 is correct answer. Q - 3 : 4 = 6 : x 3 /4 = 6 / x 3x =24 x = 8

20.

(a)40(6)10(c)9044. यदि 3:436 :: है, तो . का क्या मान होगा -

Answer»

x= 8 is the correct answer of the given question

3/4=6/x3x=6×43x=24x=8

3/4=6/x3x=6×43x=24x=8answer

correct answer for this question is 8

8 is correct answer.

Q - 3 : 4 = 6 : x 3 /4 = 6 / x 3x =24 x = 8

Discussion

21.	Evaluate \frac{\sec 17^{0}}{\csc 73^{0}}+\frac{4}{3} \tan ^{2} 60^{\circ}+\cos ^{2} 44^{\circ}+\cos ^{2} 46-8 \cos ^{3} 60^{\circ}
Answer»

Discussion

22.	(3) 60(4)9015. सदिश A तथा B इस प्रकार हैं कि A + B = \|A-B सदिशA तथा B के मध्य कोण होगा -[RPMT 1999, AIPMT 2006](1) 90 (2) 60 (3) 75 (4) 45
Answer» 90°square of both side we will get cos theta= 0 means angle 90 90° will be the best ans 4:(45)is the correct answer. 45 is the correct answer 45 is correct option 45 is correct answer 45 is the right answer

22.

(3) 60(4)9015. सदिश A तथा B इस प्रकार हैं कि A + B = |A-B सदिशA तथा B के मध्य कोण होगा -[RPMT 1999, AIPMT 2006](1) 90 (2) 60 (3) 75 (4) 45

Answer»

90°square of both side we will get cos theta= 0 means angle 90

90° will be the best ans

4:(45)is the correct answer.

45 is the correct answer

45 is correct option

45 is correct answer

45 is the right answer

Discussion

23.	A box contains 90 disc, numbered from 2 to 90. If one disc is drawn at random from the box, the probability that it bears a prime number less than 23 is
Answer» The given box contains disc numbered as 1 to 90. The number of elements in the sample space is n(S) = 90.The prime numbers less than 23 are 2, 3, 5, 7, 11, 13, 17, 19So there are 8 prime numbers. If E denotes the set of these prime numbers then n(E) = 8Therefore probability of getting a prime number less than 23= n(E)/n(S) = 8/90 =4/45

Discussion

24.	hox contains 90 dises which are numbered from I to 90. If one disc is drawn at randomthe box, find the probability that it bears (i) a two-digit number (ii) a perfecquare number (ii) a number divisible by 5
Answer»

Discussion

25.	\begin{array}{l}{\frac{4 \sin ^{2} 60+\sec ^{2} 60+4 \sin ^{2} 45+3 \cos ^{2} 90}{\sec 60+\cos \operatorname{ec} 30^{\circ}-\sin 90}} \\ {\text { (a) } 0}\end{array}
Answer» sin60=√3/2 sec60=2 sin45=1/√2 cos90=0cosec30=2 sin90=1put in equation43/4+4+4/2+30/2+2-13+4+2/4-19/3=3

Discussion

26.	A box contains 90 discs ,numbered from 1 to 90.If one disc is drawn at random from the box,find the probability that it bears a prime number less than 23.
Answer»

Discussion

27.	cost of 5 wristwatches of the same type is6250. What is the cost of 16 such wristwatches?Solution:
Answer» 5 are of 6250 so 16 are of 6250×16/5 = 20000 Rs.

Discussion

28.	A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at randomfrom the box, find the probability that it bears () a two-digit number (i) a perfectsquare number (ii) a number divisible by 5.18.
Answer»

Discussion

29.	市刌市可Tat
Answer»

Discussion

30.	factorise by the following.ů) a3_63+ gab tat
Answer»

Discussion

31.	77す礻肖き9528.1282, Tat'at
Answer» wrong

Discussion

32.	Isimplity = 55 +13Egr-Sn-tat
Answer»

Discussion

33.	न शभलैसक- ७ Sec = 0Fhoiapyoke tat bew = P+ L
Answer»

Discussion

34.	5. Find three rational numbers between - 2 and - 1.TAT.
Answer» -25/15, - 15/15-10/5, - 5/5Three rational numbers between - 2and -1 are-6/5, - 7/5, - 8/5

Discussion

35.	가나 largest- Syaane that Canchiawncliam etrrLe.nt tんe whe tat
Answer»

Discussion

36.	рди \| 2NN= =
Answer» x + 2 7-------- = ------x - 2 3 3( x + 2) = 7 ( x - 2) 3x + 6 = 7x - 14 7x - 3x = 20 4x = 20 x = 5 Thanks

36.

рди | 2NN= =

Answer»

x + 2 7-------- = ------x - 2 3

3( x + 2) = 7 ( x - 2)

3x + 6 = 7x - 14

7x - 3x = 20

4x = 20

x = 5

Thanks

Discussion

37.	कि हजNNi~
Answer»

Discussion

38.	that the drawn card is(1)neitherĂkinghĂśraqueet()redqueelCalu10. A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box.find the probability that it bears () a prime-number less than 23 (i) a perfect square number.
Answer» Total Numbers=90No. of prime numbers less than 23=8 (2,3,5,7,11,13,17,19)(i)Probability=8/90=4/45No. of perfect square numbers=9(1,4,9,16,25,36,49,64,81)(ii) Probability=9/90=1/10

Discussion

39.	Deduct 2 from 7and Add 1to it.Answer will be
Answer» deduction of 2 from 7 = 7-2 = 5 addition of 1 to it= 5+1 = 66 will be the answer.

39.

Deduct 2 from 7and Add 1to it.Answer will be

Answer»

deduction of 2 from 7 = 7-2 = 5

addition of 1 to it= 5+1 = 66 will be the answer.

Discussion

40.	!! ĐąŃ The-ratio of the present ages of Abha and her: 5. At the time of Abha's birth, heronsmother is 2ber mothers age was 27 years. Find the present ages ofrseAbha and her mother.
Answer» Let the present age of Abha be x yearsHence the age of her mother is x + 27 years. Given: x/(x + 27) = 2/5 5x = 2 (x + 27) 5x = 2x + 54 3x = 54 x = 18 years Answer - The present age of Abha is 18 years and her mother's age is (18 + 27 = 45 years)

40.

!! ĐąŃ The-ratio of the present ages of Abha and her: 5. At the time of Abha's birth, heronsmother is 2ber mothers age was 27 years. Find the present ages ofrseAbha and her mother.

Answer»

Let the present age of Abha be x yearsHence the age of her mother is x + 27 years.

Given:

x/(x + 27) = 2/5

5x = 2 (x + 27)

5x = 2x + 54

3x = 54

x = 18 years

Answer - The present age of Abha is 18 years and her mother's age is (18 + 27 = 45 years)

Discussion

41.	a right triangle has hypotenuse of length p cm and one side of length q cm. if p-q=1, find the length of the third side of the triangle
Answer»

Discussion

42.	Fimel the enton and correct the Satament axb=, \|asb are the multiples of where as cia the factorof a and be
Answer» axb=c//c-a=b;;c-b=a. yes it the correct answer is ab=c//c-a=b::c=a acb=c//c-a=b;;c-b=a is anwer ab=c//c-a=b::c=a is the correct answer a*b=c//c-a=b::c=a is the answer of the following axb=c-a=b;c-b=a. is the correct answer

42.

Fimel the enton and correct the Satament axb=, |asb are the multiples of where as cia the factorof a and be

Answer»

axb=c//c-a=b;;c-b=a.

yes it the correct answer is a*b=c//c-a=b::c=a

acb=c//c-a=b;;c-b=a is anwer

a*b=c//c-a=b::c=a is the correct answer

a*b=c//c-a=b::c=a is the answer of the following

axb=c-a=b;c-b=a. is the correct answer

Discussion

43.	— (Al(A1) ०0६ ०9800 + ,0¢ 205पा= (m
Answer» Like my answer if you find it useful!

Discussion

44.	find the AP 7,13,19,.......205
Answer» FindAP 18,15_1/2,13,. ....,-47

Discussion

45.	The sum of the ages of a mother and a daughter is 50years. Also, 5 years ago, the mother's age was 7 timesthe age of the daughter. The present ages of the motherand the daughter respectively are:
Answer» The age of mother is 40 and daughter is 10

Discussion

46.	From a point Q. the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is
Answer»

Discussion

47.	a point Q, the length of the tangent to a circle is 24 cm and the distance of Q froncentre is 25 cm. The radius of the circle is
Answer»

Discussion

48.	1. From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q fromthe centre is 25 cm. The radius of the circle is
Answer»

Discussion

49.	From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q fromthe centre is 25 cm. The radius of the circle is
Answer»

Discussion

50.	The present age of girl is two fifth the age ofher father.' Express the above statement as alinear equation in two variables. Also find:(a) the age of the girl when father is 40years.(b) the age of the father when the girl is 22(CBSE 2012)years.
Answer» Thnk u

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The angle of elevation of cloud from point ‘h’ m above surface of lake is θ and the angle of depression of its reflection in lake is ɸ. Prove that height of cloud from lake is h[(tanɸ + tanθ)/(tanɸ-tanθ)]

yS0o -y s07O R ARGV uisz-yusपश्पा ग*०्य्त LT

ⓒ Compare the(リ3.anel

4 सु e penie) BRE 2 0 QSR धन T

12.8 cm28. From a cubical piece of wood of side 21 cm, a hemisphere is carved ouin such a way that the diameter of the hemisphere is equal to the side othe cubical piece. Find the surface area and volume of the remainingpiece.20 A

An article was purchased for Rs.1239 including GST of 18%. Find the price of the article before added the GST.

EXERCISE 1B1. Represent each of the following numbers on the number line:(iii) 15

EXERCISE 1B1. Represent each of the following numbers on the number line:(iii) 1 -(iv) 2(v) 3(vi) 5(vii) 4(viii) 8

cimal7. Rahul attempted in of the total numberof questions in an examination. If of theanswers were wrong, what fraction of theattempted questions did he answer correctly?

51. 8963-5413-2869=?(1) 861 (2) 663(5) इनमें से कोई नहीं(3) 681(4) 654

b61 The solution of differential equationdy-ex-y + x²e-Y isdx36813Y+C

vatives so that the order of difterentiation is immaterial.10.Prove that dicurlA=0,i.ะต.,โฝ-(TXA)-2-Romhav 681

7. What is an earthquake?

Which visual fraction model correctly shows the shaded region for theexpression?

3Saran is 4 times as old as his bon.After 16 years, he will be twice as oldas his son find his son's present age.

Evaluate:cosec? (90° - 0) न tanzﬁ-o4(cos? 48° + cos? 42°)2 tan? 30°.sec* 52°.sin” 38sec? 70° — cot~ 20°

42. If sin θ2x and x cos θ-2, 0°&lt; θ &lt; 90°, then the value of 2 | x2 +-11 is :

EXERCISE 8.1t.) The angles of quadrilateral are in the ratio 3 5: 9 13. Find all the angles ofquadrilateral.bon how tbat it is a rectang

If 0 &lt; S 90°, solve for 'e' wherecos? - 3 cos + 2 = 2 sin? O.A)60°B)45°C)90°D)30°

(a)40(6)10(c)9044. यदि 3:436 :: है, तो . का क्या मान होगा -

Evaluate \frac{\sec 17^{0}}{\csc 73^{0}}+\frac{4}{3} \tan ^{2} 60^{\circ}+\cos ^{2} 44^{\circ}+\cos ^{2} 46-8 \cos ^{3} 60^{\circ}

(3) 60(4)9015. सदिश A तथा B इस प्रकार हैं कि A + B = |A-B सदिशA तथा B के मध्य कोण होगा -[RPMT 1999, AIPMT 2006](1) 90 (2) 60 (3) 75 (4) 45

A box contains 90 disc, numbered from 2 to 90. If one disc is drawn at random from the box, the probability that it bears a prime number less than 23 is

hox contains 90 dises which are numbered from I to 90. If one disc is drawn at randomthe box, find the probability that it bears (i) a two-digit number (ii) a perfecquare number (ii) a number divisible by 5

\begin{array}{l}{\frac{4 \sin ^{2} 60+\sec ^{2} 60+4 \sin ^{2} 45+3 \cos ^{2} 90}{\sec 60+\cos \operatorname{ec} 30^{\circ}-\sin 90}} \\ {\text { (a) } 0}\end{array}

A box contains 90 discs ,numbered from 1 to 90.If one disc is drawn at random from the box,find the probability that it bears a prime number less than 23.

cost of 5 wristwatches of the same type is6250. What is the cost of 16 such wristwatches?Solution:

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at randomfrom the box, find the probability that it bears () a two-digit number (i) a perfectsquare number (ii) a number divisible by 5.18.

市刌市可Tat

factorise by the following.ů) a3_63+ gab tat

77す礻肖き9528.1282, Tat'at

Isimplity = 55 +13Egr-Sn-tat

न शभलैसक- ७ Sec = 0Fhoiapyoke tat bew = P+ L

5. Find three rational numbers between - 2 and - 1.TAT.

가나 largest- Syaane that Canchiawncliam etrrLe.nt tんe whe tat

рди | 2NN= =

कि हजNNi~

that the drawn card is(1)neitherĂkinghĂśraqueet()redqueelCalu10. A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box.find the probability that it bears () a prime-number less than 23 (i) a perfect square number.

Deduct 2 from 7and Add 1to it.Answer will be

!! ĐąŃ The-ratio of the present ages of Abha and her: 5. At the time of Abha's birth, heronsmother is 2ber mothers age was 27 years. Find the present ages ofrseAbha and her mother.

a right triangle has hypotenuse of length p cm and one side of length q cm. if p-q=1, find the length of the third side of the triangle

Fimel the enton and correct the Satament axb=, |asb are the multiples of where as cia the factorof a and be

— (Al(A1) ०0६ ०9800 + ,0¢ 205पा= (m

find the AP 7,13,19,.......205

The sum of the ages of a mother and a daughter is 50years. Also, 5 years ago, the mother's age was 7 timesthe age of the daughter. The present ages of the motherand the daughter respectively are:

From a point Q. the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is

a point Q, the length of the tangent to a circle is 24 cm and the distance of Q froncentre is 25 cm. The radius of the circle is

1. From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q fromthe centre is 25 cm. The radius of the circle is

From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q fromthe centre is 25 cm. The radius of the circle is

The present age of girl is two fifth the age ofher father.' Express the above statement as alinear equation in two variables. Also find:(a) the age of the girl when father is 40years.(b) the age of the father when the girl is 22(CBSE 2012)years.

vatives so that the order of difterentiation is immaterial.10.Prove that dicurlA=0,i.ะต.,โฝ-(TXA)-2-Romhav 681

42. If sin θ2x and x cos θ-2, 0°< θ < 90°, then the value of 2 | x2 +-11 is :

If 0 < S 90°, solve for 'e' wherecos? - 3 cos + 2 = 2 sin? O.A)60°B)45°C)90°D)30°

!! ĐąŃ The-ratio of the present ages of Abha and her: 5. At the time of Abha's birth, heronsmother is 2ber mothers age was 27 years. Find the present ages ofrseAbha and her mother.