81279 + Interview Questions in Mathematics QA in Mathematics

1.	1a. There are three events A, B, C one of which must happen and only one can happen ata time. If the odds are 8 to 3 against A, 5 to 2 against B; find the odds against C.
Answer»

Discussion

2.	nd her loss percentage.n buys Diwali cards at850 per 100 cards and sells then at? 136 a 1mand his gain per cent.
Answer» Rs of one card 850/100=8.5RsRs of 10 cards = 108.5=85RsProfit Rs = 136-85=51Rsprofit of 100 cards = 5110 = 510gain percent = 510/850*100 = 60 %

Discussion

3.	The dimensions of a rectangular box are in the ratio of 2: 3:4 and the difference between the costof covering it with a cloth at the rate of 10 and ? 11 per mbox13.isă1,300. Find the dimensions of thend 1 5 m deen is to be tiled. If each tile is
Answer» Let common multiple of 2:3:4 be x=> Breadth = 2x=> Length = 3x=> Height = 4x Surface area = 2(2x3x + 3x4x + 4x2x) = 2(6x²+12x²+8x²) = 52x² cm² As per question,=> Rs. [11(52x²)-10(52x²)] = Rs. 1300=> 1(52x²) = 1300=> x² = 1300/52 = 25=> x =5length= 25= 10cmbreadth= 35= 15height = 45= 20

3.

The dimensions of a rectangular box are in the ratio of 2: 3:4 and the difference between the costof covering it with a cloth at the rate of 10 and ? 11 per mbox13.isă1,300. Find the dimensions of thend 1 5 m deen is to be tiled. If each tile is

Answer»

Let common multiple of 2:3:4 be x=> Breadth = 2x=> Length = 3x=> Height = 4x

Surface area = 2(2x*3x + 3x*4x + 4x*2x) = 2(6x²+12x²+8x²) = 52x² cm²

As per question,=> Rs. [11(52x²)-10(52x²)] = Rs. 1300=> 1(52x²) = 1300=> x² = 1300/52 = 25=> x =5length= 2*5= 10cmbreadth= 3*5= 15height = 4*5= 20

Discussion

4.	kg of rice at t 36 per kg and 25 kg of rice at 32 per kg. He mixed the twond sold the mixture at 38 per kg. FInd his gain per cent in the wholetransaction
Answer» Cost of 1kg rice = ₹36Cost of 20kg rice = ₹36 × 20 = ₹720 Cost of 1kg rice = ₹32Cost of 25kg rice = ₹32 × 25 = ₹800 Total weight = 45kg Total cost = ₹1520Selling price of 45kg rice = ₹38 × 45 = ₹1710 Gain = 1710 - 1520 = 190 Gain% = (190/1520) × 100 = 12.5%

Discussion

5.	ed for348000, its value depreciates at 10% per annum during the first year andA car is purchasat 20% per annum during the second year.9.What will be its value after 2 years?
Answer»

Discussion

6.	Identify the mode of nutrition where sunlight is used along withCO2 and water to prepare food
Answer» The mode of nutrition here is autotrophic nutrition and this type of autotrophic nutrition is photoautotrophs which undergo photosynthesis

Discussion

7.	2. Additive inverse of - 3 - 4i is(a) - 3+4i,(b) +3+4i.(c) 3+4i.(d) +3-4i.
Answer» c is the correct ans explanation : additive inverse is the no. which on adding gives 0 for eg : additive inverse of -5 is 5 as -5+5 would give 0 now in this case 3+4i on addition with -3-4i would 0 hope u understood

Discussion

8.	\frac \frac 53 2 \times 26.5 \times \frac 106 4 - \frac 33 2 \times \frac 66 4 \times 16.5 \frac 53 2 \times \frac 106 4 %2B \frac 106 4 \times 16.5 %2B \frac 66 4 \times 16.5
Answer» 1st one ans is 91101.656 2nd one answer is 14025.129

8.

\frac \frac 53 2 \times 26.5 \times \frac 106 4 - \frac 33 2 \times \frac 66 4 \times 16.5 \frac 53 2 \times \frac 106 4 %2B \frac 106 4 \times 16.5 %2B \frac 66 4 \times 16.5

Answer»

1st one ans is 91101.656

2nd one answer is 14025.129

Discussion

9.	A ball falls vertically after being dropped.The ball falls a distance d metres in a time of t seconds.d is directly proportional to the square of tThe ball falls 20 metres in a time of 2 seconds.a)Find a formula for d in terms of t.
Answer» d is proportional to the square of tSo we can write: (1) . . d = K * t^2 . . where K is some constant. At the moment we don't know the value of this constant. But we do know that the ball has fallen 20 metres after 2 seconds. This info will give us the value of K. Substituting d=20 and t=2 into equation (1), we get 20 = K * 2^220 = K * 4K = 5 So, using the value 5 for K, equation (1) becomes: d = 5t^2 . . (d in metres, t in seconds) This is the formula for d in terms of t

9.

A ball falls vertically after being dropped.The ball falls a distance d metres in a time of t seconds.d is directly proportional to the square of tThe ball falls 20 metres in a time of 2 seconds.a)Find a formula for d in terms of t.

Answer»

d is proportional to the square of tSo we can write:

(1) . . d = K * t^2 . . where K is some constant.

At the moment we don't know the value of this constant. But we do know that the ball has fallen 20 metres after 2 seconds. This info will give us the value of K.

Substituting d=20 and t=2 into equation (1), we get

20 = K * 2^220 = K * 4K = 5

So, using the value 5 for K, equation (1) becomes:

d = 5t^2 . . (d in metres, t in seconds)

This is the formula for d in terms of t

Discussion

10.	1 \times 2 + 2 \times 3 + 3 \times 4 + 4 \times 5 +
Answer»

Discussion

11.	\frac { 4 ^ { n + 4 } - 5 \times 4 ^ { n + 2 } } / { 4 ^ { n + 1 } times 11 }
Answer»

Discussion

12.	Directions (Q. Nos. 24-25) If f(-x) = -f(x), then f(x) isf(x) is evenodd function and if f(-x) = f(x), thenfunction.2[f(x), if f (x) is evenAlso, I flo) dx=112f(x), if f (x) is odd- The value of the integral, sinâx dx is(d) 1-TC(a) o(b)cC/2
Answer» By integral value I understand that you are asking the geometrical meaning of an integral of a function. values in the integer are integral value. Like1,2,3 ,4,5etc are integer values. The Anti Derivative of any function/Number/Variable is it's Integral value.

Discussion

13.	f(I)+f(3) + f(x)f(21+f(-) + f(l/2)32=35, then x =2x-1, if x>1If f(x)=Ä°x2 +1, ifand if-1x1
Answer»

Discussion

14.	Let f be differentiable for all x, if f (1) =-2 and f' (x)2 2 for all x e [1,6], then(A) f (6) < 8(C) f (6)·25(B) f (6) 2 8(D) f (6) s5
Answer» Hence, option (B) is correct.

Discussion

15.	There are 12 boys and 6 girls in how many ways A commity of 5 can be form. Such that it is contain 2 boys and 3 girls
Answer»

Discussion

16.	There are 12 boys and 6 girls in how many ways A committee of 5 can be form. Such that it is contain 2 boys and 3 girls
Answer» 12C2 × 6C3 = 12×11/2 × 6×5×4/3×2 = 6×11×5×4 = 120×11 = 1320

Discussion

17.	\left(x^{3}+4 x^{2}+16 x+61\right) \div(x-4)
Answer» xxx-4xx+8xx-32x+48x-192+131 =xx(x-4)+8x(x-4)+48(x-4)+131 =(xx+8x+48)(x-4)+131 so q=x*x+8x+48 reminder = 131

Discussion

18.	4. 5, 6, 16, 2, 244, 1245(A) 28 (B) 55 (C) 57 (D) 61 (E) ofthese
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Discussion

19.	8.Given below are the marks of 7 studentsin a science test.6, 7, 8,7,9,9,10Use the data to answer the following questions.A. What is the range of the data?B. Find the mean of the marks obtained by the7 students.
Answer» Writing the numbers in increasing order 6,7,7,8,9,9,10 A. Range : 6-10 B. Mean = 6+7+7+8+9+9+10/7 = 56/7 = 8 Like my answer if you find it useful!

19.

8.Given below are the marks of 7 studentsin a science test.6, 7, 8,7,9,9,10Use the data to answer the following questions.A. What is the range of the data?B. Find the mean of the marks obtained by the7 students.

Answer»

Writing the numbers in increasing order

6,7,7,8,9,9,10

A. Range : 6-10

B. Mean = 6+7+7+8+9+9+10/7

= 56/7

= 8

Like my answer if you find it useful!

Discussion

20.	a = \frac { 1 } { 2 + \sqrt { 3 } } \text { and } b = \frac { 1 } { 2 - \sqrt { 3 } } \text { then the value of } 2 a ^ { 2 } + 3 a b - 2 b ^ { 2 }
Answer»

Discussion

21.	(i) In how many ways can 6 boys and 4 girls be seated in a round tableso that two girls never be seated together.
Answer» Let us treat two girls as a single entity(for sake of ‘togetherness’) Now these two girls can be selected from 4 girls in 4c2 ways. Now,total no of members =6 boys+3 girls (2 girls has been counted as one). We know that n members can be seated in a circle in (n-1)! Ways. So 9 members can be seated in 8! Ways. And the two girls who were treated as one could exchange their position in 2! Ways. So total no of ways so that 2 girls be seated together= [(8!×2!×4c2)] So,required answer is 9!-(8!×2!×4c2)

21.

(i) In how many ways can 6 boys and 4 girls be seated in a round tableso that two girls never be seated together.

Answer»

Let us treat two girls as a single entity(for sake of ‘togetherness’)

Now these two girls can be selected from 4 girls in 4c2 ways.

Now,total no of members =6 boys+3 girls (2 girls has been counted as one).

We know that n members can be seated in a circle in (n-1)! Ways.

So 9 members can be seated in 8! Ways.

And the two girls who were treated as one could exchange their position in 2! Ways.

So total no of ways so that 2 girls be seated together= [(8!×2!×4c2)]

So,required answer is 9!-(8!×2!×4c2)

Discussion

22.	n(S)1113. 6 boys and 6 girls sit in a row randomly, find the probabilityEx.t all the 6 girls sit together.
Answer»

Discussion

23.	Example 14. In how many ways 8 boys and 6 girls can be arranged in a row sothat no two girls are together?[R.G.T.U. 2007
Answer» One boys one girlb- g-b-g-b-g-b-g-b-g-b-g two boys then one boy one girl b-b-g-b-g-b-g-b-g-b-g-b-g-b one boys one girl b-g b-g one boys one girlb- g b- g

23.

Example 14. In how many ways 8 boys and 6 girls can be arranged in a row sothat no two girls are together?[R.G.T.U. 2007

Answer»

One boys one girlb- g-b-g-b-g-b-g-b-g-b-g

two boys then one boy one girl b-b-g-b-g-b-g-b-g-b-g-b-g-b

one boys one girl b-g b-g

one boys one girlb- g b- g

Discussion

24.	allsEx. 13. 6 boys and 6 girls sit in a row randomly, find the probability[L. I. T.79]that all the 6 girls sit together.
Answer»

Discussion

25.	Find the actual lower class limits, upper classlimits and the mid-values of the classes10- 19, 20 - 29, 30-39 and 40 - 49.
Answer»

Discussion

26.	Find the sum of the lower limit of the median class and the upper limit of the modalclass :Classes10-2020--3030-4040-5060 - 7050-60I 7FrequencyI 519
Answer»

Discussion

27.	(1) UUUUUU2If 4x+i (3x-y) = 3+i(-6), where x and y are real numbers, then find the values of xand y.Seatt
Answer» By comparison😊 we compare the real part and the imaginary parts so we got this value 4x= 3 so x= 3/43x-y= -63(3/4)-y= -69/4+6= y33/4= y thanks

27.

(1) UUUUUU2If 4x+i (3x-y) = 3+i(-6), where x and y are real numbers, then find the values of xand y.Seatt

Answer»

By comparison😊

we compare the real part and the imaginary parts so we got this value

4x= 3 so x= 3/43x-y= -63(3/4)-y= -69/4+6= y33/4= y

thanks

Discussion

28.	14, k का मान ज्ञात कीजिए यदि बिन्दुk, 2-2 k ),(-k+1,2 k) तथा(-4-k, 6-2 k)संरेख हैं।
Answer»

Discussion

29.	owiing qlestions: (Any One)04From the top of a lighthouse, 100 m above sea level, the angle of depression of aship, sailing towards it, changes from 30 to 450. Determine the distance trathe ship during the period of observation.i)velled by
Answer»

Discussion

30.	26. A ship sails out to an island at the rate of 15 km/hr and sails back to thestarting point at 10 km/hr. Find the average sailing speed for the wholejourney
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Discussion

31.	Exam. 15.01.2017) (IInd Sitting)43. Three Science classes A, B andC take a Life Science test. Theaverage score of class A is 83.The average score of class B is76. The average score of class Cis 85. The average score of classA and B is 79 and average scoreof class B and C is 81. Then theaverage score of classes A, B andC is
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Discussion

32.	The points A(1,-2), B(2,3), C (k,2) and D(-4,-3) are the vertices of a parallelogram. Findthe value of k.ORFind the value of k for which the points (3k-1,k-2), (k,k-7) and (k-1,-k-2) are collinear
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Discussion

33.	r,s and t are real numbers and r v s, then show that the roots of the equation(r-s)x2+7r+ s)x-3(r-s)-0 are real and unequal.
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Discussion

34.	30. Find the value (s) of k for which the points (3k -1,k-2),(k, k -7) and (k -1,-k-2)CBSE 2014]are collinear
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Discussion

35.	3 2i7 +4iFind real numbers A and B, if A + iB
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Discussion

36.	43)If sin Î¸ =, then find cose
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Discussion

37.	Find the distance between the points (a cos θ, a sin e) and (-a sin θ, a cose).
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Discussion

38.	2 keagecR) â ((atBLeed) =P st R (aBecAr 20 2)
Answer» LHS = (tanA + cosecB)^2 - (cotB-secA)^2 = (tan^2A + 2tanAcosecB + cosec^2B) - (cot^2B - 2cotBsecA + sec^2A) = tan^2A + cosec^2B + 2tanAcosecB - cot^2B - sec^2A + 2cotBsecA Substituting (tan^2A = sec^2A - 1) and (cosec^2B = 1 + cot^2B) in the above step: (sec^2A - 1) + (1 + cot^2B) + 2tanAcosecB - cot^2B - sec^2A + 2cotBsecA = 2tanAcosecB + 2cotBsecA = 2(tanAcosecB + cotBsecA) RHS = 2tanAcotB(cosecA + secB) = 2tanAcotB((1 / sinA) + (1 / cosB)) = 2(tanA / sinA)cotB + 2tanA(cot B / cosB) = 2(sinA / (cosAsinB))cotB + 2tanA(cosB / (sinBcosB)) = 2(1 / cosA)cotB + 2 tanA(1 / sinB) = 2secAcotB + 2tanAcosecB = 2(secAcotB + tanAcosecB)

38.

2 keagecR) â ((atBLeed) =P st R (aBecAr 20 2)

Answer»

LHS = (tanA + cosecB)^2 - (cotB-secA)^2 = (tan^2A + 2tanAcosecB + cosec^2B) - (cot^2B - 2cotBsecA + sec^2A) = tan^2A + cosec^2B + 2tanAcosecB - cot^2B - sec^2A + 2cotBsecA

Substituting (tan^2A = sec^2A - 1) and (cosec^2B = 1 + cot^2B) in the above step: (sec^2A - 1) + (1 + cot^2B) + 2tanAcosecB - cot^2B - sec^2A + 2cotBsecA = 2tanAcosecB + 2cotBsecA = 2(tanAcosecB + cotBsecA)

RHS = 2tanAcotB(cosecA + secB) = 2tanAcotB((1 / sinA) + (1 / cosB)) = 2(tanA / sinA)cotB + 2tanA(cot B / cosB) = 2(sinA / (cosAsinB))cotB + 2tanA(cosB / (sinBcosB)) = 2(1 / cosA)cotB + 2 tanA(1 / sinB) = 2secAcotB + 2tanAcosecB = 2(secAcotB + tanAcosecB)

Discussion

39.	6. If a- cose + i sin e, then find the value of(1- a)
Answer»

Discussion

40.	For any two vecioShow that the points A(-2i +3j +5k), B(i+2j +3 k) and C (7i k)are collinear.
Answer»

Discussion

41.	6, Find real numbers x and y if (x-iy) (3+5i) is the conjugate of-6-24i.
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Discussion

42.	: REAL NUMBERS:1.The LCM of two numbers is 760 and their product is 6080. Find their HCFd LcE of hers to he 378 and 18 respectively?
Answer» LCM*HCF=product of two numbershenceHCF=6080/760=8hence HCF is 8

Discussion

43.	. As observed from top of light house, 100m high above the sea levdepression of a ship sailing directly towards it, changes from 30 to 60distance travelled by the ship during the period of observation.ind the
Answer» thank you

Discussion

44.	Q22. From the top of a vertical tower, the angles of depression of two cars, in thesame straight line with the base of the tower at an instant are found to be 30° and60°. If the cars are 100m apart and are on the same side of the tower, find theheight of the tower.
Answer»

Discussion

45.	Real NumbersV Find the HF of 13.5 and 345 wing Euclid'sdivision lemma.
Answer» By using Euclid's division algorithm, Since 345 > 135, we've to divide 345 by 135. By usingEuclid's division lemma, 345 = 135 * 2 + 75 Since, r ≠ 0, we've to divide 135 by 75 to get, By usingEuclid's division lemma, 135 = 75 * 1 + 60 Since r ≠ 0, we've to divide 75 by 60 to get, By usingEuclid's division lemma, 75 = 60 * 1 + 15 Since, r ≠ 0, we've to divide 60 by 15 to get, By usingEuclid's division lemma, 60 = 15 * 4 + 0 Since, r = 0, the divisor of the last step will be the divisor of the given two numbers. Therefore, 15 is the HCF of 135 and 345.

45.

Real NumbersV Find the HF of 13.5 and 345 wing Euclid'sdivision lemma.

Answer»

By using Euclid's division algorithm,

Since 345 > 135, we've to divide 345 by 135.

By usingEuclid's division lemma,

345 = 135 * 2 + 75

Since, r ≠ 0, we've to divide 135 by 75 to get,

By usingEuclid's division lemma,

135 = 75 * 1 + 60

Since r ≠ 0, we've to divide 75 by 60 to get,

By usingEuclid's division lemma,

75 = 60 * 1 + 15

Since, r ≠ 0, we've to divide 60 by 15 to get,

By usingEuclid's division lemma,

60 = 15 * 4 + 0

Since, r = 0, the divisor of the last step will be the divisor of the given two numbers.

Therefore, 15 is the HCF of 135 and 345.

Discussion

46.	3 \times 8+6 \times 11+9 \times 14+\ldots
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Discussion

47.	\frac { 3 \times 7 \times 11 ^ { 8 } } { 21 \times 11 ^ { 3 } }
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Discussion

48.	118/517 (Basement), Kaushalpuri, NealIn the given figure. ABCD is a quadrilateral. A line through D, parallel to AC, MeetsProduced in PProve that: ar (A ABC)- ar (quad. ABCD)
Answer» There is something wrong in the question. In the given figure triangle ABC is a part of quadrilateral. So area of ∆ABC will always be less than area of quadrilateral ABCD.

48.

118/517 (Basement), Kaushalpuri, NealIn the given figure. ABCD is a quadrilateral. A line through D, parallel to AC, MeetsProduced in PProve that: ar (A ABC)- ar (quad. ABCD)

Answer»

There is something wrong in the question.

In the given figure triangle ABC is a part of quadrilateral.

So area of ∆ABC will always be less than area of quadrilateral ABCD.

Discussion

49.	\frac { 3 \times 7 ^ { 2 } \times 11 ^ { 8 } } { 21 \times 11 ^ { 3 } }
Answer» 3×7^2×11^8/21×11^33×7^2×11^8=3.15×10^1021×11^3=279513×7^2×11^8/21×11^3=3.15×10^10/27951=1126972.201=1.126×10^6

Discussion

50.	If cosec O=18+! FindBo Sin Ox cose
Answer»

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

1a. There are three events A, B, C one of which must happen and only one can happen ata time. If the odds are 8 to 3 against A, 5 to 2 against B; find the odds against C.

nd her loss percentage.n buys Diwali cards at850 per 100 cards and sells then at? 136 a 1mand his gain per cent.

The dimensions of a rectangular box are in the ratio of 2: 3:4 and the difference between the costof covering it with a cloth at the rate of 10 and ? 11 per mbox13.isă1,300. Find the dimensions of thend 1 5 m deen is to be tiled. If each tile is

kg of rice at t 36 per kg and 25 kg of rice at 32 per kg. He mixed the twond sold the mixture at 38 per kg. FInd his gain per cent in the wholetransaction

ed for348000, its value depreciates at 10% per annum during the first year andA car is purchasat 20% per annum during the second year.9.What will be its value after 2 years?

Identify the mode of nutrition where sunlight is used along withCO2 and water to prepare food

2. Additive inverse of - 3 - 4i is(a) - 3+4i,(b) +3+4i.(c) 3+4i.(d) +3-4i.

\frac \frac 53 2 \times 26.5 \times \frac 106 4 - \frac 33 2 \times \frac 66 4 \times 16.5 \frac 53 2 \times \frac 106 4 %2B \frac 106 4 \times 16.5 %2B \frac 66 4 \times 16.5

A ball falls vertically after being dropped.The ball falls a distance d metres in a time of t seconds.d is directly proportional to the square of tThe ball falls 20 metres in a time of 2 seconds.a)Find a formula for d in terms of t.

1 \times 2 + 2 \times 3 + 3 \times 4 + 4 \times 5 +

\frac { 4 ^ { n + 4 } - 5 \times 4 ^ { n + 2 } } / { 4 ^ { n + 1 } times 11 }

Directions (Q. Nos. 24-25) If f(-x) = -f(x), then f(x) isf(x) is evenodd function and if f(-x) = f(x), thenfunction.2[*f(x), if f (x) is evenAlso, I flo) dx=112*f(x), if f (x) is odd- The value of the integral, sinâx dx is(d) 1-TC(a) o(b)cC/2

f(I)+f(3) + f(x)f(21+f(-) + f(l/2)32=35, then x =2x-1, if x&gt;1If f(x)=Ä°x2 +1, ifand if-1x1

Let f be differentiable for all x, if f (1) =-2 and f' (x)2 2 for all x e [1,6], then(A) f (6) &lt; 8(C) f (6)·25(B) f (6) 2 8(D) f (6) s5

There are 12 boys and 6 girls in how many ways A commity of 5 can be form. Such that it is contain 2 boys and 3 girls

There are 12 boys and 6 girls in how many ways A committee of 5 can be form. Such that it is contain 2 boys and 3 girls

\left(x^{3}+4 x^{2}+16 x+61\right) \div(x-4)

4. 5, 6, 16, 2, 244, 1245(A) 28 (B) 55 (C) 57 (D) 61 (E) ofthese

8.Given below are the marks of 7 studentsin a science test.6, 7, 8,7,9,9,10Use the data to answer the following questions.A. What is the range of the data?B. Find the mean of the marks obtained by the7 students.

a = \frac { 1 } { 2 + \sqrt { 3 } } \text { and } b = \frac { 1 } { 2 - \sqrt { 3 } } \text { then the value of } 2 a ^ { 2 } + 3 a b - 2 b ^ { 2 }

(i) In how many ways can 6 boys and 4 girls be seated in a round tableso that two girls never be seated together.

n(S)1113. 6 boys and 6 girls sit in a row randomly, find the probabilityEx.t all the 6 girls sit together.

Example 14. In how many ways 8 boys and 6 girls can be arranged in a row sothat no two girls are together?[R.G.T.U. 2007

allsEx. 13. 6 boys and 6 girls sit in a row randomly, find the probability[L. I. T.79]that all the 6 girls sit together.

Find the actual lower class limits, upper classlimits and the mid-values of the classes10- 19, 20 - 29, 30-39 and 40 - 49.

Find the sum of the lower limit of the median class and the upper limit of the modalclass :Classes10-2020--3030-4040-5060 - 7050-60I 7FrequencyI 519

(1) UUUUUU2If 4x+i (3x-y) = 3+i(-6), where x and y are real numbers, then find the values of xand y.Seatt

14, k का मान ज्ञात कीजिए यदि बिन्दुk, 2-2 k ),(-k+1,2 k) तथा(-4-k, 6-2 k)संरेख हैं।

owiing qlestions: (Any One)04From the top of a lighthouse, 100 m above sea level, the angle of depression of aship, sailing towards it, changes from 30 to 450. Determine the distance trathe ship during the period of observation.i)velled by

26. A ship sails out to an island at the rate of 15 km/hr and sails back to thestarting point at 10 km/hr. Find the average sailing speed for the wholejourney

The points A(1,-2), B(2,3), C (k,2) and D(-4,-3) are the vertices of a parallelogram. Findthe value of k.ORFind the value of k for which the points (3k-1,k-2), (k,k-7) and (k-1,-k-2) are collinear

r,s and t are real numbers and r v s, then show that the roots of the equation(r-s)x2+7r+ s)x-3(r-s)-0 are real and unequal.

30. Find the value (s) of k for which the points (3k -1,k-2),(k, k -7) and (k -1,-k-2)CBSE 2014]are collinear

3 2i7 +4iFind real numbers A and B, if A + iB

43)If sin Î¸ =, then find cose

Find the distance between the points (a cos θ, a sin e) and (-a sin θ, a cose).

2 keagecR) â ((atBLeed) =P st R (aBecAr 20 2)

6. If a- cose + i sin e, then find the value of(1- a)

For any two vecioShow that the points A(-2i +3j +5k), B(i+2j +3 k) and C (7i k)are collinear.

6, Find real numbers x and y if (x-iy) (3+5i) is the conjugate of-6-24i.

: REAL NUMBERS:1.The LCM of two numbers is 760 and their product is 6080. Find their HCFd LcE of hers to he 378 and 18 respectively?

. As observed from top of light house, 100m high above the sea levdepression of a ship sailing directly towards it, changes from 30 to 60distance travelled by the ship during the period of observation.ind the

Q22. From the top of a vertical tower, the angles of depression of two cars, in thesame straight line with the base of the tower at an instant are found to be 30° and60°. If the cars are 100m apart and are on the same side of the tower, find theheight of the tower.

Real NumbersV Find the HF of 13.5 and 345 wing Euclid'sdivision lemma.

3 \times 8+6 \times 11+9 \times 14+\ldots

\frac { 3 \times 7 \times 11 ^ { 8 } } { 21 \times 11 ^ { 3 } }

118/517 (Basement), Kaushalpuri, NealIn the given figure. ABCD is a quadrilateral. A line through D, parallel to AC, MeetsProduced in PProve that: ar (A ABC)- ar (quad. ABCD)

\frac { 3 \times 7 ^ { 2 } \times 11 ^ { 8 } } { 21 \times 11 ^ { 3 } }

If cosec O=18+! FindBo Sin Ox cose

The dimensions of a rectangular box are in the ratio of 2: 3:4 and the difference between the costof covering it with a cloth at the rate of 10 and ? 11 per mbox13.isă1,300. Find the dimensions of thend 1 5 m deen is to be tiled. If each tile is

Directions (Q. Nos. 24-25) If f(-x) = -f(x), then f(x) isf(x) is evenodd function and if f(-x) = f(x), thenfunction.2[f(x), if f (x) is evenAlso, I flo) dx=112f(x), if f (x) is odd- The value of the integral, sinâx dx is(d) 1-TC(a) o(b)cC/2

f(I)+f(3) + f(x)f(21+f(-) + f(l/2)32=35, then x =2x-1, if x>1If f(x)=Ä°x2 +1, ifand if-1x1

Let f be differentiable for all x, if f (1) =-2 and f' (x)2 2 for all x e [1,6], then(A) f (6) < 8(C) f (6)·25(B) f (6) 2 8(D) f (6) s5

2 keagecR) â ((atBLeed) =P st R (aBecAr 20 2)