Explore topic-wise InterviewSolutions in Current Affairs.

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1.

At a point on level ground, the angle of elevation of a vertical tower is found to.such that its tangent is . On walking 192 m towards the tower, the tangen: fangle is found to be 3. Find the height of the towes.

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Let x be the height of the tower. As shown in the figure, let A be the initial position and B be the final position. Then,

h/192 + x = 5/12 ⋯ 12h = 960 + 5x ⋯⋯(1)

h/x = 3/4 4h = 3x x = 4h/3

Substituting the value of x in (1) 12h = 960 + 5 × 4h/3 12h = 960 + 20h/336h = 2880 + 20h 16h = 2880 h = 2880/16 = 180m

2.

At a point on level ground, the angle of elevation of the top of a vertical tower is found to be such that its tangent is 5/12.on walking 192 metres towards the tower the tangent of the angle is found to be 3/4. Find the height of the tower

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3.

At a point on the level ground, the angle of elevation of a verticaltower is found to be such that its tangent is 5/12, on walking 192 mtowards the foot of the tower, the tangent of the angle is found to be%. Find the height of the tower.

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4.

1.एक खुदरा विक्रेता एक रेडियो थोक विक्रेता से 20% छुट परखरीदता है। वह उसके मूल्य में 200 रुपये की वृधि कर देताहै तथा बेचते समय न्कित मूल्य पर 10% की छूट देता है।इसप्रकार उसे 148 रुपये का लाभ होता है। वस्तु का आरंभिकअंकित मूल्य ज्ञात करें 12

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148 is correct answer

5.

22.The suitable formula to find the sum of first n terms of the A.P. 1+3+5+7+D) n(n-l)C) ㎡

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6.

ATIC EQUATIONSEXE1. Find the nature of the roots of the ffind them:dir 2x2-3x + 5 = 0

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D= b^2-4acas herea= 2 b= -3 and c= 5D= (-3)^2-4*2*5= 9-40= -31roots will be imagineryas Discriminant <0

7.

4. A motor boat whose speed is 24 km/h in stillwater takes 1 h more to go 32 km upstreamthan to return downstream to the samespot. Find the speed of the stream.CBSE 2016

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8.

Find the 15th tem of the AP 3, 6, 9. Using suitable formula.

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Here a= 3d= 315 the term= a+14d3+14*3= 45

9.

EXERCİSChoose the greater decimal number from(a) 5.9 8.30d) 13.68, 9.92 (e) 0.831, 0.509(b) 0.6, 1.34

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greatest decimal numbera) 8.30b)1.34c)13.68d)0.831

tq

10.

LYNOMIALSEXE. Find the zeroes of the following quadthe zeroes and the coefficients.(i) x-2x -8(ii) 4

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x^2-2x-8=x^2-4x+2x-8=x(x-4)+2(x-4)=(x+2)(x-4)so zeros are x-4=0 x=4x+2=0 x=-2

again

more information

11.

Find the sum of the following series up to n terms:

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12.

\frac{(x+1)^{3}-(x-1)^{3}}{(x+1)^{2}-(x-1)^{2}}=2

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Thank you so much

13.

EXEFind, in each case, the remainder when:G) - 3x2 + 2x + 1 is divided by x-1ii)33x2 -12x +4 is divided by x-ii) 1 is divided by x + 1.

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1. x - 1 = 0= x = 1.p(1) = 1^4 - 3*1^2 + 2 * 1 = 1 - 3 + 2 + 1 = 1.

2. x - 1 = 0= x = 1.p(1) = 1^3 + 3*1^2-12*1+4 = 1+3-12+4= - 4.

3. x + 1 = 0= x = -1.p(-1) = (-1)^4 + 1= 1+1 = 2.

14.

(ii) Find the number of terms in the following series.4,7,10,...,148

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Given series 4, 7, 10,...... 148 is an AP

First term a = 4, common difference d = 7 - 4 = 3

nth term of AP is given byan = a + (n - 1)d

Let number of terms in series be mso,148 = 4 + (m-1)3148 = 4 + 3m - 33m = 148 - 13m = 147m = 147/3 = 49

Therefore,Number of terms in given series is 49

Given -AP = 4,7,10,......,148First term ( a ) = 4 common difference (d) = 7-4=3n term of AP is indicated by an = a+(n-1)d an = 148 ( given )148 = 4+(n-1)3148 = 4+3n-3147 = 3n147/3 = n49 = nSo, no. of terms are 49.

15.

Find the side of the two squares.21) A motor boat whose speed is 18 km /h in still water takes 1Upstream than to return downstream to the same stop. Finur nore to go 24 km

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16.

5.Test convergence and absolute convergence of the following series.22x 32 4!

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17.

f \frac { 2 x + 3 } { 2 x - 1 } = \frac { 3 x - 1 } { 3 x + 1 }

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18.

The studelIEXERCISE-41 aChoose the greater decimal number from each pai)598.30 (b) 0.6, 1.34(d) 3.68, 9.92 (e) 0.831, 0.509(c) 0.75

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19.

LICH PULL.1) Find the cubic polynomial whose zeroes are 5, 3 and -2.

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20.

12. Kitu can row abwisulalltspeed of rowing in still water and the speed of the currerit.Lotor boat can travel 30 km upstream and 28 km downstreamin7 hours. It c[NCERT EXE21 km upstream and return in 5 hours. Find the speed of the boat inFleurs 30 mi

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let the speed of the boat be x and the speed of stream be y

30/x-y + 28/x+y =7

21/x-y + 21/x+y=5

therefore 1/x-y=a,1/x+y=b

30a+28b=7...(1)×21

21a+21b=5.....(2)×30

630a+588b=147

630a+630b=150

(1)-(2/

-42b=-3

b=1/14

substituting the value of b in(1)

a=1/6

a=1/x-y

1/6=1/x-y

x-y=6...(.3)

b=1/x+y

1/14=1/x+y

x+y=14......(4)

(3)+(4)

2x=20

x=10

x+y=14

y=14-10=4

therefore speed of boat in still water is 10km/hr and speed of stream is 4km/hr

21.

Integrate the functions in Exe2x

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∫ 2x/(1 + x²) dx ....(1)

Let 1 + x² = t

2xdx = dt

∫ 1/t dt

log (t) + C

put t = 1 + x²

log ( 1 + x²)

22.

Exevalent to each of2019.03.24

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the answer for this question is 0.8

23.

dx34.[CBSE 2000C, '04](2sin x + cos x + 3)ANSWERS (EXE

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24.

EXEFind each of the following products(a)1.3 x (-1)

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25.

3x+x +1BSEB 2012C]

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26.

2 The area of an equilateral triangle is numerically equal to its perimeter.Find a side of the triangle [Take 3 1-73].

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Let the side of an equilateral triangle is a

perimeter of equilateral triangle= area of equilateral triangle

3a= (√3/4)a^2a= (4×3)/√3a= (4×3)×√3/ √3×√3. ( by rationalising)a= 4√3side = 4√3= 4×1.73=6.92

27.

n of two circles are 19 respectiyhe radius of the circle wbicih hassum of the circumferences of the two clesndií ottwocircles are 8㎝md6cm respecovetriodjus of the circle having area eqpal totesnfhethe radiusreas of the two circles

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28.

Using integration find the area bounded by the ellipse+= 1

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29.

10)Find the area of the circle of radius 'a' using integration.

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30.

7¡The axis of the parabola x2 +2x + 4y + 13 = 0

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31.

(a) Define ellipse as a set of points. Derive its equation in the form x^2/a^2+y^2/b^2=1

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32.

ia)The product of two rational numbers is always a

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Ans= A rational number

33.

s Using integration, find the area of the region common to the circlr[CBSE 2012Ca2+y16and the parabola y'-6x

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34.

5. निम्न चित्र में त्रिभुजों की संख्या ज्ञात कीजिए-(A) 13(B) 16 (C) 17Par (Triangles) 01(D) 18(Sam

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35.

कीSS I9X =01S

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36.

7.Using integration find the area of the region l(x, y):x2 + yS 2ах, угax, x, y

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37.

3. Using integration, find the area bounded betweenthe parabola x2 4y and the line y - 4.

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38.

Using integration, find the area of the region bounded by the line y - 3x + 2, X-axis, x--1

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39.

Lot A(acos e,0).B(0,a sine) be any two pointa then the diatanoebetvrees two polnts ia1) lal units2) a2 units3)vaunits4)y2a units

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40.

From the top of a cliff, 50 m high, the angle of depression of a buoy is 30°. Calculate to theTake 3 1.732]1 1 , ia 12-/3 m. What is the angle ofnearest metre, the distance of the boy from the foot of the cliff.t 19. m

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60 degree kaha se aya

41.

e the volume and surface area of a sphere are numerically the same, then its radius isa) none of these(a) 3 units(b) 2 units(c) 4 units(d) none of these

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42.

48 Using integration find the area of region bounded by the triangle whose vertices are (1,0), (2,2) and (3,1

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43.

Using integration find the area of region bounded by the triangle whose verticesare (-1, 0), (1, 3) and (3, 2).

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44.

Define ellipse

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In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. ... An ellipse may also be defined analytically as the set of points for each of which the sum of its distances to two foci is a fixed number.

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45.

Find the area of the region bounded by the ellipse + 01916

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thanks

46.

21tr6 The region bounded between two radius and an arc isSector

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the region bound between two radius and an arc is called sector

47.

5.।एक व्यक्ति की मासिक आय 7000 है.अपनी आय का कितना प्रतिशत वह खर्च करता है?आय 7000 रु. है तथा वह 140 रु प्रतिमाह बचाता है तो वह

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So7000-14005600 वा खर्च करता हैतब5600/7000*10080%

48.

a-4' unitseand the area of the region bounded by the parabola

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49.

EXERCISELEVEL-11, Construct a Δ ABC in which BC = 3.6 cm, AB + AC = 4.8 cm and ZB =60°.

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50.

Question 5. Find the area of the region bounded by the elliseY.(0,3)

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thanks