Explore topic-wise InterviewSolutions in Current Affairs.

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1.

Find the numberwhen increased by 20% becomes 72?

Answer»

x + 20x/100 = 72

120x = 7200

x = 7200/120

x = 60

2.

n Each questior carles' mars7. Find the ratio in which the line segment 2x 3y 1 - 0 divides the line segmentjoined by the points (5, 6) and (-4,-3).

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Let line divides 2x+3y-1=0 to the segment joining (5,6) and (-4,-3) in k:1let point of intersect be (a,b)by intersection formula(a,b)=(-4k+5/k+1 , -3k+6/k+1)a=-5k+5/k+1 and b=-3k+6/k+1these point will also lie on line 2x+3y-1=0.hence point will satisfy this equation2×(-4k+5/k+1) + 3×(-3k+6/k+1) -1 =0-8k+20-9k+18-k-1=0-18k+37=0k=37/18ratio will be 37:18

3.

EXERCISE 7.2Find he coordinates of the point which divides the join off, 73 รกnd (4,-3in the2

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A = (-1, 7) and B = (4, -3)

So,x1=−1,y1=7,x2=4andy2=−3

We also have;m1=2andm2=3

Let us assume P is the point of division

Coordinates of P can be calculated as follows by using section formula:

x=m1x2+m2x1/m1+m2

=2×4+3×−1/5

=8−3/5=5/5=1

y=m1y2+m2y1/m1+m2

=2×−3+3×7/5

=−6+21/5=15/5=3

Hence, P = (1, 3)

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4.

The points C and D are on the line segment joining A(4, 7) andB(5, 13) such that AC=CD = DB. Then find the co-ordinates of pointsC and D

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5.

3 Find five rational numbers between 3/5 and4/5.2.1

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Five rational number3/5 and 4/5multiplying by 515/25 and 20/25now rational number will be 15/25 16/25 17/25 18/25 19/25 20/25

thanks

6.

(c) For what value of k, will the points (k, -1)nd (4, 5) lie on a line?(2. 1) a

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Slop should be same nowslop= y2-y1/x2-x1here1-(-1)/2-k= 5-1/4-22/2-k= 22= 4-2k2k= 2k= 1

7.

3.Ifsin6-4 then find cosa)15nd sin

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8.

nd the radius of the c(i) 8 cm(ii) 4

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the question you have posted is incomplete

9.

Ifa and Bare Zeroes of the polynomial x-X-6, then find the values of

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I think 1 But..... .

10.

Q.10. If a and Bare zeroes of p(x) = x2 + ax + b, then find a polynomial whose zeros are

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jdjejdkdkddbbd f fnfkfodndndndf

We have p(x)=x^2+ax+balpha +betta =a and alphabetta=bLet the required polynomial be f(x) whose zeroes are 1/alpha and 1/betta1/alpha + 1/betta = alpha +betta /alphabetta =a/b1/alpha *1/betta=1/bThe required polynomial is given by

11.

2. Piaget was a/an(A) Swiss psychologist(B) American psychologist(C) African psychologist(D) of the above

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Piaget was a Swiss psychologist

12.

9P5' = 7 POAPJP में PM/ यह माध्यिका है । )= 4,22=4.नबाई अति जिए ।A AMB' में ग्व AM यह माध्यिका है। य?2=22,C=4नाबाई ज्ञात कीजिए।ICT Tools or LinksStory on the life of Pythagoras25

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Born on the island of Samos, off Greece, in the Mediterranean Sea,Pythagoraswas the son of Mnesarchus. Little is known about his earlylife. After studying in Greece, he fled to southern Italy to escape the harsh rule of Polycrates (died c. 522 B.C.E. ), who came to power about 538 B.C.E.

13.

Draw a line segment of length 6.4 cm and divide it into four equal parts. What isthe length of each part?

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here.. the colored lines Divides 6.4 into 4 equal parts..

each part having length = 6.4/4 = 1.6

14.

28 ) Find the value of a", "show that (z+1) and (2-1) are factors z' + az + 22 -32+b

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If these are factors hence put z=1 and z=-1he CE(1)^4+a(1)^3+2(1)^2-3(1)+b=01+a+2-3+b=0a+b=0and(-1)^4+a(-1)^3+2(-1)^2-3(-1)+b=01-a+2+3+b=0a-b=6adding both the equationshence2a=6a=3andb=-3

15.

2. Show that the system equation 2x-y+32 =9,x+y+z=&x-y+z=2are consistent and Solve them.

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2x-y+3z=9,x+y+z=6,x-y+z=2 solve in matrix method. 2x-y+3z=9,x+y+z=6,x-y+z=2 solve i

2x - y + 3z = 9x + y + z = 6x - y + z = 2

Thus matrix can be formed as[ 2 -1 3 1 1 1 1 -1 1 ] [ x y z ] = [ 9 6 2 ]orA X = BA inverse Can be calculated asAdj A = [ 2 0 -6 -2 -1 1 2 -1 -1 ]l A l = 2 (1 +1) - 1 (1 - 1) + 3 (-1 - 1) = 4 - 0 -6 = -2ThusA inverse = [ -1 0 3 1 1/2 -1/2 -1 1/2 1/2 ]Thus

X = A inverse B[x y z ] = [ -1 0 3 1 1/2 -1/2 -1 1/2 1/2 ] [ 9 6 2 ] = [ -3 11 -5 ]Thusx = -3y = 11z = -5

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16.

15.Find (i) vm1(Gi) /16y8x4

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Under root m12=m6 Under root 16y8x2=4y4x2

17.

Find the coordinates of the points which divide the line segment joining AC- 2, 2) andB(2, 8) into four equal parts.9.

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18.

Find the coordinates of the points which divide the line segment joining A (-2, 2) andB (2, 8) into four equal parts.

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19.

SE 11 (A)2. In the given figure, a circle isdivided into four equal parts bythe lines AOD, AOC, BOC, CBOD? How many times is theBangle AOB of angle AOC ?dinte 16 equal

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Since circle is divided into 4 equal parts and complete circle is 360 degree. AOD=AOC=BOC=BOD= 360/4 = 90 degree. BOD is a straight line = 180 degree. 180 = 2*90AOB = 2 times AOC

Angle AOB is twice the angle AOC.

angle AOC = 45

angle AOB = 90

therefore angle AOB = 2×AOC = 2×45 = 90angle AOB is twice the angle AOB

20.

24. Find the co-ordinates of the points which divide the line segment joining A(5, -6) and B(-1, 8) intofour equal parts.

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21.

9. Find the coordinates of the points which divide the line segmentjoining A (- 2, 2) and B (2, 8) into four equal parts.ndD (edivide the line segment

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22.

4 cm4 cm4 cm

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23.

The ratio in which the line x + y4 divides the line joining the points (-1, 1) and (5, 7) is(c) 3:2

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24.

32% x 8%14. Construct an angle of 15° at the initial point of a given ray15. AD& BC are equal perpendicular to a line segment AB. Show that CD bisects AB.Ardt 2

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In triangle OAD & OBCAD=BC (GIVEN)<OAD=<OBC (EACH=90*)<AOD=<BOC (VERTICLE OPP ANGLE)THEREFORE,TRIANGLE ODA=OCB (AAS CRITERIA)

OA=OB (CPCT)

So, CD bisects AB.

25.

Which of the following numbers are perfect cubea. 729e. 74,088b. 1728d. 55,125c. 10,584

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26.

2. In the given figure, AD and BC are equalperpendiculars to a line segment AB.Show that CD bisects AB.

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27.

17. In the given figure, line III line-segment AB. Find the values of x, yand z88 32

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Thank you bhai

28.

(ii) cost of the canvas required to make the lellt,What length of tarpaulin 3 m wide will be required to make conical tent of height 8 mand base radius 6 m? Assume that the extra length of material that will be required forstitching margins and wastage in cutting is approximately 20 cm (Use π = 314).

Answer»

Given a conical tent with

Height ( h ) = 8m

Radius ( r ) = 6m

So, its length = l2= h2+ r2

= l2= ( 8 )2m + ( 6 )m2

= l2= 64m + 36m

= l2= 100m

= l = 10m

Curved surface area of the cone = TTrl

= 3.14 x 6m x 10m

= 188.4 cm2

The extra length of material that will be required for stiching margins and wastages in cutting is approx 20 cm = 0.2m

So, its length = l - 0.2m

and its width = 3m

area of sheet = CSA of tent

so the area of the trapaulln = l x b

= ( l - 0.2m ) x 3m = 188.4m2

= l - 0.2m = 62.8m2

= l = 63m

Therefore, length of the trapaulin sheet required is 63m.

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29.

12 ek pighie 0 S/ ) il कु T

Answer»

सबसे पहले इसका उलटा मान लेते हैं; यानि मान लेते हैं कि√5एक परिमेय संख्या है।ऐसी संख्या के लिये a और b दो ऐसी संख्या होंगी जहाँ b ≠ 0 तथा a और b कोप्राइम होंगे, ताकि;√5=a/bया,b√5=a

दोनों तरफ का वर्ग करने पर यह समीकरण मिलता है;5b^2=a^2इसका मतलब है कि a^25 से डिविजिबल होगा और इसलिये a भी 5 से डिविजिबल होगा।लेकिन यह हमारी पहले के मान का विरोधी है कि a और b कोप्राइम हैं, क्योंकि हमें 5 के रूप में a और b का कम से कम एक कॉमन फैक्टर मिल गया है।यह हमारे पहले मानी हुई संभावना किb√5प्रमेय संख्या है का भी विरोधाभाषी है।इसलिए एकb√5अप्रमेय संख्या है सिद्ध हुआ।

30.

Find the values of the following:(1) i? + il? + 12

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i^6×i+i^16×i+i^12=-i-i-1 = -2i-1

the right answer is 38

the right answer is 38

-1-1+1=1. bcz I=-1

31.

6. Find the perimeter of each of the following rectangles :3.5 cm21 m15 cmm4 cm4 cmWZ'O715 cm3.5 cm(a)21 m(b)(c)

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1)length= 4mbreath= 3.5 mperimeter= 2(length+breath) = 2(4+3.5) =2×7.5 =15m2 figer)length= 21m , breath= 7mperimeter= 2(length+breath) = 2(21+7) = 2×28 = 56 m3rd figer)length=15m, breath= 0.2mperimeter= 2(length+breath) =2(15+0.2) = 2(15.2) = 30.4 m

1) 15m2)56 m3) 30.4m

are the perimeters of the given figures

and the best answer.

the answers are 15m 56m30.4mrespectively

a) perimeter=4+3.5+4+3.5 =15 cmb) perimeter=21+7+21+7 =56m

C) perimeter=15+20+15+20 =70 cm

1) l=4cm , b=3.5cmP= 2(l+b) = 2(4+3.5) =2(7.5) = 15 cm

30.4 cm. cm is the correct answer me

15cm,56cm,30.4 cm is the correct answer of the given question

15,56,30.4 is the correct answer

perimeter is total of length soa) = 4+3.5+4+3.5 =15cmb) = 21+21+7+7 = 56cmc) = 15+15+ (20 +20 ) = 70cm

32.

बे T०0६ 5 (0)T (V1 ()G R AR O जा है o०09 एस (3). ०09 WS (&amp;) ०09 509 (४)0!१. हा e६ (3) ६- (8) =)1009509©T T+.09 50V4109 () = v, (V)V4100 + 10o Y UelL हि8%‘LYहै. 14

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33.

Are the points (-3,-3 ),(-3,2)and (-3,5) collinear ?give reason

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34.

3Find the value of y, if the line joining the points (3. v) and (2.7) is parallel to the line jomspoints (-1, 4) and (0,6).

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35.

बहुपद p(x)=2x+3 VS क्या है?3 (७) © 3v - 39 सा e B में से लिस खिन्ट से गजरेगा?

Answer»

p(x) = 2x + 3 = 0

2x = -3

x = -3/2

To , (b) sahi option hai

36.

If a, b, c and d are four odd perfect cube numbers,then which of the following is always a factor of(2) 8(3) 3(4) 9

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37.

FIEby 202 YT-8.280BE |-8L8106744Fecoloo's 91811 v- ceoloolOL--0001 epleeg a2001 000 oholos p30 000€ hiç )

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38.

EXERCISE 1A1. Is zero a rational number? Justify.2. Represent each of the following rational numbers on the number line(ii)6(ii) 3(iv) 1.3(v)-2.47

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39.

i will he earn in 7 hours?1464 apples can be packed in 12 cartons of the same size. How many such cartons will bepack 2318 apples?will be needed to-

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12 cartons contain apple = 14641 carton contain apple = 1464/12=122than,2318/122=19so 122 carton needed in packing in 2318 apple.

40.

2. 2002 cartons of Lassi bottles and 2618cartons of Frooti bottles are to bestacked in a store room.If each stack is of the same height andis to contain cartons of same type ofbottles, what would be the greatestnumber of cartons ench stack would(CBSE 2013)have?

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41.

144 cartons of coke cans and 90 cartons ofcans are to be stacked in a store. If each stackof same height and is to contain cartons of samedrink, then find least number of stacks requiredpeps

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42.

10. 1152 bars of soap can be packed in 8 cartons of the same size. How many such cartons willbe required to pack 3888 bars?

Answer»

3888 * 8 /1152=27 cartons

43.

LUI UULIT ULIT IL 12.2. The curved surface area of a cylinder is 1.000 cm" and the radius ons base is 21 cm. Find thesurface area of the cylinder.Licht am If the inner ride

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44.

Find the later surface area and total surface area of the following right prisms.

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45.

IfA and Bare acute angles such that sin A=sin-B.2 cos2 A = 3cos-B then

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46.

है 123. 7"(11) 35 24.%32‘ po

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good job

47.

If A and Bare two points having coordinates (-2,-2) and (2, -4) respectively,then find the coordinates of P such that AP =3/7 AB

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1

2

48.

जनकप्रश्न 5. सिद्ध कीजिए: असल secA+tanA—sinmans. 13, NCERT m\sfl

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49.

If a, b, c and d are four odd perfect cube numbscube nubesthen which of the following is always a ear

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50.

[NCERT EXEMPL13. If 2sin2 θ-cos 2e-2, then find the value of 0 .

Answer»

2sin^2--cos^2=2(cos^2+sin^2)2sin^2-cos^2=2sin^2+2cos^2-cos^2=2cos^22cos^2+cos=03cos^2=0cos^2=0cos^2∅=cos^290∅=90