Explore topic-wise InterviewSolutions in Current Affairs.

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1.

5.Quick Answers.(a) What is the product of 3.857 X 1000?

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what is the product of 3.857 × 1000

3.857×1000=3857.0 or 3857

2.

2. Express in the quadratic polynomial.(3)(i) v2, 13

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3.

find the quadratic polynomial whose zeroes are 3+root5 and 3-root5

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4.

Findand2+3quadratic polynomial. He sumproduct of whose zeloes areand 2-3 Mespectively,

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Let a and b are zeroes of polynomial

Then,a + b = 2 + root(3)a*b = 2 - root(3)

Therefore,Quadratic polynomial is given byx^2 - (a + b)x + a*b = 0x^2 - (2 + root(3))x + (2 - root(3)) = 0

5.

how to solve the substitution methods

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You can solve it with the help of- First you have to take the X value from the equation and then you have to put that value in the y in the place of x. Then you will have equation in the terms of why only then after that you can find the value of Y from there and put that value in the main equation and you will find the other value as well

6.

12 crn and BC = 13 cm, prove that <CAB8. In the given figure,OA = 3 n, OB = 4 cm, LAOB-90, AC90°

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7.

3. In the fig 11.16 points L, M and N are situatedon OA,OB and OC respectively such thatLMI AB and MMBC then show LMACFig. 11.16

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8.

If A +C- B then tan A. tan B. tan C(a) tan A + tan B +tan C(c) tan A + tan B - tan C(b) tan B -tan C-tan A(d) -(tan A +tan B+ tan C)

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Take tan both sidesTan (a+c) = tan b(tan a+tan c) /(1-tana tanc) =tanbtana +tanc =tanb - tan a tanb tancThentana tanb tanc =tanb - tana - tanc

9.

Tan 28° + Tan 72°+ Tan 80°= Tan 28°. Tan72°Tan 80°

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10.

Prove that : tan 7α-tan 50-tan 2α = tan 7α . tan 5α tan 2α.

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11.

thatasec 58-cot 58 tan 32tan 13' tan 37' tan 45° tan 53° tan--1.-

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tanks

12.

bind the polynomial of P if (-2) is a factorof the Polynomial 23.

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8 is the correct answer

13.

Findand2+3quadratic polynomial. He sumproduct of whose revoes areand 23 despectively

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Let a and b are zeroes of polynomial

Then,a + b = 2 + root(3)a*b = 2 - root(3)

Therefore,Quadratic polynomial is given byx^2 - (a + b)x + a*b = 0x^2 - (2 + root(3))x + (2 - root(3)) = 0

14.

P. TTan13 A-Tan 4 A +Tan9 A +Tan4 A. Tan 9 A.Tan13 ATan 28° Tan 72 + Tan 80°- Tan 28°. Tan72°Jan 80%

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Prove that: tan13A-tan9A tan4A=tan13Atan9Atan4A

For this equation we will use the formula: i) tan 2a= tan(a + a) and,ii)tan (a + b)= (tan a+ tan b)/(1-tan a tan b)

From (i), we can say tan 13A= tan (9A+4A)but, tan(9A+4A)=(tan 9A + tan 4A)/ (1-tan 9Atan 4A)

Therefore tan13A=(tan 9A+tan4A)/(1-tan9Atan4A)

=tan13A-tan13Atan9Atan4A=tan 9A+tan 4A

therefore,tan13A-tan9A-tan4A=tan13Atan9Atan4A

tan13A=tan9A+tan4A+tan13Atan9Atan4A

15.

. tan 5째 tan 25째 tan 45째 tan 65 tan 85째

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16.

Add.a. L TTh Th Hо2 1 2Imnол+639Ол

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The correct answer is851,880

the answer of your question is 851880

17.

Tl L PR ULT के द्वए9 न 5 हा वह टाथातर ह कि ञ

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Sn=5n^2 +11nS1=a1=5 (1×1)+11×1=5+11=16

S2=a1+a2=5(2×2)+11×2=42a2=42-16=26

d=a2-a1=26-16=10

Tn=a+(n-1)×dTn=16+(n-1)10Tn=16+10n-10Tn=6+10n

18.

1 mEXERCISE 11.20.8 mThe shape of the top surface of a table is a trapezium. Find its areaifits parallel sides are l mand l.2 m and perpendicular distancebetween them is 0.8 m.1.TL ..THㅏ1.2 m

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19.

डे! 6 <8/:0नएठाफिडरि लिव्ली/B0 e~ &. L. A 2 Ao Bas. s RS Tl

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20.

\frac { 7 x + 10 } { 5 x + 10 } = \frac { 9 } { 7 }

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49x+70=45x+90so 4x=20so x=5

21.

You may check that (-1) raised toand (-1) raised to any even powe(iv) (-10)3 =(-10) (-10) X (-10) =(v) (-5)4 = (-5) X(-5) (-5) X(-5EXE1. Find the value of:(1) 26(ii) 932. Express the following in exponen(1) 6x6x6x6 (ii) t(iv) 5 x 5x7x7x7 (v) 2

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1)(1)=2×2×2×2×2×2=642)9×9×9=81×9=729(2)6×6×6×61296(4)5×5×7×7×7=85754)(-10)3=-1000(y)(-5)×(-5)×(-5)×)-5)=625

(1) = 2×2×2×2×2×2 = 4×4×4 = 16×4 = 64

(2) = 9×9×9 = 81×9 = 729

1 (I) 2×2×2×2×2×2=64 (ii) 9×9×9=729 answer

question, 1. answer. 1296

question, 4. answer. 8575

(1) = 2×2×2×2×2×2 = 4×4 = 16×4 = 64

(2) = 9×9×9 = 81×9 = 729

(1) =2×2×2×2×2×2 =4×4×4 =16×4 =64

(2) =9×9×9 =81×9 =729

1=64,2=729 question 2=6sqare 4 . 4=5sqare 2 7sqare =3

22.

-3. || , the beroesLa-by a athof the polynomial 23-32212+larefind a and b

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Given polynomial is f(x) = x³ - 3x² + x + 1 .

Here a = 1 , b = -3 , c = 1 , d = 1 .

Let α = ( a - b ) , β = a and γ = ( a + b ) .

As we know,

→ α + β + γ = -b/a .

⇒ ( a - b ) + a + ( a - b ) = -(-3)/1 .

⇒ 3a = 3 .

⇒ a = 3/3 .

∴ a = 1 .

And,

→ αβ + βγ + γα = c/a .

⇒ a( a - b ) + a( a + b ) + ( a + b )( a - b ) = 1/1 .

⇒ a² - ab + a² + ab + a² - b² = 1 .

⇒ 3a² - b² = 1 .

⇒ ( 3 × 1² ) - b² = 1 . { ∵ a = 1 }

⇒ 3 - b² = 1 .

⇒ b² = 3 - 1 .

⇒ b² = 2 .

∴ b = ±√2 .

Hence, it is solved .

23.

U be the set of all boys and girls in a school. G beset of all girls in the school, B be the set of all boysn the school and S be the set of all students in thewho take swimming. Some but not all studentsINCERT Exemplar)Letthechooln the school take swimming

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What is your question here? Do you need the Venn Diagram?

yes

S be the best of luck to the world of the United nations and its leaders and the people of America who are going

24.

money did he spc(ix) On a vacation trip, Megha spent one-eighth of her time reading books,one-eighth of her time in watching TVand two-sixths of her time in sleeping.She used the rest of the time forswimming and other outdoor activites.What fraction of her time was spent inswimming and other outdoor activites?

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let total time be Xhencetime spend on outdoorsX-(1/8x+2/6x)X-(6+16/48x)X-22/48x48x-22x/4826x/4813x/24hence she spent 13/24th of her time

25.

W/hat is the square of 25?

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square of 25 = 25^2 = 625

26.

W/hat is the squane of 25?

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square of 25= 25²

= 25×25= 625

27.

An article w!lcassold for540 at a loss of5%.what was its cost price?

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sp=540loss%=5%cp=100/(100-loss%)×spcp=100/(100-5)×540cp=100×540/95cp=568.42

28.

Jer Represent the following statement algebraicallySum of x, y, z divided by 3.ge the following statements using expressions into statements in ordinary languageChanMonika is x years old. Her father's age is 4x years old.A pencil costs p. A pen costs 3p.

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i) (x+y+z)/3

i) Monika's father's age is 4 times Monika's age ii) A pen costs 3 times pencil's cost.

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29.

5 x^{3}+7+6 x-5 x^{2} \text { from } 3 x^{3}-9 x-x^{2}

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30.

1) Solve the following simultaneous equations :

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please like my answer if you find it useful

31.

l) Solve the following simultaneousequations.-15; 으+--77

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32.

Solve the following simultaneous equations graphically:

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33.

. Solve the following simultaneous equations16

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Please hit the like button if this helped you

34.

Solve the following simultaneous equations.:: 15 ,-+--=77

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35.

In the adjoining figure, AB/CDare cut by a transversal t at E and F respectively. If2 : <15 4, find the measure of each one of the marked angles

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36.

Solve the following simultaneous equations!m2 16 . 77

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2/x - 3/y = 158/x + 5/y = 77

∴ [ let 1/x = p & 1/y = q ]

Now,

2p - 3q = 15------------(1)8p + 5q = 77-----------(2)

FROM-----(1) & -------(2)Multiply by (4) in ----(1)

we get,

8p - 12q = 608p + 5q = 77(-)___(-)___(-)----------------------17q = - 17

⇒q = 1 put in --(1)

we get,

2p - 3(1) = 15

⇒2p = 15 + 3

⇒ 2p = 18

⇒p = 9

⇒1/x = 9∴ [ 1/x = p ]

⇒x = 1/9

AND,

q = 1/y = 1∴ [ q = 1/y ]

⇒y = 1 , x = 1/9

2/(1/9) - 3(1) = 15

⇒18 - 3 = 15

⇒15 = 15

And,

8/(1/9) + 5(1) = 77

⇒72 + 5 = 77

⇒77 = 77

2/x - 3/y = 15; 8/x + 5/y =77; 1/x = k, 1/y = a;; 2a - 3k =15; 8a +5k = 77; 8( 2a - 3k = 15)= 16a-24k = 120 2(8a+5k =77)= 16a +10k=154 _ _______________ 24k+10k /34; k = 34/34 =1; ; 2a -3k =15, 2a -3(1)=15; 2a = 15 +3=18; a = 18/2=9; a=1/x=9; k= 1/y =1;

37.

Solve the following simultaneousequations : Sx-3y-8 : 3xty-21)

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5x - 3y = 8 .....(1)

3x + y = 9 ......(2)

(1) + 3 × (2)

5x - 3y = 8

9x + 3y = 27

14x = 35

x = 5/2

So, y = 9 - 3x = 9 - 15/2 = 3/2

38.

e the following simultaneous equations.3a + 3b = 26; a + 5b = 22

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3a+5b=26- - -eqn 1a+5b=22- - - eqn2From eqn 2a+5b=22a=22-5bPut a=22-5b in eqn13(22-5b)+5b=2666-15b+5b=2666-10b=26-10b=26-66-10b=-4010b=40b=40Put b=40in eqn 2

39.

(1) Solve the following simultaneous equations:3x-4y 10; 4x+3y 5

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let,

3x-4y = 10 ----------> {1}

4x+3y = 5 ------------> {2}

{1} × 3 = 9x - 12y = 30

{2} ×4 = 16x + 12y = 20===================== 25x = 50

x = 50/25

x = 2

therefore , x = 2

now place x in eq 1

(3×2) - 4y = 10

6 - 4y = 10

-4y = 4

y = (-1)

so ,

x = 2y = (-1)

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thank you for answer

40.

17. AB and AC are two chords of a circle of radius r such that AB = 2AC.If p and q are the distances of AB and AC from the centre then provethat 49" p2 + 3r2

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41.

solve by substitution method 3x-5y=-1 and. 2x-y=-3

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(3x-5y=-1)2; (2x-y=-3)3; 6x-10y=-2; 6x-3y=-9//7y=-7; y=-2; 3x-5y=-1; 3x-5(-2)=-1; 3x+7=-1; 3x=6; x=2

42.

Solve the following by the substitution method:3x - y = 39x - 3y = 9

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43.

Solve the following by the substitution method 3x -y = 39x-3y =9

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44.

. Solve the following system of equations by substitution method:3x+2y = 14-x+ 4y =7.

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45.

(iii) 8x+3y=143x +y=5(Usesubstitutionmethod)

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46.

3x + 4y = 10 and 2x - 2y = 2 solve by substitution method mathematics

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2x-2y=2 (given)2 (x-y)=2x-y=1x=1+yagain,3x+4y=10subatituting the vale of x= 1+y in this equation we have,3 (1+y)+4y=10or 3+3y+4y=10or 7y=10-3or y=1also,x = y+1 =1+1 =2hence x =2 and y =1

47.

uof car co ver a di stance f R6O m in howrond he pedhe Car

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48.

Tdctice Set 9.1If marked price1700, selling price1540 then find the disrmuntondf marked pricegg0

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49.

EXERCISE 7.2In an isosceles triangle ABC, with AB = AC, the bisectors ofeach other at O. Join A to O. Show that:l.B and L C intersect个(ii) AO bisects<A2. In A ABC,AD is the perpendicular bisector of BC(see Fig. 7.30). Show that Δ ABC is an isoscelestriangle in whichAB ACFig. 7.30

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50.

Write True (T) or False (F) against cach of the following statemenis(a) 16:24:: 20:30 (b) 21:6: 35: 10 (e) 12:18 28: 1225tion

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