Explore topic-wise InterviewSolutions in Current Affairs.

This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.

1.

tan 01-cot θ + 1-tan θ=1+sec θ cosec θ = 1 + tan θ + cot θ.(iii)cot θ

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2.

If 1 + sin2 = 3 sincos e, then prove that tan 0 = 1 or tan 0 =

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1++sin^2A=3sinAcosA , divide both side by cos^A.

sec^2A+tan^2A=3tanA

1+tan^2A+tan^2A=3tanA

2tan^2A-3tanA+1=0

2tan^2A-2tanA-tanA+1=0

2tanA(tanA-1)-1(tanA-1)=0

(tanA-1)(2tanA-1)=0

Either tanA-1=0

tanA=1 , proved

Or 2tanA-1=0

tanA= 1/2 (possible value).

3.

Basic Mathematis (FY.ip sem6 1EXERCISES(1) Without using calculator, find the value of(a) cos 15(c) cos 103(b) sin 15(d) tan 15

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a.

4.

Without using a calculator evaluate 0.27 - 0.106 by convertingeach decimal to a fraction first. Give your answer as a fraction in itssimplest form.

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27/100-106/1000270-106/1000164/100041/250

5.

4sinf -~. If 4tanf =3, then(Msmflcose) '4sin0 + cos B

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6.

I237. If a cose b sinec, prove that a sine + b cose t a +b-cICB

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7.

3x2 - 5xy + आग .

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it's answers is -2xy

8.

6.If sin=-, then show that b sin 0 = a cose.

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9.

EXERCISE 10(A)1.John bought 27.5 m of cloth. How many cm of cloth did he buy?2. Rina walked 2 km in the morning and 3,000 m in the evening. Whatdistance covered by Rina in km?

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1. 1m = 100cm27.5m = 27.5*100 = 2750cm

2. 1km = 1000m3000m = 3km. 2km+3000m = 2km+3km= 5km.

Please hit the like button if this helped you.

10.

14) Multiply: (3xy+2y) by 5xy

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(3xy+2y)*5xy3xy*5xy+2y*5xy15x^2y^2+10xy^25xy^2(3x+2)

11.

x+y=5xy3x+2y=13xy

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12.

2) Each problem carries 4 marks.4x4=1610. a) Prove that rootn is not a rational number, if n is not a perfect square.

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Let , us assume that √n is rational .

so, √n = a/b where a and b are integers and b is not equation to zero .

Let, a/b are co- prime taking square both side ,we get

=> n = a^2/b^2=> nb^2 = a^2 ......(1)so, n divide a^2 it means n also divide a for some integer ca = nc

now squaring both side a^2 = n^2c^2=> nb^2 = n^2c^2 [ from (1) ]=> b^2 = nc^2

so , n divide b^2

it means b also divide b

so, a and b have n as a prime factor

but this contradict the fact that a and b are co- prime .

therefore , our assumption is wrong .hence, √n is irrational

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13.

3.If v/3 sin-cos, find the value of sin0-tan 0-(1+ cot 6)sin 6 + cose

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Let theta = xGiven,sinx/cosx = 1/sqrt(3)tan x = 1/sqrt(3)

Value ofsin x. tan x. (1 + cot x) /sin x + cos x

= sin x. tan x. (1 + cot x) / sin x ( 1 + cos x/sin x)

= sin x. tan x. (1 + cot x) / sin x (1 + cot x)

= tan x

= 1/sqrt(3)

14.

3. If the first term and last terms of an A.P (a, a) are gigiven and theon difference is not given, then sum of n terms of A.FP.

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Sum of n terms = n/2 × [a(1) + a(n) ]

please give solution

S(n) =Sum of n terms = n/2×( 2a + (n-1)d )

Now we simply this,

We know a(n) = a + ( n - 1) d ......(1)

So, S(n) = n/2×( a + a + (n-1)d )

S(n) = n/2×( a + a(n) ) ..... Using (1)

a is first term.

Proved.

Please like my answer if you find it helpful

15.

1) Differentiate the given terms with respect to x:y = e*.3*.

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16.

Calculate the Mean, Median and Mode for the following ungroupeddata.20.5, 10, 6, 9. ,6. 11

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thank u

17.

• यदि x+y = 5xy तथा x-y=7xyतब, 3 = १ ५ = १

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18.

in the. What is the constant termequation 2x – 3 = 0?

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-3 is the constant term in the equation 2x-3=0

3/2 is the correct answer of the given question

-3is the constant term in the equation

-3 is the constant term in the equation 2x-3=0

-3 is the constant term

-3 is the correct answer

-3 is the constant term

19.

3(2x +y)=Txy और 3(x+3y)= 11xy4 £

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20.

) can have a linear term but the constant term is positive.Which of the following is not the graph of a quadratic polynomial?(B)(D)C

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the 1 ans. is onesecond one is onethird one is twofourth one is three

21.

2. What is the constant term in 3x - 2x + 5?

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In the expression, 3x² - 2x + 55 is the constant term

5 is the constant term

the answer of your question is 5 because it is a constant term

In the expression 3x2- 2x +55 is the constant term

5 is the constant term

22.

solve by elimination 3(2x+y)=7xy3(x+3y)=11xy

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6x+3y=7xy3x+9y=11xy. =3x=11xy-9y6x+3y=7xy2(11xy-9y)+3y=7xy22xy-18y+3y=7xy15xy=15yx=13x=11xy-9y3×1=11×1×y-9y3=11y-9yy=3/2i hope this answer is helpful for youHIT THE LIKE BUTTON IF YOU ARE SATISFIED

23.

(7xy - 8x) - (- 5xy + 3x)

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(7xy-8x)-(-5xy+3x)=7xy -8x + 5xy-3x=7xy+5xy-8x-3x=12xy-11x

7xy+5xy-8x-3x12xy-11x

(7xy-8x)-(-5xy+3x)7xy-8x+5xy+3x7xy+5xy-8x+3x12xy-5x

12xy-11x right answer

2xy-11x its ans

12xy-11x is the correct answer

12xy-11x is the correct answer h

(7xy-8x) - (-5xy+3x)7xy-8x+5xy-3x7xy+5xy-8x-3x12xy-11x ans

(7xy - 8x) - (-5xy + 3x)7xy - 8x + 5xy - 3x+7xy + 5xy - 8x - 3x+12xy - 11x

12xy-11x is correct answer

12xy-11x is right answer.

(7xy - 8x) - ( - 5xy + 3x)

7xy - 8x + 5xy - 3x

+ 7xy + 5xy - 8x - 3x

+ 12xy - 11x

7xy-5xy-8x-3x2xy-11x

(7xy -8xy )- (-5xy+3x ) = 7xy -8x +5xy -3xy = 7xy +5xy -8xy -3x so the answer is = 12xy -11x

(7xy-8x)-(-5xy+3x)(7xy-8x+5xy-3x)7xy+5xy-8x-3x12xy-11y

(7xy-8x)-(-5xy+3x)7xy-8x+5xy-3x7xy+5xy-8x-3x12xy-11x

(7xy-8x)+5xy-3x7xy+5xy-8x-3x12xy-11x Ans.

7xy-8x+5xy-3x=12xy - 11x

1

Remove parentheses.

7xy-8x+5xy-3x7xy−8x+5xy−3x

2

Collect like terms.

(7xy+5xy)+(-8x-3x)(7xy+5xy)+(−8x−3x)

3

Simplify.

12xy-11x12xy−11x

Done

(7xy-8x)-(-5xy+3x)=7xy-8x+5xy-3x=12xy-11x

7 xy_8 X+5 xy_3 X 7 xy +5. xy_8 x_3 X 12 xy_ 11 x

(7xy-8x)-(-5xy+3x)7xy-8x+5xy-3x12xy-11x

7xy-8x+5xy-3x7xy+5xy-8x-3x12xy-11x

= (7xy - 8x) - (-5xy + 3x)= 7xy - 8x + 5xy + 3xGrouping the like terms= 7xy + 5xy - 8x + 3x= 12xy - 11x

Therefore, (7xy - 8x) - (- 5xy + 3x) = 12xy - 11

7xy + 5xy - 8x-3x 12x-11x

24.

prove that : (sinA-2sin^3A/ 2 cos^3-cosA)=tanA

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LHSsin A ( 1 - sin ² A ) / [ cos A ( 2 cos ² A - 1 ) ]

sin A ( 2 cos ² A - 1 )/cos A ( 2 cos ² A - 1 )sin A/cos AtanA

25.

3. If4tan A = 3, evaluate: (1tsinALEH S... 2> {(1+cosA) (1- cosA)

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Given tanA= 3/4(1+sinA)(1-sinA)/(1+cosA)(1-cosA)= (1- sinA^2)/(1-cosA^2)

Using sinA^2 + cosA^2 = 1

= cosA^2 /sinA^2= cotA^2

As tanA = 3/4 then cotA = 4/3

= (4/3)^2= 16/9 = 1.7 ans

26.

if m= cosecA-sinA, n= secA-cosA prove that(m^2n)^2/3+(mn^2)^2/3=1

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the question seems wrong.can you put up a picture?

27.

. हल करें - 6x + 3y = 6212x + 4y = Sxy

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Hit like if you find it useful

28.

d the common factors of the given terms in each.(1) 8x, 24(iv) 4.6m". 8m(ii) 3a, 21ab (iii) 7xy, 35xy(vi) 4x'. 6xy, 8yx (vii) 12. 18.iv) 15p, 20gr: 25rp

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1. 8x ,24 common factor. 82. 3a,21abc f 3a3. c f 7xy4. c f 2m5. c f 56 . c f 2x 7 . c f 6xy

8 is the right answer

29.

Subtract:(a)7xy from 2xy

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2xy -7xy=-5xy

30.

Subtract:(a)7xy from 2vy

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5xy is the answer of your question

-5xy is the right answer

31.

EXERCISEthe mean and variance for each of the data6,7, 10, 12, 13, 4, 8, 120

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32.

Exercise 14c(b) 4 h 12 min by 3

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33.

2x+3y=2xy,6x+12y=7xy

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34.

(2), 2x+3y = 2p, 6x +12y = 7xy

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35.

¢ 5’( o .ड अं न८ 5६... ०: किला acdsy f निज दि 6 न्त्ष्पि जि (5 है को 2 नाग, ७(९०३ ke Ui हा o

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use factor theorem it will gives you two equations and solve them to get answer

36.

3(2x+y)=7xy;3(x+3y)=11xy

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3(2x+y) = 7xy -> 6x+3y = 7xy 3(x+3y) = 11xy -> 3x+9y = 11xy Multiply 2nd equation by 2 and subtract from 1st equation 6x + 3y - 6x - 18y = 7xy - 22xy -15y = -15xy xy - y = 0 x(y-1) = 0 x = 0 or y = 1 x = 0 -> 6*0 + 3y = 0 so y = 0 y = 1 -> 6x + 3 = 7x so x = 3

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wrong

37.

Write the constant term of : x2y - xy2 + 7xy - 3

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Constant terms are: -1, 7,-3

38.

(23. In the given figure, find 3 tan 0-2 sin a +4 cosa

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3(8/3)-2(8/17)+4(8/17)=8-4%17

3(8/3)-2(8/17)+4(8/17)=8-4/17+32/17=8-36/17=24/17

39.

1. Add Sxy, 6xy and 9xy

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5xy + 6xy + 9xy

11xy + 9xy

20xy

20xy is right answer ,.,. make sure to thanks

40.

Exercise 12.21. Add 5xy, 6xy and 9xy.

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the answer for this is 20xy

Answer is 6xy + 5xy + 11xy = 20xy

41.

.Find the value of-4x2y2+6xy+ 8x + 12y-1, when x=-2, y =-1.

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-4x²y²+6xy+18x+12y

x=-2 y=-1

-4(-2)²(-1)²+6*2+18(-2)+12(-1)

-4*4+12-16-12

-16+12-12-16

=-32

42.

What must be subtracted from 3x2 -6xy 3y -1 to get 4x2 -7xy -4y + 1?

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43.

Subtract:() - 8xy from 7xy1) from (4y - 5x)2 - 3y2 + 6xy

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=-xy answer your this

44.

. In Fig. 6.17, POQ is a line. Ray OR is perpendicularto line PQ. OS is another ray lying between raysOP and OR. Prove thatZROS ( QOS- POS).2

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45.

7. (i) sec B(1 —sin B)(sec 6 +tan 0) = 1

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46.

| हे। पद ? टन (कि (०6 Heen b?usd बह Val7 on 0t (o

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47.

For what values of k are the points (8, 1), (3, -2k) and (k, -5) collinear ?

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48.

4.For what values of k are the points (8, 1), (3,-2k) and (k, -5) collinear?

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49.

actorize the following:(1 6xy+12y - 9x-18

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fast we take a comman 3(2xy+4y_3x_6 )this is a right answer

(x+2)(6y-9)

3(2xy+4y_3x-6) this is a riget answer

(1).6xy + 12y - 9x -18solve=2y(3x+6) -3(3x+6) (2y-3)(3x+6). And..

6xy+12y-9x-186y(x+2)+9(x+2)(x+2)(6y+9)

fast we take a cmman 3(2xy+4y_3x_6)this is a right answer

2y(3x+6) -3(3x+6)=(2y-3)(3x+6)

This answer is correct ( X + 2 ) ( 6 y - 9 )

3(2xy+4y-3x-6) this is its factorise form

6y(x+2)-9(x+2)(6y-9)(x+2)

6xy+12y=18xy218xy2-9x=9y29y2-18=-9y2 answer -9y2

(6y+9) (x+2) this is a right answer

6xy+12y-9x-186y(x+2)-9(x-2)6y(x+2)-9(x+2)(6y-9)(x+2)

6xy+12y-9z-183y(2x+4)-3(2z+5)

Q 6xy+12y-9x-18=6y(x+2)-9(x+2)=(x+2)(6y-9)

6y(x+2)-9(x+2)(x+2)(6y-9)Answer

50.

. In Fig. APB is a tangent to a circle with centre O, atpoint P. If ZOPE 50*, then themeasure of POO is:Fig. 2(A) 120(B) 100 (C) 140°(D) 150

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