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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Answer» 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). |
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| 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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Answer» a. |
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| 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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Answer» 27/100-106/1000270-106/1000164/100041/250 |
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| 5. |
4sinf -~. If 4tanf =3, then(MsmďŹcose) '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 + ŕ¤ŕ¤ . |
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Answer» it's answers is -2xy |
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| 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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Answer» 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. |
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| 10. |
14) Multiply: (3xy+2y) by 5xy |
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Answer» (3xy+2y)*5xy3xy*5xy+2y*5xy15x^2y^2+10xy^25xy^2(3x+2) |
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| 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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Answer» 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 Like my answer if you find it useful! |
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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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Answer» 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) |
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| 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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Answer» 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 |
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| 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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Answer» thank u |
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| 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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Answer» -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 |
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| 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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Answer» the 1 ans. is onesecond one is onethird one is twofourth one is three |
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| 21. |
2. What is the constant term in 3x - 2x + 5? |
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Answer» 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 |
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| 22. |
solve by elimination 3(2x+y)=7xy3(x+3y)=11xy |
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Answer» 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 |
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| 23. |
(7xy - 8x) - (- 5xy + 3x) |
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Answer» (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 |
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| 24. |
prove that : (sinA-2sin^3A/ 2 cos^3-cosA)=tanA |
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Answer» 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 |
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| 25. |
3. If4tan A = 3, evaluate: (1tsinALEH S... 2> {(1+cosA) (1- cosA) |
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Answer» 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 |
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| 26. |
if m= cosecA-sinA, n= secA-cosA prove that(m^2n)^2/3+(mn^2)^2/3=1 |
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Answer» the question seems wrong.can you put up a picture? |
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| 27. |
. हल करें - 6x + 3y = 6212x + 4y = Sxy |
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Answer» Hit like if you find it useful |
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| 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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Answer» 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 |
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| 29. |
Subtract:(a)7xy from 2xy |
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Answer» 2xy -7xy=-5xy |
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| 30. |
Subtract:(a)7xy from 2vy |
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Answer» 5xy is the answer of your question -5xy is the right answer |
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| 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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Answer» use factor theorem it will gives you two equations and solve them to get answer |
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| 36. |
3(2x+y)=7xy;3(x+3y)=11xy |
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Answer» 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 If you find this answer helpful then like it. wrong |
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| 37. |
Write the constant term of : x2y - xy2 + 7xy - 3 |
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Answer» Constant terms are: -1, 7,-3 |
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| 38. |
(23. In the given figure, find 3 tan 0-2 sin a +4 cosa |
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Answer» 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 |
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| 39. |
1. Add Sxy, 6xy and 9xy |
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Answer» 5xy + 6xy + 9xy 11xy + 9xy 20xy 20xy is right answer ,.,. make sure to thanks |
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| 40. |
Exercise 12.21. Add 5xy, 6xy and 9xy. |
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Answer» the answer for this is 20xy Answer is 6xy + 5xy + 11xy = 20xy |
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| 41. |
.Find the value of-4x2y2+6xy+ 8x + 12y-1, when x=-2, y =-1. |
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Answer» -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 |
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| 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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Answer» =-xy answer your this |
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| 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 âsin 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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Answer» 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 |
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| 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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