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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. |
(-sin(5*theta) %2B sin(7*theta))/(cos(5*theta) %2B cos(7*theta))=tan(theta) |
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Answer» Sin/cos= tanthanks |
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| 2. |
4*(x - 3) %2B 12=-5*(x %2B 6) %2B 15 |
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| 3. |
4*x %2B x^3 - 3*x^2 - 12 |
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Answer» 3x^2 x^3 - 3x^2 + 4x - 3x^2(x - 3) + 4(x - 3)(x - 3)(x^2 + 4) |
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| 4. |
\frac { \operatorname { sin } 7 \theta - \operatorname { sin } 5 \theta } { \operatorname { cos } 7 \theta + \operatorname { cos } 5 \theta } = \operatorname { tan } \theta |
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Answer» LHS sin7x-sin5x/cos7x+cos5x=2cos(7x+5x/2).sin(7x-5x/2)/2cos(7x+5x/2).cos(7x-5x/2)i.e; cos(12x/2).sin(2x/2)/cos(12x/2).cos(2x/2)i.e., cos(6x).sin(x)/cos(6x).cos(x)i.e.,sinx/cosxi.e.,tanx=RHS similarly, |
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| 5. |
\tan \theta=1\frac{8 \sin \theta+5 \cos \theta}{\sin ^{3} \theta-2 \cos ^{3} \theta+7 \cos \theta} = ? |
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| 6. |
. If you subtract 5 from half of a number,the result is 20. What is the number? |
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Answer» 50 50 Let the number be xNow(1/2)x-5=20x-10=20×2x-10=40x=40+10x=50 Thus the number is 50 15 is correct answer 50 is the correct answer 50 is correct answer the number is =50half of the number =25subtract 5 from half of the number =25-5 =20Answer =50 50 is the right answer. 50 is the correct answer 12.5 Step-by-step explanation: Let's suppose that number is - x x/2 -5 = 20 x/2 = 20 + 5 x/2 = 25 x = 25/2 = 12.5 Therefore the number is 12.5 |
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| 7. |
Show that the points (2, 0), (-2, 0) and (0, 2) are the vertices of a triangleAlso state with reason the type of the triangle. |
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| 8. |
3 \operatorname { sin } ^ { - 1 } x = \operatorname { sin } ^ { - 1 } ( 3 x - 4 x ^ { 3 } ) , x \in [ - \frac { 1 } { 2 } , \frac { 1 } { 2 } ] |
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| 9. |
-x^(5/7) %2B x^(12/7) |
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Answer» x^12/7-x5/7x^12/7-x^5/7x^12/7/x-5/7x^12/7-5/7x^7/7x x is the correct answer x is correct answer in this questions x^12/7 -x^5/7=x12/7-5/7=x^7/7=1 |
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| 10. |
L.What should be added to 3.189 to get 7? |
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Answer» 7-3.189=4.189 this is the answer. |
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| 11. |
6. When you multiply a number by 6 and subtract 5 from the product, you get 7. Find the number. |
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Answer» sir your questions answer will be 2 as because if 2*6 Let x be the number.6x - 5 = 7 6x = 12 x = 2 x×6-5=77+5=1212÷6=2so x=2 6×2=12,, then 12-5=7 ,,,THE NUMBER IS 12 |
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| 12. |
3 \sin ^{-1} x=\sin ^{-1}\left(3 x-4 x^{3}\right), x \in\left[-\frac{1}{2}, \frac{1}{2}\right] |
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| 13. |
10 When 0° <A <90, solve the following equations:(i) sín 3A = cos 2A(ii) tan 5A-cot A. |
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Answer» sin3A = cos2Asin3A = sin(90- 2A)Cancelling sin from both sides.We get,3A = 90 - 2A5A = 90therefore A = 90/5 = 18 degrees. If you ask why did i change cosA on the RHS to sin(90-2A)....I used the identity cosA = sin(90-A).If you ask why did i cancel sin then i'll say sin3A is not sin of angle 3A and it is not to be confused with sinA because sinA is sin of angle A and sin3A is three times sin of angle A or Sin * 3A.. |
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| 14. |
\cos \theta=1 / 2, \text { find } \frac{\sec \theta+\csc \theta}{7-2 \sec \theta \cdot \csc \theta} |
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Answer» Cos theta = 1/2 = b/hb = 1, h = 2 , p= ?we know that,(h)² = (b)² + (p)²(p)² = (2)²-(1)²(p)² = 4-1p = ✓3cmTherefore,Sec theta = h/b = 2/1 tan theta = p/b = ✓3/1Cosec theta = h/p = 2/✓3Therefore,Sec theta + tan theta /7-2sec theta × Cosec theta.. give me full ans |
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| 15. |
3 \sin ^ { - 1 } x = \sin ^ { - 1 } \left( 3 x - 4 x ^ { 3 } \right) , x \in \left[ - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right] |
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Answer» thanks Bhaia |
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| 16. |
की. 2. एप 2 L 0. दरनरक पासे VT ST ta%m <की साधिकला रिलिखिश - o |
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Answer» Probability of getting an even number=3/6=1/2 |
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| 17. |
4 \cot \theta = 3 , \text { show that } \frac { \sin \theta + \cos \theta } { \sin \theta - \cos \theta } = 7 |
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| 18. |
If tan theta =5/7,find the value of 3sin theta +4cos theta/9sin theta - 4cos theta |
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| 19. |
State True or False. Give reason also.The angle of elevation of the top of a tower is 30°.If the height of the tower is doubled, then the angleof elevation of its top will also be doubled." (2) |
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| 20. |
| 64, 3x-Sy ~10 =0 (&° 6x — 10y =20 QIR पर में WK |
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Answer» a1/a2=b1/b2=c1/c2=1/2then the lines are coincidingtherefore many solution |
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| 21. |
विधा 8 Wk कह 0नट+सघ टन तट ol 2058]: 2 |
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Answer» 3x² - 2√6x + 2 = 0 (√3x)² - 2 × (√3x) × √2 + (√2)² (√3x - √2)² = 0 So, x = √2/√3 |
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| 22. |
The number increased by 10 is 16,find the number |
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Answer» First make the word statement into numeric X + 10 = 16X = 6 is the answer |
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| 23. |
8 What number should be subtracted from to get-3?7127(d) 13 |
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| 24. |
311. What number should be subtracted from to get 7 |
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| 25. |
\frac{\sin A+\sin 5 A+\sin 9 A}{\cos A+\cos 5 A+\cos 9 A}=\tan 5 A |
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| 26. |
\frac { \sin 4 A + \sin 5 A + \sin 6 A } { \cos 4 A + \cos 5 A + \cos 6 A } = \tan 5 A |
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Answer» (sin4a + sin5a + sin6a) / (cos4a + cos5a + cos6a) = = (2sin ((4a + 6a) / 2) * cos ((6a-4a) / 2) + sin5a) / (2cos ((4a + 6a) / 2) * cos ((6a-4a) / 2) + cos5a) = = (2sin5a * cosa + sin5a) / (2cos5a * cosa + cos5a) = = (sin5a (2cosa + 1)) / (cos5a (2cosa + 1)) = sin5a / cos5a = tan5a |
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| 27. |
cos(sin^-1 3/5+sin^-1 5/13) |
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Answer» sin^-1 (3/5) + sin^-1 (5/13) = sin^-1 (3/5 * 12/13 + 5/13* 4/5) = sin^-1 (56/65) = cos^-1(33/65) Now cos (cos^-1 33/65) = 33/65 |
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| 28. |
3 \sin \theta+5 \cos \theta=55 \sin \theta-3 \cos \theta=\pm 2 |
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Answer» 3sinx +5cosx=5squaring both siods9 sin^2x +25cos^2x+30sinxcosx=259+16cos^2x+30sinxcosx=2516cos^2x+30sinxcosx=1630sinxcosx=16sin^2x30sinxcosx-16sin^2x=0 sinx(30cosx-16sinx)=0either sinx =0 or tanx = 15/81) sinx=0cosx=15sinx-3cosx=-3 |
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| 29. |
(5*sin(theta) %2B 3*cos(theta))/(5*sin(theta) - 2*cos(theta))=7/2 |
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Answer» cotx=5/4; 5sinx+3 cosx/5sinx-2 cosx=7/2; 5(4/-3)+3(5/-3)/5(4/-3)-2(5/-3)=20+15/-3//20-10/-3=35/-3 x-10/-3=-350/-3=7/2=-3×7/350x2=21/700=3/10 7/2 is the correct answer of the given question 4cotA= 5cotA=5/4cosA/sinA=5/4cosA/5=sinA/4=k (let)cosA=4ksinA=4k5sinA+3cosA/5sinA-2cosA= 5×4k+3×4k/5×4k-2×5k20k+12k/20k-10k36k/10 sorry answer posted not complete so I am posting againcosA=5k sinA=4k5×4k+3×5k/5×4k-2×5k20k+15k/20k-10k35k/10k35/10=7/2 5 sinx+3 cosx / 5 sinx-2 cosx=5(4/3)+3(5/3)/5(4/3)-2(5/3)=20/3+15/3/20/3-10/3=35/3/10/3=35/10=7/2 |
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| 30. |
14. Find the zeros of the polynomial 5v5 x2 + 30x + 8/95. |
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Answer» 5√5x² + 30x + 8√5 = 0 5√5x² + 20x + 10x + 8√5 = 0 5x ( √5x + 4) + 2√5 ( √5x + 4) = 0 (5x + 2√5) ( √5x + 4) = 0 x = -4/√5 and -2√5/5 |
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| 31. |
244. What type of decimal form will the no.1.show?Give reason also.(2) |
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Answer» 0.192 is the best answer we get a type of decimal form which gives us an exact remainder |
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| 32. |
कल, दि. केक, केस- N Wk |
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| 33. |
1. The number decreased by 7 is 25, find the number.7 The number increased by 10 is 16 find the number. |
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Answer» Let x be the required number.x - 7 = 25 x = 25 + 7 = 32 let the no =x according to question x-7=25 x =25+7=32 |
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| 34. |
| ki) bele 55— जन X Wk T THE=X () |
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| 35. |
What should be added to twice the rational number -7/3 to get 3/7? |
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| 36. |
S) A two digit number is 3 more than 4 times the sum of its digits. If IS is added to thisnumber, the sum is equal to the number obtained by interchanging the digits. Find thenumber7 ninmsand the total cost of 7 books and 5 pens |
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Answer» Let the digits be x and y.Thus, number=10x+yNow,(10x+y) - 4(x+y)= 3.....(i)and(10x+y)+ 18=10y+x.....(ii) Solving (i)10x+y-4x-4y=3or,6x-3y=3or,2x-y=1....(1)Solving (ii)10x+y-10y-x=-18or, 9y-9x=18or,y-x=2...(2) (1)+(2)2x-y+y-x=1+2or,x=3Thus, y=x+2 (from (2))y=5Therefore the number= 10x+y=10x3+5=35 |
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| 37. |
Wk 0o o e T = |
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| 38. |
।।।।||||।।27. यदि 4 sin° 0 = 3 और 0" < 0 <90°, तब 1 + COS 9 का मान मालूम करें ।। |
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Answer» Sinx^2=3/4; Sinx=V3/2; Sinx^2+ cosx^×=1; (V3/2)^2-1= 3/4-1=3-4/4=1/4=1/2; V3/2=1+ 1/2 sinx^2+ cosx^2=1; (3/4)+ cosx^2=1; cosx^2=1-(3/4)=(4-3/4)=1/4; cosx=1/2; 1+cosx=1+1/2=2+1/2=3/2 |
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| 39. |
weget5U.Phat. Find two numbers such that one of them exceeds the other by 18 and their sum is 92 |
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| 40. |
1. State Euclid's division lemma and apply it to solve the following problems:(i) A number when divided by 27 gives 364 as quotient and 7 as remainderFind the number.(if) Find the number by which 546 should be divided to get 7 as quotient and7 as remainder. |
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Answer» Euclid’s division lemma: Euclid’s division lemma, states that for any two positive integers ‘a’ and ‘b’ we can find two whole numbers ‘q’ and ‘r’ such that a = b × q + r where 0 ≤ r < b. Euclid’s division lemma can be used to find the highest common factor of any two positive integers and to show the common properties of numbers. Can you please become my maths helper please. Can you help me on whatsapp please please this is my request please. =>let the number be x 7 should be the quoteient as well as remainder quoteient is 7 so, => 546 = x*7 +7 =>546 = 7x +7 =>7x = 546 - 7 =>7x = 539 =>x = 539/7 =>x = 77 Please add me on whatsapp this is my mom's Mobile so no is 9306418325 pleaae |
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| 41. |
2. Find the unknown angles marked in each ofthe following fgures:lii) P2x(iii)(iv)3x40%90°2x1100A(vi) A75°120°65°110°ach of the fallotui |
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Answer» I need all answers which are in the picture Please let me know the 6th sum also |
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| 42. |
5. Find the missing angle in each of the following:024040°90° 4765° |
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Answer» Please Tal Me Answer |
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| 43. |
5*(sin(100^circ)*cos(27^circ) %2B sin(27^circ)*cos(100^circ)) |
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| 44. |
find the relue of nandy with GolutionHy=7-0ta tyll -- 0 |
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Answer» x=4 and y=9 substitute these values in given equation |
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| 45. |
2yl |
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| 46. |
y?* -yl - 0)-x* |
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Answer» y² - xy ( 1 - x) - x³ y² - xy + x²y - x³ y ( y - x) + x² (y - x) ( x² + y) ( y - x) |
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| 47. |
What valie of yl make1.64 |
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Answer» 6.4-1.6y-1.6y+2.4 = 0 ; 8.8=3.2yy=8.8/3.5 = 2.5 |
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| 48. |
The points D, E, F of sides of triangle ABC are(3,4),(8, 9) and (6,7). Find thecoordinates of the vertices of the triangle. |
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| 49. |
Integrate : http://www.onlinebu.comL‘ (_\.2 5 c’.vt Yl |
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| 50. |
Mathematics for Class 63. Mark the following integers on a number line:(i) -5() -2(iv) 7(v) -13 |
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Answer» represent the follwing additions on a number line |
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