Saved Bookmarks
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. |
\frac { \cos 9 x - \cos 5 x } { \sin 17 x - \sin 3 x } = - \frac { \sin 2 x } { \cos 10 x } |
| Answer» | |
| 2. |
If sin x =-/5 , sin y =-10 , where 0 < x <豆,20 < y <-, then what is (x + y) equal to ? |
| Answer» | |
| 3. |
1.Evaluate each of following:(a) (\begin{array}{l}{(-24)+5} \\ {(-49)+(49)} \\ {-32 )+[(-15)+(1-2)+1-11\}}\end{array} |
|
Answer» a) -25÷ 5 = -5b) 25 ÷ (-5) = -5c) -36 ÷ (-9) = 4d) -49 ÷ (49) = -1e) 13 ÷ [ (-2) + (-11)] = 13 ÷ (-13) = -1f) 0 ÷ (-13) = 0g) -32 ÷ ( -15 + 13) = -32 ÷ -2 = 16 |
|
| 4. |
5. If sin (x - 20)cos (3x - 10)°, then find the value of x. |
|
Answer» wrong |
|
| 5. |
\text { prove that }\frac { \cos 9 x - \cos 5 x } { \sin 17 x - \sin 3 x } = - \frac { \sin 2 x } { \cos 10 x } |
|
Answer» LHS = (cos9x - cos5x)/(sin17x-sin3x) Use the formula,cosC - cosD = 2sin(C + D)/2.sin(D-C)/2 sinC-sinD = 2cos(C+D)/2.sin(C-D)/2 = {2sin(9x+5x)/2.sin(5x-9x)/2}/{2cos(17x+3x)/2.sin(17x-3x)/2}=-(sin7x.sin2x)/(cos10x.sin7x)= - sin2x/cos10x = RHS |
|
| 6. |
4, A cylinder is open at one end. The external diameter is 15 cm and its thickness is 3 cm. If the height ofthe cylinder is 11 cm and if 1 cm weighs 9 gm, find:(i) The capacity of the cylinder(ii) Weight of the metal used in the cylinder. (π = 3.14) |
|
Answer» Cylinder volume with external Diameter of 15 cm with height of 11 cm V₁ = πd²h/4 = π x 15² x 11 / 4 = 2475π/4 cm³ Cylinder volume of internal empty space with diameter of 9 cm (2 x 3 mm of thickness reduced) with height of 8 cm (3 cm thickness at bottom reduced and top is open) V₂=πd²h/4 = π x 9² x 8/4 = 648π/4 cm³ Effective volume of Cylinder material = V₁ - V₂ ⇒ (2475-648)π/4 = 1827π/4 = 1827 x (22/7) / 4 ⇒ 261 x 22/4 = 261 x 11/2 = 2871/2 = 1435.5 cm³ 1 cm³ weighs = 9 gm 1435.5 cm³ weighs = 1435.5 x 9 = 12,919.5 gms |
|
| 7. |
Question numbers 1 to b carry 1 nark eacH1. a and b are two positive integers such that the least prime factor of a is 3 and the least prime factor of b is5. Then calculate the least prime factor of (a + b).2 The ratio of the height of a tower and the length of its shadow on the ground is1. What is the |
| Answer» | |
| 8. |
K L M and N are points on side AB BC CD and DA respectively of a square ABCD such that AK=CM=DN. prove that KLMN is square |
|
Answer» As ABCD is a square, so AB = BC = CD = DA ...(1) Also AK = BL = CM = DN .....(2) Subtracting (2) from (1) We get AB- AK = BC - BL = CD - CM = DA - DN BK = CL = DM = AN ...(3) So now we have AK = BL = CM = DN AN = BK= CL = DM Squaring and adding AK² + AN² = BL² + BK²= CM² + CL² = DN² + DM² ...(4) But <A = <B = <C = <D = 90° By Pythagorean theorem (4) Becomes KN² = KL² = LM² = NM² So KN = KL = LM = NM So KLMN is a rhombus But <1 = <3 as triangles are congruent And < 1 + <2 = 90 So <2 + <3 = 90 Hence <KNM = 90° Therefore KLMN is a square |
|
| 9. |
K,L,M, N are points on the sides AB, BC, CD and DA respectivelyof square ABCD such that AK = BL = CM=DN. Prove that KLMN is a square |
| Answer» | |
| 10. |
25. K, L, M and N are points on the sides AB, BC, CD and DA respectivelyof a square ABCD such that AK = BL = CM = DN. Prove that KLMN is asquare. |
| Answer» | |
| 11. |
25. K, L, M and N are points on the sides AB, BC, CD and DA respectivelyof a square ABCD such that AK = BL = CM = DN. Prove that KLMN is asquare |
| Answer» | |
| 12. |
rectarigle25, K, L, M and N are points on the sides AB, BC, CD and DA respectivelyof a square ABCD such that AK--BL = CM = DN. Prove that KLMN is asquare. |
| Answer» | |
| 13. |
is.Howmanydifferentnumbers,greater than 50000 can be formed with the dis1, 1, 5, 9 |
| Answer» | |
| 14. |
If $ T_{n}=\sin ^{n} \theta+\cos ^{n} \theta, $ prove that:$ \frac{T_{3}-T_{5}}{T_{1}}=\frac{T_{5}-T_{7}}{T_{3}} $ |
| Answer» | |
| 15. |
\lim _ { n \rightarrow \infty } \frac { \pi } { n } \left\{ \sin \frac { \pi } { n } + \sin \frac { 2 \pi } { n } + \ldots + \sin \frac { ( n - 1 ) \pi } { n } \right\} |
|
Answer» answer is 2 |
|
| 16. |
Sarah bought a camera priced at? 2500. The store gave 15% off as discount. Hownuch did Sarah pay ? |
|
Answer» Cost price = 2500 Discount = 15% Discount rate = 2500*15/100 = 375 Sarah paid = 2500-375 = Rs.2125 Like my answer if you find it useful! |
|
| 17. |
Page:Date:_what is AR從, |
|
Answer» So AC = AB + BC 15 = AB + 9 AB = 15 -9 = 16 thx |
|
| 18. |
( a ) \operatorname { sin } ^ { 2 } ( n + 1 ) \theta - \operatorname { sin } ^ { 2 } n \theta = \operatorname { sin } ( 2 n + 1 ) \theta \cdot \operatorname { sin } \theta |
| Answer» | |
| 19. |
face. The total height of the toy is i5.5 cm. Find the tota9 How many terms of an A.P 9, 17, 25,...must be taken to give a sum of 636? |
|
Answer» A.p= 9,17,25a=9d=17-9=8Sum of n terms=n÷2[2a+(n-1)d 636=n÷2[2(9)+(n-1)8]636=n÷2[18+8n-8]636=n÷2[10+8n]1272=10n+8n^28n^2+10n-1272=02[4n^2+5n-636]=04n^2+5n-636=04n^2+53n-48n-636=0n(4n+53)-12(4n+53)=0(n-12)(4n+53)=0n-12=0n=12 12 terms must be given to sum of 636 |
|
| 20. |
s 30 circalar plates, aack of nadius 14 cm and thickness 3placnd one abvoce the other to form a cylindrical solid.Find () the total surface area,() rohume of the cylinder so formod |
| Answer» | |
| 21. |
2. Enter the value of x that makes the equation -8(x + 2) + 5x = 11 true. |
|
Answer» -8(x+2)+5x=11-8x -16 +5x = 11-3x = 27x= -9 |
|
| 22. |
Gar? Din the diffrence betweenvalue andthe blocethe face value of27650934in |
|
Answer» The place value of 7 in 27650934 = 70 lakhs = 70,00,000The face value of 7 in 27650934 = 7∴∴Required difference =7000000‒77000000‒7= 69,99,993 |
|
| 23. |
| O 12ay(e ‘-lfias"‘) iby\szt“;) £ |
|
Answer» hit like if you find it useful |
|
| 24. |
Fill in the missing numbers:35 5 |
| Answer» | |
| 25. |
NEW STYLETnsible for deflection of galvanometer neeWhich electrical phenomenon is respoin the given figure ?4.0 |
|
Answer» Electromagnetic Induction |
|
| 26. |
The mean of five consecutive odd numbers a, b, c, d, e is |
|
Answer» 1+3+5+7+9=25/5 answer:5 five consecutive odd numbers so mean is the middle number which is c. |
|
| 27. |
Monday, March 250Sarah measureHer meaWOSCE1. Enter the value of n so that the expression (-y + 2) + (9y - 7) is equivaleto (ny - 5).enter the valuen= |
|
Answer» (-y + 2) + (9y - 7) = ny - 5 (9y - y) + (2 - 7) = ny - 5 8y - 5 = ny - 5 ny = 8y n = 8 |
|
| 28. |
In a perfectly symmetrical distribution, the mode and mean are 42 and 49respectively. The approximate median of this distribution is(A) 47(C) 49(B) 48(D) s0 |
| Answer» | |
| 29. |
n7 Sin?Z & sin?Z s6 4 - |
| Answer» | |
| 30. |
Mahesh invested an amount of 12050 atsimple interest. He got an amount of13496 at the end of 2 yr. At what rate ofinterest did he invest? |
|
Answer» If you like the solution, Please give it a 👍 |
|
| 31. |
e moining33 km in the evcing Housfor does she hunin all 2 |
|
Answer» Seema runs in the morning = 2.37 kmSeema runs in the evening = 3.8 km Seema runs total distance = 2.37 + 3.8 = 6.17 km |
|
| 32. |
DuDatenadius ar well as huight of a conu aumis phuu and a cytindn aru sam hun ind |
| Answer» | |
| 33. |
ge nadiun ar well an huighd of a coneaanu samu hun Findhumis phuu and a cytindannaho of in Noluus |
|
Answer» please can you explain me how r square turned into cube |
|
| 34. |
49:59— nAO [n=1 |
|
Answer» 5n 2n---- - 4 - ---- = 19 9 5n - 2n-------------- = 5 9 3n = 9 × 5 n = 15 |
|
| 35. |
If (49-5-2 + (70-615) = as |
|
Answer» 4√3-5√5+7√3-6√5=a√3+b√511√3-11√5=a√3+b√5 Comparing a=11, b=-11 |
|
| 36. |
PAGE:I. IR ā=32-49-5 Ř is vectors inSpace them lal is |
|
Answer» |a|= 5✓2 is the correct answer. |
|
| 37. |
The deflection of a beam is given by y = 2x^3-9x^2+12x. Find themaximum deflection. |
|
Answer» By comparing d/dx with 0 we will get max value of xso dy/dx=6x^2-18x+12=0so x^2-3x+2=0so x=1 and 2so when x=1 y=2-9+12=5when x=2 y=16-36+24=4so max deflection=5 |
|
| 38. |
2. Are the numbers 35, 49, 5, 8 in proportion? |
|
Answer» For numbers to be in proportion Product of extremes = product of means Now,For numbers 35, 49, 5, 8Product of extremes = 35*8 = 280Product of means = 49*5 = 245 As, Product of extremes =/= product of means Therefore, given numbers are not in proportion |
|
| 39. |
\begin { equation } \lim _{x \rightarrow a} \frac{(\cos x-\cos a)}{(x-a)} \end { equation } |
| Answer» | |
| 40. |
The average of five consecutive odd numbers is 41. Whatis the largest number?(1) 47(2) 45(3) 43(4) 49(5) of these |
|
Answer» 45 is the answerif you need solutionjust comment 45 is the correct answer oknow likeacceptmeasbest 45 is the correct answer 45 is the correct answer. 45 is the correct answer 45is ths correct answer 45 is the correct answer..... |
|
| 41. |
5 In a perfectly symmetrical distribution, the mode and mean are 42 and 49respectively. The approximate median of this distribution is(A) 47(C) 49(B) 48(D) 50 |
| Answer» | |
| 42. |
A seller would make a profit of 12 % by selling a lunch box at Rs. 392. At what price should he sell it to make a profit of 15 %? |
| Answer» | |
| 43. |
Solve the equation for x: /3 cosx + sin zlve the equation for x :v2.V3 cos x + sin x = |
|
Answer» Divide both side by 2 3/√2∗cosx+1/2∗sinx=1 =>sinπ/3∗cosx+cosπ/3∗sinx=1 =>sin(x+π/3)=1 =>x=2kπ+π/6 k could be any integer. Plz give full ans |
|
| 44. |
Find the number of solutions of the equation $\tan x+\sec x=2 \cos x$$\cos x \neq 0,$ lying in the intervial $(0, \pi)$ |
| Answer» | |
| 45. |
) Solve the equationcos x-cos 2x + cos 3x0. |
|
Answer» cos 3x + cos x - cos 2x = 0[cos 3x + cos x ] - cos 2x = 02 cos [(3x + x)/2] .cos [(3x-x)/2] - cos 2x = 02 cos 2x . cos x - cos 2x = 0cos 2x [ 2 cos x - 1 ] = 0cos 2x = 0 or cos x = 1/2 = cosπ/32x = (2n +1 )π/2 or x = 2mπ +-π/3x = (2n + 1 )π/4 or x = 2mπ +-π/3 ; where n , m∈ I Like my answer if you find it useful! |
|
| 46. |
60. The H.C.F. of 2(x2 - y2) and 5(x3 - y2) is: |
|
Answer» H.C.F is (x-y) |
|
| 47. |
3- What value of the missing base would make these triangles similar?25 in60 in20 in48 in40 in |
|
Answer» Similar triangles have an equal ratio of sides.25/20 = 60/48 = 40/x 5/4 = 40/x x = 32 in |
|
| 48. |
5.9 A cantilever beam is as shown in figure. Themoment to be applied at free end for zero verticaldeflection at that point is9 KN |
|
Answer» Answer : 12 kN.m anti-clockwise |
|
| 49. |
9. How many pieces of 13 cm length can be cut from a 330 cm long rod? |
|
Answer» allegretto en he of Mr Webb mi oh egg by the my RM by oh that's jr RM my the pH Tu JG egg ki pH QF no |
|
| 50. |
G10. If vectors a 2+2j+3k, b+2) +kand 31+are such that(a + λ) is perpendicular to e, then find the value of λ. |
| Answer» | |