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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. |
If the slope of the line passing through the two points (2,5) and (5,8) s representédtana, (where 0°<θ <90°), then find angle"e:by |
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Answer» slope of line =tan Φ8-5/5-2 = tan Φ3/3 = tan Φ1= tan Φtan 45 = tan Φ45 = ΦΦ = 45 |
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| 2. |
If the slope of the line passing through the two points (2,5) and (5,8) is represented bytano, (Where 00 0 <90), then find angle '0' |
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| 3. |
17. For the circuit shown in the diagram below4 V122312 |
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| 4. |
If x changes from 4 to 4.01 then find the approximate change in log x. |
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Answer»
X =4 take log both sideslogx = log 4 x +dx =4.01 take log both side log(x +dx) =log4.01 divide both expression,log(x +dx )/x =log(4.01)/log4 log(x +dx -x ) =log(0.01)logdx =log(10)⁻²log dx = -2 log10 = -2 × 2.3 = -4.6 log 10=2.3? |
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| 5. |
change the percent2.5 |
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Answer» 2/5×100=200/5=40Therefore,3:4=40% Sorry By mistake,2:5=40% Given 2:5 so 2/5×100=40%Therefore,40% |
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| 6. |
The base of a triangle is increased by 25% and theheight is decreased by 25%. What is the percentchange in the area of the triangle? |
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Answer» Area = 1/2 base x height= A= 1/2( 1.5b)(0.75h)1/2bh(1.125)) 1.125Aarea increased by 1.125-1= 0.125*100= 12.5 percentage |
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| 7. |
9. The value of a machine depreciates at the rate of 10% per annum. It was purchased 3 yearsago for 60000. What is the present value of the machine?(a) 53640 (b)51680(c)43740(d) 43470 |
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| 8. |
6. Prove that p l| m80° |
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Answer» In ΔPQR,45+35+Angle P=180Angle P=180-80Angle P=100 therefore, Angle DPA=180-100Angle DPA=80 Angle BOA=Angle DPA=80 Therefore p is parallel to m |
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| 9. |
6. Prove that V2 is a irrational number. |
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Answer» we cannot get it out of square r |
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| 10. |
6. Prove that:n!(n+2)n!(n + 1)! |
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| 11. |
6. Prove that 5 is irrational |
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Answer» it was not question |
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| 12. |
squangleuare of ride 5 cm. Four isoceless tri-with one side 5cm and the height fromosite corner to the side is 8em. Forconstructing a square pyramid by jointshem, how much paper will be required forit? (in cm2) |
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Answer» thanks a lot |
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| 13. |
If the length of one of the legs of a right tri-le is decreased by 10%, and the length of theangle rother leg is increased by 20%, then what is theapproximate percent change in the area of thetriangle? |
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Answer» Let original length of right triangle sides be B and HArea of triangle A =1/2xBxH If B decreased by 10% then length of leg= B - Bx10/100= Bx9/10 If H increased by 20% then length of leg= H + Hx20/100= Hx6/5 Area of triangle with changed dimentionsA1 = 1/2(Bx9/10)(Hx6/5)A1 = 27/50xBxH Percent change in Area of triangle = [(A1 - A) /A] x100= [(27/50XBXH - 1/2xBxH)/1/2XBXH]x100= [(2/50xBxH)/(1/2xBxH)]x100= 1/50x100= 2% |
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| 14. |
ĺş(The Cannizzaro's reaction is not given by) |
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Answer» Ans : ( b) Acetaldehyde Explanation:Cannizzaro's reaction doesn't undergoes containing of alpha-H atom in compound. Acetaldehyde is alpha - H atom containing compound while formaldehyde , benzaldehyde , furfural doesn't contain alpha- H atom . That's why acetaldehyde doesn't give Cannizzaro's reaction while all other compounds give it . |
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| 15. |
2. When a carpet is beaten with a stick, dust comes out of it. Explain.Ans Dust narticles have inertia of rest. As the carpet is beaten, it moves. But dust |
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Answer» Dust particles were at rest on the carpet. However when you beat the carpet, you are forcing the dust to move along with the carpet. Due to the dust having inertia, it doesn't move, or rather, it resists motion. This is why dust comes out of a carpet when it is beaten with a stick |
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| 16. |
\lim _{x \rightarrow 0} \frac{(1-\cos 2 x)}{(\cos 2 x-\cos 8 x)} |
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| 17. |
\begin{array}{l}{\text { Prove that }} \\ {\cos 2 x \cos \frac{x}{2}-\cos 3 x \cos \frac{9 x}{2}=\sin 5 x \sin \frac{5 x}{2}}\end{array} |
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| 18. |
21. एक वृत्त में यदि PQ वृत्त का व्यास है और R वृत्त कीपरिधि पर है जिससे /POR = 30°, तो ZRPQ= |
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Answer» 60° is the correct answer of the given question |
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| 19. |
e. The angle of clevation of the top of a building from the foot of the triangle of clevation of the top of the sower from the foot of the building is 6s S0 as bigh, find the height of the buildinghoe |
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| 20. |
50,Ifa is a root of 25 cos2 θ + 5 cos θ-12-0,<α<π,then sin 2α is equal toAIEEE 20021 |
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| 21. |
triconmity all formula please |
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| 22. |
x \text { and } y, \left\{\begin{array}{l}{x \cos ^{3} y+3 x \cos y \cdot \sin ^{2} y=14} \\ {x \sin ^{3} y+3 x \cos ^{2} y \cdot \sin y=13}\end{array}\right. |
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| 23. |
(छ (0 1९ छाए ० 30 3० SR 30, (21 89%) का मान हैं। |
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Answer» tan 1 . tan 2 . tan 3 ... tan 87 . tan 88 . tan 89 = LHS tan 1 . tan 2 . tan 3 ... tan (90 - 3 ) . tan ( 90 - 2 ) . tan ( 90 - 1) tan 1 . tan 2 . tan 3 ... cot 3 . cot 2 . cot 1 tan 1 . cot 1 . tan 2 . cot 2 . tan 3 . cot 3 ... tan 89 . cot 89 1 x 1 x 1 x 1 x ... x 1 As 1ⁿ = 1 = RHS Where n = any positive integer hit like if you find it useful |
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| 24. |
o. A 1.5 m tall boy is standing at some distance fromi a 30g that there is 11 tal building hie anglerclevation from, his eyes to the top of thc burldimg ine rcassthe huldinetowards the building. Find the distance he walked ws30 x7. From a porni on the erunut iln and the top s a |
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Answer» I want to ask a question of your soliution 28.5 how written as 57/2 |
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| 25. |
TT st. 30, 27, 24, 21, 18, す TTEOTFM 켜fsTQ1Find the maximum sum of the A.P. 30, 27, 24, 21, 18,..... |
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| 26. |
35 49 2112 30 40Find the HCF \frac{35}{12}, \frac{49}{30} \text { and } \frac{21}{40} |
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| 27. |
Ne add the additive inFdditive inverse oferse, T-21-2130 30r more rational numbers, thenumbers :(vii) |
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Answer» rational number are as follows-10/13 , -9/13 , -8/13 •••••• -1/ 13 ' 0/13 , 1/13 ••••••7/13 , 8/13 rational no. are 10/13,-9/13,-8/13...._1/13,0/13 |
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| 28. |
gh, a microwave whose marked price is . 18,000 at 20% discount. If the rate of VAT was Shi, thense ao pay for purchasing the crowave. Also find the profit percent, if the yout price oine |
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| 29. |
Prove that 3 + 2V5 is irrational |
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Answer» 3 + 2√5 = a/ b 2√5 =a/b -3 √5 =a-3b/2b √5 is rational. This contradicta the fact that √5 is irrational.So our supposition is incorrect. Hope this will help you. |
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| 30. |
Tfthe length of a rectangle is reduced by 50% and the breadth is increased by 25% it takes theshape of a square. Find the ratio of (i) the areas of the rectangle and the square, and(ii) the perimeters of the rectangle and the square. |
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Answer» If initial dimensions are l and b, then area = l*bNow new dimensions are 1.5 l and 1.25 b , then are = 1.5*1.25*l*b = 1.875 l*bratio is 1:11:1.875 No |
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| 31. |
13) Area of rhombus is 240cm2. If the ratio onength Ol 24. Volume of a cuboid shaped tank is 81 times its height. If length and height are 8cm and 5cm. Find itsbreadth62 2 tf breadl751 m I its breadth is 2(2x 5/21m. Find the perimeter of park.x 5/2)m. Find the perimeter of park. |
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Answer» in answer 8 is there or not thankyou |
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| 32. |
1. Examine the derivabilityhe specified points:(i)1x1 at x = 0 |
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Answer» |x| , when x > 0 then |x| will be x and its differentiation is 1 when x < 0 , then |x| will be -x and its differentiation is -1 since both differentiation are not equal. so it is not differentiable at x = 0 |
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| 33. |
2. Prove that 3+2V5 is irrational |
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| 34. |
4 x ^ { 2 } + 12 x + 3 = 0 ( b ) \cdot 2 x + 1 = \frac { 5 } { x + 2 } ( c ) \frac { x + 1 } { x } - \frac { x } { x + 1 } = 0 |
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| 35. |
Prove that 3 +2V5 is irrational. |
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| 36. |
2. Prove that 3 +2V5 is irrational |
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| 37. |
2. Prove that 3 +2v5 is irrational. |
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Answer» To prove: 3 + 2 root 5 is irrational Let 3 + 2 root 5 is rational therefore 3 + 2 root 5=a/b(where a and b are co prime integer ) root 5=a-3/2bbecause a-3/2b is rational therefore root 5 will also be rational But we know that,root 5 is irrationalthat is our assumption is wrongthat is 3+2 root 5 is irrational Like if you find it useful |
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| 38. |
Prove that 3 + 2V5 is irrational. |
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Answer» 3 + 2√5 = a/ b 2√5 =a/b -3 √5 =a-3b/2b √5 is rational. This contradicta the fact that √5 is irrational.So our supposition is incorrect. Hope this will help you. |
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| 39. |
11Vmi शक वस्तु ₹ 784 में खरीदी जिसमें 12% जीःएस.ही.1 वस्तु का मुल्य कया था? |
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| 40. |
mahima bought microwave whose Marked price is 18000 at 20% discount if the rate of vat 8% then find the amount she had to pay for purchasing the microwave also find the profit percent if the cost price of the microwave is Rs 12000 |
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| 41. |
12. A retailer sells a microwave oven for 26,400. There is a 25% profit on the cost price. How much didretailer pay for the microwave oven?Solit |
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Answer» Pots a clear picture please please solve |
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| 42. |
100br Find what length of canvas 2 m in width is required to make a conical tent 12m indiameter and 6.3 m in slant height. Also find the cost of the canvas at the rate ofRs. 12.50 per meter. (take n = 22/7)- L circular con are in the ratio 512 Tf its109CE |
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Answer» width of the canvas(L)=2m slant height=6.3m diameter =12m=> 2 × radius=12m=>radius(r)=6m therefore, area of canvas = curved surface of conical tent=>L × B=22/7 × rl=>L × 2=22/7 × 6 × 6.3=>L=59.4m It is given that, cost per 1 meter is Rs.12.50 therefore, cost of 59.4m cloth=Rs.12.50 × 59.4=Rs.742.50 |
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| 43. |
i2. In Fig. 9.41, if AB II DE and BD II FG such that ZFGH 125° and B55, find xand y.55"125Fig. 9.4113. In Fig. 9.42, side B of |
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| 44. |
वन द्विघात समीकरणों के मूलों की प्रकृति ज्ञात कीजिए। यदि मलों काज्ञात कीजिए।(i) 2-3x+5=0(i) 3 -43 x+4=0ii) 21-6r+3=0गीकरण में 1 का ऐसा मान ज्ञात कीजिए कि |
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| 45. |
Sa11V- 40-422. Expre2. Expressas a rational number with denominator 7.98 |
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| 46. |
1 3 21 [1Find x if [1x1]| 0 5 1||1|=00 3 2 x |
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| 47. |
If p = 3.42 X 10^5 and q = 12.3X10^-2, find the value of 3p x 2q |
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Answer» 3px2q=3(3.42*10^5)x2(12.3*10^-2)=10.26*10^5*24.6*10^-2=252.396*10^3 |
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| 48. |
I Calculate the value of ve |
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Answer» Value of √2 = 1.414 approximatelythanks The answer is 1.414 2^1/2=1.414213562373095048801688........ |
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| 49. |
Calculate the value of x |
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Answer» Total angles in this figure is 360°7x + 3x + 4x + 10x = 36024x = 360x = 360/24x = 60/4 = 15x = 15 |
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| 50. |
2. x + y = 5, x - y = 33. y = 2x - 6, y = 04. p = 2q - 1,9 = 5 - 3p5. 9x + 4y = 5, 4x - 5y = 96. x + 3y = 5, 3x - y = 5 |
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