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. |
Let parabolas `y=x(c-x)` and `y=x^(2)+ax+b` touch each other at the point `(1,0)` then `b-c=` |
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Answer» Correct Answer - 1 `y=x(c-x) y=x^(2)+ax+b` `(dy)/(dx):|_("(1,0)")` `=c-2m_(1)(dy)/(dx):|_("(1,0)")=2x+a=2+a=m_(2)` Curve are touching at `(1,0)` so `m_(1)=m_(2)` `2+a=c-2`………..i Also `(1,0)` lies both the curve so `c=1`……….ii and `a+b=-1`……….iii by i, ii, iii `b=2,c=1,a=-3` |
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| 2. |
There are ________ in the classroom but only one teacher. A) many people B) much pupils C) a lot people D) a lot of pupils |
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Answer» Correct option is D) a lot of pupils |
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| 3. |
Mrs. Johnson is washing the girls’ hair. A) He is washing her hair. B) She is washing her hair. C) He is washing their hair. D) She is washing their hair |
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Answer» Correct option is D) She is washing their hair. |
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| 4. |
If the curve `C`in the `x y`plane has the equation `x^2+x y+y^2=1,`then the fourth power of the greatest distance of a point on `C`from the origin is___. |
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Answer» Correct Answer - 4 Let `x=rcostheta,y=rsintheta` `:.r^(2)(1+costheta,sintheta)=1` or `r^(2)=2/(2+sin2theta)` or `r_(max)^(2)=2` |
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| 5. |
You can’t eat that pear. It isn’t ______ yet. A) best B) pale C) ripe D) mature |
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Answer» Correct option is C) ripe |
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| 6. |
Tony is looking at ________ . A) she B) he C) her D) here |
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Answer» Correct option is C) her |
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| 7. |
Mrs. Johnson said that the mayor was very arrogant. A) official B) crude C) haughty D) attractive |
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Answer» Correct option is C) haughty |
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| 8. |
If the slope of the line through the origin which is tangent to the curve `y=x^(3)+x+10` is `m`, then the value of `m-12` is |
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Answer» Correct Answer - 1 `(dy)/(dx):|_(x_(1),y_(1))=3x_(1)^(2)+1=(y_(1))/(x_(1))` `3x_(1)^(3)+x_(1)=x_(1)^(3)+x_(1)+16` `x_(1)=2`, or `y_(1)=26:.m=13` |
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| 9. |
Chris became aware of his mistake instantly A) entirelyB) frequently C) obviously D) immediately |
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Answer» Correct option is D) immediately |
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| 10. |
If 3x = cosecθ and \(\frac{3}{\text{x}}\) = cotθ, find the value of 3 \((x^2-\frac{1}{x^2}).\) |
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Answer» Given that 3x = cosecθ and \(\frac{3}{x}\) = cotθ Now, cosec2θ = (3x)2 = 9x2. And cot2θ = \((\frac{3}{x})^2=\frac{9}{x^2}.\) We know that cosec2θ - cot2θ = 1 ∴ 9x2 - \(\frac{9}{x^2}=1\) ⇒ 9 \((x^2-\frac{1}{x^2})=1\) ⇒ 3 \((x^2-\frac{1}{x^2})=\frac{1}{3}.\) Hence, the value of 3 \((x^2-\frac{1}{x^2})\) is \(\frac{1}{3}.\) |
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| 11. |
The curve `y=2e^(2x)` intersect the `y`-axis at an angle `cot^(-1)|(8n-4)/3|` then the positive value of `n` is |
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Answer» Correct Answer - 2 `y=2e^(2x)` intersect `y` axis at `(0,2)` `(dy)/(dx)=4e^(2x):.(dy)/(dx):|_("at"x=0)=4` `:.` Angle of intersection with `y`-axis `=(pi)/2-tan^(-1)4=cot^(-1)4` `:.n=2,-1` |
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| 12. |
Find the rate of change of the volume of a sphere with respect to itssurface area when the radius is 2cm. |
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Answer» Correct Answer - 1 `V=4/3pir^(3),S=4pir^(2)` `(dV)/(dr)=4pir^(2),(dS)/(dr)=8pir^(2)` `implies(dV)/(ds)=(dV//dr)/(dS//dr)=r/2` when `r=2` `(dr)/(dS)=1` |
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| 13. |
The tangents from `(1, 2sqrt2)` to the hyperbola `16x^2-25y^2 = 400` include between them an angle equal to:A. `(pi)/6`B. `(pi)/4`C. `(pi)/3`D. `(pi)/2` |
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Answer» Correct Answer - D `(1,2sqrt(2))` lies on director circle or `(x^(2))/25-(y^(2))/16=1` i.e. `x^(2)+y^(2)=9` `:.` Required angle `pi//2` |
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| 14. |
Find the equation of the parabola whose focus is S(3, 5) and vertex is A(1, 3). |
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Answer» Equation of the axis y – 3 = (3 - 5/ 1 - 3) (x - 1) = x – 1 x – y + 2 = 0 The directrix is perpendicular to the axis. Equation of the directrix is x + y + k = 0 Co-ordinates of Z be (x, y) A is the midpoint of SZ Co-ordinates of A are (3 + x/2, 5 + y/ 2) = (1, 3) 3 + x/2 = 1, 5 + y/2 = 3 3 + x = 2, 5 + y = 6 x = 2 – 3 = – 1, y = 6 – 5 = 1 Co-ordinates of Z are (–1, 1) The directrix passes through Z (–1, 1) – 1 + 1 + k = 0 ⇒ k = 0 Equation of the directrix is x – y = 0 Equation of the parabola is (x – α)2 +(y – β)2 (lx + my + n)2/ l2 + m2 (x – 3)2 + (y – 5)2 = (x + y)2/ 1 + 1 ⇒ 2(x2 – 6x + 9 + y2 – 10y + 25) = (x + y)2 ⇒ 2x2 + 2y2 – 12x – 20y + 68 = x2 + 2xy + y2 i.e., x2 – 2xy + y2 – 12x – 20y + 68 = 0. |
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| 15. |
Evaluate : ∫xe4dx for x∈[1, 2] |
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Answer» [xex]21 - ∫ex. dx for x ∈ [1, 2] |
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| 16. |
Evaluate: ∫(1/(5e-x))dx |
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Answer» 1/5∫exdx = 1/5ex + c |
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| 17. |
In the figure S and S’ are foci of the ellipse, \(\frac{x^2}{25}+ \frac{y^2}{16} =1\) and P is a viable point on the ellipse.1. Find the co-ordinate of foci. 2. Find the distance between S and S1.3. What is the maximum area of the triangle PSS’. |
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Answer» 1. Since 25 > 16 the standard equation of the ellipse is \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) ⇒ a2 = 25; b2 = 16 c2 = a2 – b2 = 25 – 16 = 9 ⇒ c = 3 Coordinate of foci are (±3, 0). 2. Distance between the two focus is 3 + 3 = 6. 3. Maximum area is attained when the point P reaches the point the ellipse meet the y |
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| 18. |
The line x – 1 = 0 is the directrix of a parabola, y2 = kx then1. Find the value of k.2. Find the vertex, focus, axis of parabola and length of latus rectum of the parabola. |
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Answer» 1. Given directrix x – 1 = 0, so a = 1, then the equation of the parabola is y2 = -4ax ⇒ y2 = -4x Hence k = – 4 2. Vertex is (0, 0) Focus of SS’ = (-1, 0) Length of latus rectum = 4 × 1 = 4. |
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| 19. |
Evaluate: ∫(1/x)dx for x ∈ [1, 2] |
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Answer» (log x)21 = log2 |
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| 20. |
Evaluate ∫\(\frac{3^xlog3}{(3^x + 1)}dx\) |
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Answer» = log(3x + 1) + C ∴ ∫\(\frac{f^1(x)}{f(x)}dx\) = log(3x + 1) |
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| 21. |
Evaluate ∫\(\frac{1 + cos2x}{1 - cos2x}dx\) |
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Answer» \(= \int\frac{2cos^x}{2cosx} {d}x = \int\cos^2dx \) \(= \int(cosec^2x - 1)dx = - cosx - x + c\) |
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| 22. |
Evaluate : \(\int\frac{3}{x}dx\) |
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Answer» \(\int\frac{3}{x}dx = 3\int\frac{1}{x}dx = 3logx + C\) |
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| 23. |
Find the equation of the straight line passing through (–4, 5) and cutting off equal intercepts on the coordinate axes. |
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Answer» Let a, b be the intercepts of the line Intercepts are equal => a = b Equation of the line is x/a+ y/b=1 =>x + y = a The line passes through (–4, 5) => –4 + 5 = a => a = 1 So, Equation of the required line is x + y = 1. |
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| 24. |
Don't forget to explain. |
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Answer» Cost price = RS.1600. Profit =12% of cost price = Rs1600*12/100=Rs192 So selling price =cost price + profit =RS.(1600+192)=RS.1792. Cost Price of Cycle = Rs 1600 Sold at profit 12% = 12% of 1600 = 1600×12/100 = 16×12 = Rs 192 i.e when cycle was sold then the profit = Rs 192 So, Selling Price of Cycle = Cost Price + Profit Therefore, Selling Price = Rs 1792 |
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| 25. |
What was the percentage of scouts from Ahmedabad, if in a scout camp 40% of scouts were from Gujarat and 20 % of these were from Ahmedabad? |
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Answer» Let the total number of scouts be 100 As 40 % of the total scouts are from Gujarat. So, 40 % of 100 = (100*40)/100 = 40 scouts are from Gujarat. 20 % of the total scouts from Gujarat are from Ahmedabad. So 20 % of 40 = (40*20)/100 = 8 scouts Percentage of scouts in the camp from Ahmedabad = (8*100)/100 = 8 % |
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| 26. |
Nidiya limited was incorporated on 1stApril 2017 with registered office in Mumbai. The capital clause of memorandum of Association reflected a registered capital of 8,00,000 equity shares of Rs.10 each and 1,00,000 preference shares of Rs.50 each. Since some large investments were required for building and machinery the company in consultation with vendors,Ms.VPS Enterprises, issued 1,00,000 equity shares and 20,000 preference shares at par to them in full consideration of assets acquired. Besides this the company issued 2,00,000 equity shares for cash at par payable as Rs 3 on application, 2 on allotment, 3 on first call and 2 on second call. Till date second call has not yet been made and all the shareholders have paid except Mr. Ajay who did not pay allotment and calls on his 300 shares and Mr. Vipul who did not pay first call on his 200 shares. Shares of Mr. Ajay were then forfeited and out of them 100 shares were reissued at Rs.12 per share. Based on above information you are required to answer the following questions. 1. Shares issue to vendors of building and machinery, Ms. VPS Enterprises, would be classified as: a. Preferential Allotment b. Employee Stock Option Plan c. Issue for Consideration other than cash d. Right Issue of Shares 2. How many equity shares of the company have been subscribed? a. 3,00,000 b. 2,99,500 c. 2,99,800 d. None of these 3. What is the amount of security premium reflected in the balance sheet at the end of the year? a. ₹200 b. ₹600 c. ₹400 d. ₹ 1,000 4. What amount of share forfeiture would be reflected in the balance sheet? a. ₹600 b. ₹900 c. ₹200 d. ₹ 300 |
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Answer» 1. ( c) Issue for consideration other than cash. 2. ( c) Rs.2,99,800 3. ( c) Rs.400 4. (a) Rs. 600 1.c2.c 3.a 4.b |
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| 27. |
Apples, salad, and grass are all usually ___ |
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Answer» Correct answer is green |
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| 28. |
The name of the periodical published by Gandhi during his stay in South Africa was (a) Navjivan (b) India Gazette (c) Afrikaner (d) Indian Opinion |
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Answer» (d) Indian Opinion |
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| 29. |
'Family of orientation' is that in which-(a) One is born(b) One is reared up(c) One is educated(d) One is matured. |
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Answer» 'Family of orientation' is that in which One is born. |
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| 30. |
Grapes are usually green or ___. |
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Answer» Correct answer is purple |
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| 31. |
VIJAYA SHANKAR, an Ex-Indian cricketer decided to start a cricket academy to train the young enthusiastic players of down south. With the support and guidance of his family he started the Star cricket academy at Tirunelveli township area on 1st April 2020. Land was donated by his grandfather worth Rs. 10,00,000 as per his will. His father Shankar donated Rs.5,00,000 for the construction and running the academy. He spent Rs.3,00,000 for construction of the pavilion. 200 players of Tirunelveli joined the academy and they paid yearly subscription of Rs.1200 each. 10 players paid in advance for the next year 2021 -22. Vijayashankar appointed well experienced coach for them, the coach fee amounted to Rs. 1,20,000 p.a. The maintenance expenses amounted to Rs.75,000. Bats and balls purchased during the year amounted to Rs.15,000. Closing stock of bats and ball amount to Rs.1000. Based on the above information you are required to answer the following question. 1. What is the Primary source of income for the academy? 2. The amount of subscription to be credited to income and expenditure account----------- 3. How will you treat the land donated by his grandfather? 4. The liability towards advance subscription amounted to: (a) Rs. 12,000 (b) Rs.24,000 (c) Rs.1,200 (d) Rs.1,20,000 5. The amount of subscription received as per Receipts and payments Account of Star cricket club is: (a) Rs.2,52,000 (b) Rs.2,40,000 (c) Rs.2,50,000 (d) None of the above 6. What amount should be charged to the Income and Expenditure account for bats and balls consumed during the year? (a) Rs.15,000 (b) Rs.16,000 (c) Rs.14,000 (d) Rs.13,500 |
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Answer» 1. Subscription 2. Rs.2,40,000 3. Vijaya Shankar’s grandfather donated a land for cricket coaching which is to be treated as legacy and is to be capitalized. 4. (a) Rs.12,000 5. (a) Rs.2,52,000 6. ( c) Rs.14,000 |
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| 32. |
Sterlingenterprises is a partnership business with Ryan, Williams and Sania as partners engaged in production and sales of electrical items and equipment. Their capital contributions were Rs.50,00,000, Rs.50,00,000 and Rs.80,00,000 respectively with the profit the sharing ratio of 5:5:8. As they are now looking forward to expanding their business, it was decided that they would bring in sufficient cash to double their respective capitals. This was duly followed by Ryan and Williams but due to unavoidable reasons Sania could not do so and ultimately it was agreed that to bridge the shortfall in the required capital a new partner should be admitted who would bring in the amount that Sania could not bring and that the new partner would get share of profits equal to half of Sania’s share which would be sacrificed by Sania only. Consequent to this agreement Ejaz was admitted and he brought in the required capital and Rs.30,00,000 as premium for goodwill. Based on the above information you are required to answer the following questions. 1 What will be the new profit-sharing ratio of Ryan, Williams, Sania and Ejaz?(a) 1:1:1:1 (b) 5:5:8:8 (c) 5:5:4:4 (d) None of the above 2 What is the amount of capital brought in by the new partner Ejaz? (a) Rs.50,00,000 (b) Rs.80,00,000 (c) Rs.40,00,000 (d) Rs.30,00,000 3 What is the value of the goodwill of the firm? (a) Rs.1,35,00,000 (b) Rs.30,00,000 (c) Rs.1,50,00,000 (d) Cannot be determined from the given data. 4. What will be correct journal entry for distribution of Premium for Goodwill brought in by Ejaz? (i) Ejaz Capital A/c ……..Dr. 30,00,000 To Sania’s Capital A/c 30,00,000 (Being………..) (ii) Premium for Goodwill A/c……Dr. 30,00,000 To Sania’s Capital A/c 30,00,000 (Being……..) (iii) Premium for Goodwill A/c……Dr 30,00,000 To Reyan’s Capital A/c 8,33,333 To William’s Capital A/c 8,33,333To Ejaz’s Capital A/c 13,33,333 (Being………..) (iv) Premium for Goodwill A/c……Dr 30,00,000 To Reyan’s Capital A/c 10,00,000 To William’s Capital A/c 10,00,000 To Ejaz’s Capital A/c 10,00,000 (Being……..) |
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Answer» 1 ( c) 5:5:4:4 2 (b) Rs.80,00,000 3 (a) Rs.1,35,00,000 4 (b) Premium for Goodwill A/c…………….Dr 30,00,000 To Sania’s Capital A/c 30,00,000 |
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| 33. |
What drink is usually made from grapes and is classified as red, white or rose? |
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Answer» Correct answer is wine |
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| 34. |
India’s population is projected to increase from 1.2 billion today to an estimated 1.6 billion by 2050. This happens due to(a) Population momentum (b) Population explosion (c) Population policy (d) National Health Policy |
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Answer» (a) Population momentum |
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| 35. |
When the wine is distilled and matured it becomes ___ |
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Answer» Correct answer is brandy |
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| 36. |
Ageing population implies(a) Low dependency ratio (b) High dependency ratio (c) Window of economic opportunity (d) High death rate |
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Answer» (b) High dependency ratio |
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| 37. |
Swami Dayananda had translated the _______ into Hindi. (a) Rig Veda and Yajur Veda(b) Four Vedas (c) Sama Veda and Atharva Veda (d) Sama Veda and Yajur Veda |
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Answer» (a) Rig Veda and Yajur Veda |
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| 38. |
Dandi March started on _____ 1930. (a) 12th March (b) 12th April (c) 12th February (d) 12th May |
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Answer» (a) 12th March |
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| 39. |
Who wrote ‘Shakunthala’? |
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Answer» Kalidasa wrote the famous drama Shakunthala. |
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| 40. |
Which of the following factors is not responsible for the caste system to become invisible for the upper caste, urban middle and upper classes in the contemporary period? (a) Sub sidised public education (b) Expansion of state sector jobs after independence (c) opportunities offered by rapid development (d) no inherited educational or economic capital |
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Answer» (d) no inherited educational or economic capital |
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| 41. |
The Dandi March undertaken by Gandhi was (a) Aroutine March (b) Apart of the Quit India Movement (c) Apart of the Civil Disobedience Movement(d) Ademonstration of Congress power |
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Answer» (c) Apart of the Civil Disobedience Movement |
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| 42. |
Who had conceived and founded the Ramakrishna Mission? (a) Swami Muktananda (b) Annie Besant (c) CR Das (d) Swami Vivekananda |
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Answer» (d) Swami Vivekananda |
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| 43. |
Madame HP Blavatsky had laid the foundation of the Theosophical Society in the year (a) 1853 (b) 1864 (c) 1875 (d) 1886 |
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Answer» Madame HP Blavatsky had laid the foundation of the Theosophical Society in the year 1875. |
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| 44. |
When did the first Battle of Panipat take place? |
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Answer» In 1526 C.E. |
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| 45. |
Name the founder of the Bahamani dynasty. |
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Answer» Allaud-din-Hasan Gangu Bahaman Shah. |
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| 46. |
What are the two important issues which gave rise to trial movements? |
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Answer» The issues relating to control over vital econimic resouces like land and specially forests and matters relating to eithnic-cultrural identity. 2.The coming of private property in land has also adversely affected tribes. 3.The most recent such example is the series of dams being buile on the Narmada. 4. Dikas-migrant traders and money lenders-grabbed wealth, leading to impoverishment. 5. Acquisition of land for large irrigarion projects 6. Survey and settlement operations, which were held up, camps closed down etc. 7. Collection of issue rent and cooperative duse which were resisted. |
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| 47. |
Name the farmer centric TV Channel launched by the PM Narendra Modi on 26th May 15?1. Krishi TV2. Harith TV3. Kisan TV4. DD Kisan |
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Answer» Correct Answer - Option 4 : DD Kisan The correct answer is DD Kisan.
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| 48. |
Name the Capital of the Dutch in India. |
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Answer» Pulicat was the capital of the Dutch in India. |
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| 49. |
What is meant by the age structure of the population |
| Answer» The age structure of the population sefezs to the propontion of persona in dfferent ags in relacion to the total popalation. The age of development and the average ife expectanicy Eg:0-14, 15-59,60+ age groups. | |
| 50. |
Which was the birth place of Madhwacharya? |
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Answer» Pajaka near Udupi was the birth place of Madhwacharya. |
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