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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. |
al? sinx. Evaluate : 1sin'x + cos' |
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| 2. |
T7-TT 河村丽莉阿!JH 1. (a)Lim log,x |
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Answer» using L.H rule lim x→1 (1/x)/(1) = 1/1 = 1 |
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| 3. |
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + TT. |
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| 4. |
TN न कक S RSg . el e e 0 1 1 S neg e 86 केTt sv |
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Answer» hit like if you find it useful |
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| 5. |
28. f4 affah-tan (1) + tan(2) + tan '(3) = Tt.Prove that : tan-'(1) + tan '(2)+tan (3)= m. |
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Answer» tan–1 [1] + tan–1 [2] + tan–1[3]= tan–1 1+2+3-6 ---------- 1-2-6-3= tan–1 (0)= _ ^ |
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| 6. |
30. At what price should a 6.25% 100 share be quoted when re money31, At what price should a 625% t50 share be quoted when the money is worth 10%?1 diidond of 5 |
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Answer» 6.25% worth money is 50*6.25/10=31.25 |
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| 7. |
60 each when4. Find the cost of 85 shares ofquoted at 63.25. |
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Answer» Cost of one share = 60Each share is quoted at a new value of 63.25Hence cost of 1 share = 63.25cost of 85 shares = 85 x 63.25= 5376.25 Rupees |
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| 8. |
Find s10 for an A.P.:1/6,1/4,1/3 |
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Answer» 1/6 , 1/4 , 1/3 ,... are in A.P first term = a = a1 = 1/6 common difference ( d ) = a2 - a1 d = 1/4 - 1/6 d = ( 3 - 2 ) / 12 d = 1/2 S10 = ( 10/2 ) [ 2 × 1/6 + 9 × 1/2 ] = 5 [ 1/3 + 9/2 ] = ( 5/6 ) ( 2 + 27 ) = ( 5 × 29 ) / 6 = 145/6 why you take (3-2)/12 inplace 1/3 1/2 |
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| 9. |
Given:A3=15,S10=125 find d and a10 |
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| 10. |
(2) For an A.P. 6, 4, 2, ..., find S10 |
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| 11. |
6. If each edge of a cube is tripled, then find how many times will its volume become? |
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Answer» If you find this solution helpful, Please give it a 👍 |
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| 12. |
Section - B (16(Question numbers 7 to 14 cQ. 7Find the joint equation of the lines xty-3-0 and 2x0Find Ifysinx |
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| 13. |
EXERCISE 145M36. AB and C ae duee geins on acle widh centre Osuch thas 4B0C- andLAOB PFDis a peint on the circle other |
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Answer» Given: ∠AOB = 60° ∠BOC= 30° Here,∠AOC = ∠AOB + ∠BOC ∠AOC = 60°+30° ∠AOC = 90° Since Arc ABC makes an angle of 90° at the centre of the circle. ∠ADC= 1/2∠AOC [SINCE THE ANGLE SUBTENDED BY AN ARC AT THE CENTRE IS DOUBLE THE ANGLE SUBTENDED BY IT AT ANY POINT ON THE REMAINING PART OF THE CIRCLE] ∠ADC= 1/2(90°) ∠ADC= 45° Hence, ∠ADC= 45° |
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| 14. |
In the figure,AB=AC,CD=CE. IfangleABC=50°, then findangleCED |
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| 15. |
show that the series\sum\left(\frac{1}{2}\right)converges2ăŤ1 ( |
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| 16. |
24 Reduction formula for Jtan'x dx for an integer ne2 and deduce thevalue of J tanx dx |
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| 17. |
Findthevalueof y"Sl.2. 81.3 12%n 15%of x = 4oodx = 800al x 600dx = 900 |
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Answer» 1)80002)100003)50004)6000 1)80002)100003)50004)6000 1.8,000 2.10,0003.5,0004.6,000 |
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| 18. |
Dith safet to-lce |
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| 19. |
(1) For an A.P., if S10 150 and S 126, 10(A) 24 (B) 22 (C) 26 (D) 20 |
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Answer» 150=5(2a+9d)30=2a+9d 126=(9/2)[2a+8d]28=2a+8d Subtract2=d30-18=2aa=12/2=6 t10=a+9d6+18=24Option A |
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| 20. |
godS10aoplpes1 to aet the |
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Answer» 5x/7 = 31.5 x = 31.5*7/5 x = 44.1 Amount of tin = 44.1-31.5 g = 12.6 gm |
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| 21. |
The value of stanke dx is |
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Answer» hope it helps u |
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| 22. |
dxThe value of +log x |
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| 23. |
(i) x4-2x3-3x2 + 2x + 2 |
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Answer» x*x*x*x - 2x*x*x - 3x*x + 2x + 2 = x*x*x*x - x*x*x - x*x*x + x*x - 4x*x + 4x - 2x + 2 = x*x*x(x-1)-x*x(x-1)-4x(x-1)-2(x-1) = (x*x*x-x*x-4x-2)(x-1) |
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| 24. |
= "‘V\—‘wr:éw‘\\'fi e R Syहै... ] R EE ee |
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| 25. |
Prove that sequence,\sqrt{2}, \sqrt{2 \sqrt{2}}, \sqrt{2 \sqrt{2 \sqrt{2}}}converges to 2 |
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| 26. |
9. In Fig. 10.38, AC L CE and measures ofLA: ZB: ZC are in the ratio of 3:2:1,respectively. Find the measure of ZECD.Fig. 10.38 |
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Answer» since angles A, B and C are in 3:2:1 therefore, let A=3x, B=2x, C=xnow, sum of all angles of a triangle is 180°hence, 3x+2x+x=1806x=180x=180/6x=30°=angle Cnow, angleC + angleACE +angleECD =180(they form a straight line)therefore, 30+90+angleECD=180angleECD=180-90-30angleECD=180-120angleECD=60° |
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| 27. |
If $ S_{1}, S_{2} $ and $ S_{3} $ be respectively the sum of $ n, 2 n $ and 3$ n $ terms of a G.P. prove that$ S_{1}\left(S_{3}-S_{2}\right)=\left(S_{2}-S_{1}\right)^{2} . $ What happens if common ratio is 1$ ? $ |
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| 28. |
A train departs from Delhi at 10:30 a.m. and arrives Ahmedabad at 23:50 p.m. If thespeed of the train is 75 km/h, find the distance between Delhi and Ahmedabad.. |
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Answer» time = 10;30 am to 23:50 pmduration - 13hour 20 minuteafter converting minutes to hour13.166 hours |
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| 29. |
74. If orthocenter and circumcentre of triangle arerespectively (1, 1) and (3, 2), then theco-ordinates of its centroid are |
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Answer» As we know that orthocentre, centroid and cricumcentre are collinear and centroid divides the line segment joining ortho centre and circumcentre in the ratio 2 : 1. If the points of orthocentre and circumcentre are(1,1)and(3,2)(1,1)and(3,2)respectively the co-ordinate of centroid is: (2.3+1.1/2+1,2.2+1.1/2+1)=(7/3,5/3) |
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| 30. |
an aeroplane leaves an air port and flies due north at a speed of 1000km per hour . At the time, another aeroplane leaves the same airport and flies due to West at a speed of 1200km per hour.how far apart will be the Planes after 1/2 hours? |
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| 31. |
\sqrt { - 2 + 2 \sqrt { - 2 + 2 \sqrt { - 2 + \dots \infty } } } |
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Answer» suppose x=root(-2+2root(-2+2root(-2...)))so x=root(-2+2x)by taking squarex^2=-2+2xx^2-2x+2=0x=(2+root(4-8))/2 or (2-root(4-8))/2 =(2+2i)/2 (2-2i)/2 =1+i 1-i |
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| 32. |
Factorise 2 \sqrt{2} x^{3}+\frac{1}{2 \sqrt{2}} y^{3}+\frac{6}{\sqrt{2}} x^{2} y+\frac{3 \sqrt{2}}{2} x y^{2} |
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| 33. |
T R e e il जिस कल का गुर2] Ge गिल”. |
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| 34. |
व अर रा नके ८. और # सापेक्षत: अभाज्य संख्याएँ हैं, तो उनका लस, (1.00) क्या हेंR e et e s e e R |
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Answer» यदि a और b अभाज्य संख्या है LCM = a × b = ab acetyldehyde ammonia |
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| 35. |
2 + \sqrt { 2 } + \frac { 1 } { 2 + \sqrt { 2 } } + \frac { 1 } { \sqrt { 2 } - 2 } |
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| 36. |
\frac 3 \sqrt 2 - 2 \sqrt 3 3 \sqrt 2 %2B 2 \sqrt 3 %2B \frac \sqrt 8 \sqrt 3 - \sqrt 2 |
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| 37. |
Is there any naturalnumber that has nopredecessor?Is there any naturalnumber which has nosuccessor? Is there aNd last natural number? |
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Answer» Yes 1 is a natural number which has no predecessor |
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| 38. |
SECTION-AQuestion numbers 1 to 6 carry 1 mark each.atkčąä¸˝Ifx = 3 is one root of the quadratic equation r-2k-6 = 0, then find the value of k30/1 |
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| 39. |
A train leaves Delhi at 10:30 p.m and reaches Bhopal at 6.25 a.m. How long oetake to reach Bhopal? |
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Answer» Calculate total time hence10:30pm-5:30am--7 hoursand 5:30-6:35am--55minuteshence total time will be 7hours55minutes |
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| 40. |
uestioynumbersI to 6 carry 1 mark each.clI Find the number to be added to the polynomial-5x + 4, so that 3 is the zero of thenomial2. For the following distribution |
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| 41. |
aLes Bhopal atioill velhi to Bhopalat 04 : 50 hours and reaches Bengaluru at 07:25 hours.How long,aeroplane leaves Delhidoes it take to reach Bengaluru? |
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Answer» For this calculate the timeHence04:50-06:50-2 hoursAnd from 06:50-07:25=25+10=35minutesHence total time is 2 hours 35 minutes |
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| 42. |
9. In Fig. 10.38, AC I CE and measures ofZA B C are in the ratio of 3 2 1respectively. Find the measure of ZECD13Fig. 10.38 |
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| 43. |
write a critical appreciation of the poem "if.1*2 + 2*3 +....... . n(n+1) =n(n+1)(n+2) __________ 3 |
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Answer» your first reply is good |
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| 44. |
1. If fx)log (1+x) and g(r)- e, then value of[HSB 2018/gof (x) is:(A) el +x(C) log r(D) none of these. |
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Answer» f(X)= log(1+X), g(X)=e^x. gof(X) = e^f(X)= e^[log(1+X)]=1+X. Please hit the like button if this helped you |
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| 45. |
log x) dx |
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Answer» t=log xx= e^tdx=e^tdttherefore ,integral t^2e^tdtthat is by integration by parts ,(i am denoting integral byI)t2et-I2te^tdtt^2e^t-2te^t+I2e^t dtt^2e^t- 2te^t+ 2e^t+cxlogx^2-2xlogx + 2x+c |
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| 46. |
\sin 120 ^ \circ %2B \tan 150 ^ \circ \cdot \cos 135 ^ \circ = \frac 3 %2B \sqrt 2 2 \sqrt 3 |
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Answer» sin(90+30) = cos 30tan (90+60)= -cot 60cos(135)= cos(90+45)= -sin45= 3+√2/2√3 |
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| 47. |
Evaluate the following:(i) v2 sin 135° cos 210° tan 240° cot 300° sec 330° |
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Answer» wrong way |
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| 48. |
ढि००७(135* + है) + दि ००४(0१35९ - 2 -cosAt2) -2 cos A 3) sin1)cos A : कि 4 <Ae o . N Avcona |
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Answer» hit like if you find it useful tq so much |
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| 49. |
Exrosdainal .acoat in ple |
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Answer» 26\100000=13\50000 |
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| 50. |
Question numbers 1 to 4 carry one mark eachQ.1) Find the value of V (5-2 |
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