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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. |
2. C) is any point within aABC, whose sides are 4 cm, 5 cm. and 7 cm respectively. BFig. Q.2Prove that (04 +OB +OC)> 8 cm. |
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| 2. |
In an athletic meet, a runner covered 1.5 km in 5minutes. What was his speed? |
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Answer» Speed = Distance / time = 1.5 km/ 5 min= 0.3 km/ min |
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| 3. |
24. A thief away from a Police Station with a uniform speed 100m/minutes. After one minutea Policeman runs behind the thief to catch him. He goes at a speed of 100m/minute in firstminute and tncreases the speed 10m/minute on each succeeding mimute. After how manyminutes the Policeman catches the thiet.Now answer these questions:) Which mathematical concept is being used to solve the above problem?() Which trait of personality of the policeman is showed? |
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Answer» Let the policeman catch the thief in n minutes. Given that uniform speed of the thief = 100m/min. Given that After 1 minute a policeman runs to catch him at the speed of 100 in first minutes. (n + 1) minutes = 100(n + 1) minutes. Given that speed of policeman increase by 10m/min. The speed of police in 1 minute = 100m/min. The speed of police in 2 minutes = 110m/min. The speed of police in 3 minutes = 120m/min. The speed of police in 4 minutes = 130m/min. Hence 100,110,120,130 are in AP. Let a be the first term and d be the common difference. a = 100,d = 110 - 100 = 10. We know that sum of n terms of an ap = n/2(2a + (n - 1) * d) = n/2(2(100) + (n - 1) * 10) ------ (1) The distance traveled by the thief = Distance traveled by the police 100(n + 1) = n/2(2 * 100+ (n - 1) * 10) 100n + 100 = n/2(200 + 10n - 10) 200n + 200 = 10n^2 + 190n 10n^2 + 190n - 200 = 200n 10n^2 - 10n - 200 = 0 n^2 - n - 20 = 0 n^2 -5n + 4n - 20 = 0 n(n - 5) + 4(n - 5) = 0 (n -5)(n + 4) = 0 n = 5 (or) n = -4. n cannot be negative. Therefore the time is taken by the policeman to catch the thief = 5minutes. |
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| 4. |
Find the probability that the month of January may have 5 Mondays in1) a leap year2)a non -leap year |
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Answer» Sol: Number of days in the month of January in a leap or non-leap year = 31There are four complete weeks in the month of January.There are three more extra days in the month.If the month starts on Saturday or Sunday or Monday, there are 5 Mondays in the month of January.So, the probability of getting 5 Mondays in the month of January (or any month with 31 days) = 3/7. |
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| 5. |
what is a leap year... is 2020 is a leap year? |
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Answer» leap year have 365 day...and 2020 is a leap year because its divisible by 4 |
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| 6. |
1. Fill in the blanks.(a) 1 year(b) 1 year(c) 1 leap yeardaysmonthsdays(e) 1 decade... years(g) 1 week.. days |
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Answer» 1 year =365 days1 year=12 months1 leap year=366 days1 fortnight=14 days1 decade=10 years1 century =100 years1 week=7 days |
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| 7. |
(o 30In a leap year, the probability that there are53 Tuesdays in the year, is:4.45 |
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Answer» 1 year = 365 days A leap year has 366 days A year has 52 weeks. Hence there will be 52 Tuesdays for sure. 52 weeks = 52 x 7 = 364 days 366 – 364 = 2 days In a leap year there will be 52 Tuesdays and 2 days will be left. These 2 days can be:Sunday, MondayMonday, TuesdayTuesday, WednesdayWednesday, ThursdayThursday, FridayFriday, SaturdaySaturday, Sunday Of these total 7 outcomes, the favourable outcomes are 2. Hence the probability of getting 53 tuesdays in a leap year = 2/7. can you give me in simple way Draw a clock to show half past 4 |
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| 8. |
b)of a non-leap year |
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Answer» 73 is and as the non leap year has 365 days 73 is the correct answer of the given question |
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| 9. |
comment upon the nature of triangleQ.14 A triangle has side lengths 18,24 and 30. Find the area of the triangle whose vertices are the incentre,circumcentre and centroid of the triangle.fa rectanale The other two vertices lie on the line |
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Answer» 18,24 and 30 are the sides of a right triangle, because 18^2 + 24^2 = 30^2 consider in a x-y plane pointsO(0,0), A(18,0), B(0,24) circumcenter of a right triangle is the midpoint F of hypotenuse AB(coordinates of the midpoint of a segment are the mean of the coordinates of its vertices)F(9,12) centroid G of any triangle has coordinates which are the mean of the coordinates of triangle's vertices, G(6,8) incenter H is the center of inscribed circle, whose radius isr = area/half-perimeter area = (18x24)/2 = 216half-perimeter = (18 + 24 + 30)/2 = 36 r = 216/36 = 6 as inscribed circle is tangent to both axis, incenter H has coordinates both equal to circle's radiusH(6,6) Requested triangle has verticesF(9,12), G(6,8), H(6,6) |
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| 10. |
1. Find the area of the triangle whose vertices are: |
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Answer» thanks |
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| 11. |
1.Find the area of the triangle whose vertices are |
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| 12. |
pi %2B text*(x*(di*(v*(i*(de*(db*y)))))) %2B 3*x %2B x^3 %2B 3*x^2 |
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Answer» By the Remainder Theorem, the remainder when a polynomial p(x) is divided by a polynomial x-a, is p(a). Taking a=(-π), we get the remainder as p(π) =(-π)^3 +3(-π)^2 +3(-π)+1 = -π^3 +3π^2 -3π +1(= (1-π)^3 ) yes it is correct answer |
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| 13. |
-2*x - 54*db*de*di*i^2*s*text*v*x^2*y %2B 26*x %2B 12*x^3 - 17*x^2 %2B 5 |
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| 14. |
(text*((i*(s*(di*(v*(i*(de*(db*y)))))))*(x - 3)))*(9*x %2B 2*x^3 - 5*x^2 - 8) |
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Answer» Let, f(x)=2x³-5x²+9x-8X-3=0X=3f(3)=2(3)³-5(3)²+9(3)-8=2(27)-5(9)+27-8=54-45+19=28 28 is the right answer of the following 28 is the right answer of the following |
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| 15. |
3*(text*((3*x)*(di*(v*(i*(de*(db*y))))))) %2B 9*x**3 %2B 15*x**2 %2B 5*x %2B 1 |
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| 16. |
4. एक चतुर्भुज के कोण 1 : 2 : 3 : 4 के अनुपात में हैं। इसचतुर्भुज के सभी कोण ज्ञात कीजिए।The angles of a quadrilateral are in ratio 1:2:3:4.Find all the angles of quadrilateral. |
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Answer» Let the angles be(x)°,(2x)°,(3x)°and(4x)°.(x)°,(2x)°,(3x)°and(4x)°.Sum of the angles of a quadrilateral is360∘360∘.x+2x+3x+4x=36010x=360x=36010x=36x+2x+3x+4x=36010x=360x=36010x=36 (2x)°=(2×36)∘=72∘(3x)°=(3×36)∘=108∘(4x)°=(4×36)∘=144∘(2x)°=(2×36)∘=72∘(3x)°=(3×36)∘=108∘(4x)°=(4×36)∘=144∘ |
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| 17. |
24. एक चतुर्भुज के कोण 1 : 2 : 3 : 4 के अनुपात में हैं। इससभी कोण ज्ञात कीजिए।The angles of a quadrilateral are in ratio 1:2:3 : 4.Find all the angles of quadrilateral. |
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Answer» Woooooooooooooooooooooo |
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| 18. |
When a die is thrown, what is the probability of getting a prinenumber ? 2.3, |
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| 19. |
--॥| एक चतुर्भुज के कोण 1 : 2 : 3 : 4 के अनुपात में हैं। इसचतुर्भुज के सभी कोण ज्ञात कीजिए।2The angles of a quadrilateral are in ratio 1:2:3:4.Find all the angles of quadrilateral. |
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| 20. |
: 7Ife sind = 5% तो ८०50 तथा 1970 का मान ज्ञात कीजिए |
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| 21. |
Ife is an acute angle and sin θ-cos θ, find the value of2tan2 θ + sin2 θ-1. |
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Answer» plz read the question properly |
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| 22. |
14. Ife, and ē, are unit vectors and e is theangle between them, then lë, -ē,l is equalto :of(a) 2cos(b) 2 tanold |
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Answer» I think so (b) is right answer |
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| 23. |
(a) If bdFa_d-e,prove that (b2td2+/2)(a2tc2 + e*)=(ab + cd + ef} |
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| 24. |
3*(text*((3*x)*(di*(v*(i*(de*(db*y))))))) %2B 9*x^3 %2B 15*x^2 %2B 5*x %2B 1 |
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Answer» 3x+1=0hence put X=-1/3hence15(-1/3)^2+5(-1/3)+9(-1/3)^3+3=15/9-5/3-9/27+3=5/3-5/3-1/3+3=3-1/3=8/3 |
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| 25. |
11litre's into millimetres |
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Answer» The answer is 11.000 millilitres Thanx.. |
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| 26. |
rind me pPob BC=11 cma AB 8 cm3,The perimeter of a rectangle is equal to that of a square with side 13 m: If the rectangle is tรณ m owhat is its breadth?uhose nerimeter is 36 cm?millimetres |
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Answer» Perimeter of square=4×side=4×13 m=52 m Let the breadth of rectangle= bPerimeter of rectangle= 2(l+b)2(16+b)=5216+b=52/216+b=26b=26-16 mb=10 m |
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| 27. |
3.1. The daily rainfall for each day of a weekin a certain city is given in millimetres.Find the average rainfall during the week.9, 11, 8, 20, 10, 16, 12 |
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Answer» Avg rain fall= 9+11+8+20+10+16+12/7= 86/7= 12.2 average =sum of the numbers/total numbers=9+11+8+20+10+16+12/7=86/7=12.28 |
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| 28. |
92. Find the square root of 15- |
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Answer» 3.90512484 is the right answer |
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| 29. |
Millimetres Centimetres504010080 |
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Answer» 50mm=5cm40mm=4cm100mm=10cm80mm=8cm |
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| 30. |
The daily rainfall for each day of a weekin a certain city is given in millimetres.Find the average rainfall during the week.9, 11, 8, 20, 10, 16, 12 |
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Answer» the average rainfall during this week= 9+11+8+20+10+16+12/7=86/7=12.28 the average rainfall during this week = 9+11+8+20+10+16+12/7= 86/7= 12.28 9+ 11+8+20+10+16+12/7=86/7=12.28the average of rainfall during this week= 12.28 9+11+8+20+10+16+12=86average rainfall=86/7=12.28 is the best answer. Dear friend, The answer is Average = sum of all observation / no. of observation Average rainfall during the week = 9 + 11 + 8 +20 + 10 +16 +12 / 7 = 86 /7. = 12.28 |
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| 31. |
ehal has a red ribbon that is 80 cm long and a blue ribbon, 2.20 m long. Whatof the length of the red ribbon to that of the blue ribbon?Cothor i 4 veers Shubham's mothe |
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Answer» Ratio should be taken only once all the quantities are in the same units Length of red ribbon = 80 cm Length of blue ribbon = 2.2m = 220cm. Ratio of length of red ribbon to that of blue ribbon = 80:220 = 4:11 |
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| 32. |
6. Raghav has a piece of ribbon which is 127 mm long. What isthe ribbon in cm? |
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Answer» 10mm=1cmhence127mm=127/10cm=12.7cm |
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| 33. |
ribbon?6 Find the area of a square paper of sidecm.425 mh How much dista |
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Answer» Area of a square=(side)²=(25/2)²=156.25 cm² 156.25 cm^ 2 is the correct answer of the given question |
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| 34. |
5. A piece of ribbon is cut in the ratio 2:3:4. Ifthe largest piece is 16 cm, then the length beforeit is cut is(a) 144 cm(c) 63 cm(b) 24 cm(d) 36 cm |
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Answer» thanks let the length of each piece be 2x ,3x and 4x respectively Given that larger length =16 cm so , 4x =16so x =4Now total length of ribbon = 2x + 3x + 4x = 2×4 + 3×4 + 4×4 =8 + 12 + 16 = 36 cm Therefore answer =(d) = 36cm |
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| 35. |
Identify the terms and their factors in the followShow the terms and factors by tree diagramsa) x(d) 5xy2+7r'y (e(e)-ab +2b -3a |
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Answer» Thanks |
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| 36. |
The length of a ribbon was originally 30 cm. If it was reduced in the ratio 5:3, what is its length now? |
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| 37. |
1 2 3 4Find the prime factorization of the number.455The prime factorization isQuestion 2 |
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Answer» Prime factorisation of 455 is 5 x 7 x 13 |
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| 38. |
Write prime factorization of 120 |
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Answer» Prime Factors of 120 =2, 2, 2, 3, 5 Which is the same as = 23x 3 x 5 |
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| 39. |
\lim _ { x \rightarrow a } \frac { ( 1 + x ) ^ { 6 } - 1 } { ( 1 + x ) ^ { 2 } - 1 } |
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Answer» by putting x=0 we will get 0/0 formso using L'hospital rulelim x->0 6(1+x)^5 / 2(1+x)=6/2=3 |
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| 40. |
4 83 1238 ©Y |ABC-69°,|ACB=31° T3[BDC somsttono. 3 1238 |
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Answer» In ∆ ABC ∠A + ∠ABC + ∠ACB = 180°∠A = 180° - 100° = 80°So, ∆ ABC and ∆ BDC have same base so ∠ A = ∠ D So ,∠D = 80° |
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| 41. |
\lim _{x \rightarrow 0} \frac{(1+x)^{6}-1}{(1+x)^{2}-1} |
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| 42. |
If T n+3 then the value of T3 is |
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Answer» T(n) = n² + 3 T(3) = 3² + 3 = 9 + 3 = 12 |
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| 43. |
What will come at the place of ?7.72و گومو0 26 125 (1) 28(11) 22 |
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Answer» iii) 28 is the correct answer 28 is the right answer of following questions |
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| 44. |
4. Simplify the following question/expression/ fraction14- 2- of --4-6 8 6 611 |
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| 45. |
7x=21? |
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Answer» x=3 is the right answer |
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| 46. |
(x2+2x+1, 3xSx-72 +22+2 |
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| 47. |
If 12 = 3 -- a, calculate the value of a=(2) 20(6) 12(c)-3(d) -12 |
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Answer» -3 is the correct answer -3 will be your answer option c is correct answer according to your question -12is a correct answer the answer is-12 is correct -12 is a right answer |
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| 48. |
ow the terms and their factors by tree diagrams3x+22(b) 2xy +72 & (C) |
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| 49. |
7x/9=21 |
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Answer» Verify this |
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| 50. |
21. Find product of the following(1+7y) (7x-y)1)(ĺ¸(a, + b)(a+b) |
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