Explanation:

A ও B কেন্দ্রবিশিষ্ট বৃত্তদ্বয় পরস্পর O বিন্দুতে স্পর্শ করলে ∠AOB এর মান .... । সঠিক উত্তর সরলকোণ দুইটি বৃত্ত বহিঃস্থ ভাবে স্পর্শ করলে কেন্দ্রদ্বয়ের দূরুত্ব বৃত্তের ব্যাসার্ধের সমষ্টির সমান। কেন্দ্রদ্বয় ও স্পর্শবিন্দু একই সরলরেখায় অবস্থিত বলে ∠AOB এর মান ১৮০° যা সরল কোণ বুঝায়।

Explanation:

A and B can together complete a piece of work in 4 days . If A alone can complete the same work in 12 days, in how many days can B alone complete that work? Correct Answer 6 days 1A + 1B = 14⇒112 + 1B = 14⇒1B = 14 - 112⇒1B = 3 - 112⇒1B = 212⇒1B = 16.'.B = 6 So, B taken 6 days to finish the work alone.

Explanation:

Two buses start at the same time from Delhi and Agra, which are 300 km apart, towards each other. After what time will they cross each other, if their speeds are 38 km per hour and 37 km per hour? Correct Answer 4 hours Given, Distance between Agra and Delhi = 300 km Relative speed = 38 + 37 = 75 ∴ Time taken to cross each other Distance Speed  = 30075 = 4 hours

Explanation:

একটি বৃত্তের ব্যাসার্ধ r কে বৃদ্ধি করে ব্যাসার্ধ r+n করলে বৃত্তের ক্ষেত্রফল 4 গুণ হয় । এর মান কত? সঠিক উত্তর n আমরা জানি, বৃত্তের ক্ষেত্রফল = λr2⇒λ(r + n)2  = λr2×4⇒(r + n)2  = 4r2⇒(r + n)2 = (2r)2⇒r  + n  =  2r ⇒ n  =  2r  - r⇒ n = r  .'. r = n

Explanation:

দুইটি কোণের যোগফল এক সমকোণের সমান হলে,একটি কোণ অপরটির ---- । সঠিক উত্তর পূরক ∠A + ∠B = 90° হলে ∠A কে ∠B এর পূরক কোণ বলে।

Explanation:

2x + 3y =7 , 5x -2y =7, 5x-2y -8 =0 হলে (x,y) = কত? Correct Answer (2,1) 2x + 3y = 7.......... (1) 5x - 2y = 8.......... (2) 2×(1) নং + 3×(2) নং 9x = 38 ∴x = 2 x এর মান 1 নং সমীকরণে বসিয়ে পাই, 2×2 + 3y = 7 = > 3y = 7 - 4 = > y = 3/3 ∴y = 1 x, y = (2, 1)

Explanation:

The ratio of Pens and Pencils in a shop is 3 : 2 respectively . The average number of Pens and Pencils is 180. What is the number of Pencils in the shop? Correct Answer 144 Let, number of pens and Pencils = 3x ATQ,3x + 2x2 = 180⇒5x = 180×2⇒x3605.'. x = 72.'. Pencil  = 2x = 2×72 = 144

Explanation:

(8.97)2×(15.05)2÷ 624.89=9n  then the value of n is - Correct Answer 30 s (8.97)2×(15.05)2÷624.89 = (9)2×(15)2÷625 = 81×225÷25 = 729  = 93So, n =  3

Explanation:

x+y=7 , x-y=5 হলে 8ab (a2+b2) এর মান কত? সঠিক উত্তর 24 8ab(a² + b²) = 4ab.2(a² + b²) = {(a² + b²) - (a² - b²)}{(a² + b²) + (a² - b²)} = {(✓7)² - (✓5)²}{(✓7)² + (✓5)²} = (7 - 5)(7 + 5) = 2×12 = 24

Explanation:

x2-2x+1 =0 হলে x12+1x6 এর মান কত? Correct Answer ০ x2 - 2x  + 1 = 0⇒x2 + 1  = 2x⇒x2 + 1x = 2xx⇒x + 1x = 2⇒(x + 1x)2 = (2)2⇒x2 + 2x.1x + 1x2 = 2⇒x2 + 1x2 = 2 - 2⇒x2 + 1x2 = 0.'. x12 + 1x6 = x12x6  + 1x6 = x12 - 6 + 1x6 = x6  + 1x6 = (x2)3  + 1(x2)3 = (x2 + 1x2)(x4 - x21x2 + 1x4) = (x2 + 1x2)(x4 - 1 + 1x4) = 0×(x4 - 1 + 1x4) = 0

Explanation:

A lent TK. 5000 to B for 2 years and TK. 3000 to C for 4 years on simple interest at the same from both of them as interest . The rate of interest per annum is : Correct Answer 10% We know , prn100 + p1r1n1100  = 2200⇒5000×r×2100 + 3000×r×4100 = 2200⇒10000r + 12000r100 = 2200 ⇒2200r  = 2200×100⇒r = 2200×10022000.'. r  = 10%

Explanation:

A is three as old as B. C was twice -as old as A four years ago. In four years time, A will be 31. What are the present ages of B and C? Correct Answer 9,50 Present age of A = 31 - 4 = 27 years " " " B = 273 = 9Four years ago, A's age = 27 - 4 = 23 years "  "  "  " C's   = 23×2 = 26Present age of C  = 46  + 4  = 50 years .'. Present age of B,C = 9,50

Explanation:

There are 3 green , 4 orange and 5 white color bulbs in a bag. If a bulb is picked at random, what is probability of having either a green or a white bulb? Correct Answer 2/3 Given, Green = 3 Orange = 4 White = 5 Total = 12 Either a green and white = 8 ∴ Probability = 812  = 23

Explanation:

A man can reach a certain place in 49 hours. If he reduces his speed by 1/15th , he goes 5 km less in that time. Find the total distance covered by him . Correct Answer 75 km Ratio of speed = 15: 14 Let, the speed be = 14x and 15 x ∴ 15x - 14x = 5 বা, x = 5 Total distance covered = 15 x = 15 X 5 = 75 km

Explanation:

How many iron rods, each of length 7 m and diameter 2 cm can be made out of 0.88 m3 of iron? Correct Answer 400 Given , diameter, 2r = 2cm radius, r = 1 cm = 1100mATQ, n×πr2h = 0.88⇒n×227×(1100)2×7 = 0.88⇒n = 0.88×100×10022.'. n = 400

Explanation:

x2+y2+x2 =5 , x+y+z =3 হলে yz + zx -xy এর মান কত? সঠিক উত্তর -2 দেওয়া আছে, x2 + y2 + x2 = 5,x + y - z = 3,yz + zx - xy (x + y - z)2 = (x2 + y2 + z2)  + 2(xy - yz - zx)⇒(3)2 = 5 + 2(xy - yz - zx)⇒9 = 5  + 2 (xy - yz - zx)⇒2(xy - yz - zx) = 4⇒xy - yz - xy = 2⇒yz  + zx - xy = - 2⇒yz  + zx - xy = - 2

Explanation:

দুইটি সংখ্যার গুণফল ১৮। ছোট সংখ্যাটি বড় সংখ্যাটির অর্ধেক হলে ছোট সংখ্যাটি কত? সঠিক উত্তর ৭ একটি সংখ্যা x হলে অপর সংখ্যা x/2 ∴x×(x/2) = 98 = > x2 = 196 = > x = 14 ∴ছোট সংখ্যাটি = 14/2 = 7

Explanation:

4x2-2 হতে কত বিয়োগ করলে রাশিটি পূর্ণবর্গ হবে? সঠিক উত্তর - 14x2 (2 x - 1/2x) 2 = 4 x 2 - 2 + 1 / 4x 2

Explanation:

On selling 30 pens at TK. 800. there is loss equal to the cost price of 5 pens. The cost price of a pen is - Correct Answer TK. 32 ধরি, 1 টি কলমের ক্রয়মূল্য x টাকা 5 টি কলমের ক্রয়মূল্য 5x টাকা 30 টি কলমের ক্রয়মূল্য 30x টাকা আবার, 30 টি কলমের ক্রয়মূল্য = 800 + 5x টাকা 5x + 800 = 30x 25x = 800 x = 800/25 x = 32

Explanation:

35 +125=17.88 then what will be the value of 80+65 =? Correct Answer 22.35 Given , 35 + 125 = 17.88⇒35 + 55 = 17.88⇒85 = 17.88⇒5 = 17.888.'.5 = 2.235.'. 80 + 65 = 16×5  + 65 = 45  + 65 = 105 = 10×2.235 = 22.35

Explanation:

What will be simple interest for 1 year and 4 months on a sum of Tk. 25800 at the rate of 14% per annum? Correct Answer Tk. 4816 We know, I = Prn 25800×14100×43 = Tk. 4816

Explanation:

log10x=-3 হলে x=? Correct Answer 0.0001 Log10x = - 3 = > x = 10 - 3 = > x = 1/1000 ∴x = 0.001

Explanation:

x2-4≤0 এর সমাধান কোনটি? সঠিক উত্তর -2≤x<2 x² - 4 ≤ 2 = > x² ≤ 4 = > x ≤ ±2 = > - 2 ≤ x ≤ 2

Explanation:

In the first 20 over's of a cricket game, the run rate was only 3.5 What should be the run rate in remaining 30 over's to reach the target of 289 runs? Correct Answer 7.3 প্রথম 20 ওভারে কৃত মোট রান = ( 20 × 3.5) = 70 অবশিষ্ট রান = 289 - 70 = 219 রান সুতরাং, অবশিষ্ট 30 ওভারে গড়ে প্রতি ওভারে করতে হবে = 219/30 বা 7.3 রান

Explanation:

A shopkeeper marks the price of an article at TK. 80. What will be the selling price. if he allows two successive discounts of 5% each ? Correct Answer Tk. 72.2 Given, two successive discounts of 5% ∴ 80 - 5% of 80 = 80 - 80 ×5100  = 80 - 4 = 76Again , 76 - 5% of 76  = 76 - 76×5100 = 76 - 3.8 = 72.2

Explanation:

A sum of TK. 24,500 amounts to TK. 34,300 in 5 years at a simple interest rate . What is the rate of interest ? Correct Answer 8% সুদ = ( 34300 - 24500) বা 9800 টাকা আমরা জানি, I = pnr 9800 = 24500 × 5 × r/100 r = 9800/1225 r = 8

Explanation:

১৭ দিন আগে করিম বলেছিল যে তার জন্মদিন আগামীকাল । আজ ২৩ তারিখ হলে তার জন্ম কোন তারখে? সঠিক উত্তর ৭ ২৩ - ১৭ = ৬ তারিখ ৬ তারিখ বলেছিল আগামীকাল জন্মদিন ∴জন্মতারিখ = (৬ + ১) তারিখ = ৭ তারিখ

Explanation:

How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train , if the speed of the train is 63 km / hr? Correct Answer 30 Relative speed = (63 - 3) km/hr = 60 km/hr ∴ 60 km/hr = (60) ×518) m/sec  = 503 m/sec .'. Time taken to pass the man  = (500×350)m  = 30 sec

Explanation:

A man took loan from a bank at the rate o f 12% p.a simple interest . After 3 years he had to pay Tk. 5400 interest only for the period. The principal amount borrowed by him was: Correct Answer TK. 15,000 We know, I = Prn ⇒P = 1rn⇒P = 540012100×3⇒p = 5400×10012×3⇒p = 54000036.'. P = TK.15000

Explanation:

A train traveled on an average speed of 45 km per hour from Dhaka to Chittagong and returned Dhaka from chittagong on an average speed of 36 km per hour. What was the average speed of the train over the whole journey? Correct Answer 40 km. 500 m গড়বেগ = 2xy/x + y কিমি/ঘন্টা = 2× 45 × 36 / 45 + 36 = 3240/81 = 40 কিমি/ঘন্টা

Explanation:

Nikki is 25% more efficient that Tina. Tina alone can build a craft in 20 days. Find the number of days taken by Nikki to finish the same piece of work ? Correct Answer 16 The ratio of times taken by Tina and Nikki = 125: 100 = 5: 4.Suppose Nikki takes x days to do the work.5 : 4 = 20 : x so, x = (4x20)/5 = 16 days

Explanation:

Tk. 385 has been divided among A , B,C in such a way that A receive 2/9th of What B and C together receive . Then A's share is? Correct Answer TK. 70 Let, (B + C)'s share = x A's share = x of 29 = 2x9ATQ,2x9 + x = 385⇒2x + 9x = 385×9⇒11x  = 385×9.'.x = 385×911 = Tk.315A's share  = 2×3159 = Tk.70

Explanation:

(xpxq)p+q (xqxr)q+r (xrxp)r+p এর মান কত? সঠিক উত্তর 1 (xp/xq)p + q (xq/xr)q + r (xr/xp)r + p = x(p - q)(p + q).x(q - r)(q + r).x(r - p)(r + p) = xp2 + pq - pq - q2.xq2 + qr - qr - r2.xr2 + pr - pr - p2 = xp2 - q2.xq2 - r2.xr2 - p2 = xp2 - q2 + q2 - r2 + r2 - p2 = x0 = 1

Explanation:

An error 2% in excess is made white measuring the side of a square. The percentage of error in the calculated area of the square is: Correct Answer 4.04% Let, Original length of side = 100 ∴ Area = ( 100×100) = 1000When, 2% in excess .'. Area  = (102×102) = 10404.'. Excess  = 10404 - 10000  = 404Required percentage  =  (404×10010000) = 4.04%

Explanation:

a,b ∈R;a=not 0, b=not 0 হলে a0+b0 এর মান কত? সঠিক উত্তর 2 a° + b° = 1 + 1 = 2

Explanation:

Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart , is : Correct Answer 13/102 Given, Total cards = 52 ∴ probability = C112×C113C252 = 13!1!(13 - 1)!×13!1!(13 - 1)!52!2!(52 - 2)! = 13×1352×522 = 13×131326 = 13102

Explanation:

If 2n=64 ,what will be the value of n? Correct Answer 12 Given, 2n = 64⇒2n = (64)2⇒2n = (8)2⇒2n = (23)4⇒2n = 212.'. n = 12

Explanation:

a4-51a2+1 =0 হলে a-1a এর মান কত? সঠিক উত্তর ±7 দেওয়া আছে, a4 - 51a1 + 1 = 0⇒a4 + 1 = 51a2⇒a4 + 1a2 = 51a2a2⇒a4a2 + 1a2 = 51.'. a2 + 1a2 = 51এখন, (a - 1a)2 = (a + 1a)2  - 4a1a = a2  + 2a1a  + 1a2 - 4 = a2 + 1a2  - 4 + 2 = 51 - 2  = 49.'. a - 1a = 49 = ± 7

Explanation:

Mother's age today is thrice as her daughter's . After 10 years it would be just double. How old is the daughter today? Correct Answer 10 years Let, Present age of daughter's = x years and present age of Mother's = 3x years ATQ, (3x + 10) = 2x + 20 বা, 3x + 10 = 2x + 20 বা, 3x - 2x = 20 - 10 ∴ x = 10

Explanation:

A boat covers a certain distance downstream in 1 hour, while it comes back in 1.5 hour. If the speed of the stream be 3 km/hr. What is the speed of the boat in still water? Correct Answer 15 km/hr Let, the speed of the boat in still ater = x km/hr 1st ATQ , xx + 3 = 1⇒x = x + 3..(i) 2nd ATQ, xx - 3 = 1.5⇒x = 1.5x  - 4.5 ... (ii) From (i) and (ii) we havex + 3  = 1.5x  - 4.5 .... (ii) ⇒0.5x  = 7.5⇒x = 7.50.5⇒x = 755.'. x = 15

Explanation:

Out of 80 children , 35% can play only cricket , 45% , can play only table tennis and remaining children can play both the games. In all, how many children can play cricket ? Correct Answer 44 শুধু ক্রিকেট খেলে = ( 80 এর 35/100) বা 28 জন শুধু টেবিল টেনিস খেলে = ( 80 এর 45/100) বা 36 জন দুটোই খেলে { 80 - ( 28 + 36) } জন = 16 জন সুতরাং, মোট ক্রিকেট খেলে = ( 28 + 16) = 44 জন।

Explanation:

In what time will the simple interest on Tk. 400 at 10% per annum be the same as the simple interest on TK. 1000 4 years at 4% per annum? Correct Answer 4 years W know, simple interest, I = Prn ATQ, 400×10100×n = 1000×4100×4⇒40n  = 160⇒n = 16040.'. n  = 4years

Explanation:

১,১,২,৩,৫,৮,...... ধারাটির ১১ তম পদটি কত? সঠিক উত্তর ৮৯ এখানে দ্বিতীয় সংখ্যা ও প্রথম সংখ্যার সমষ্টি হলো পরবর্ত সংখ্যা ১ + ১ = ২ ২ + ১ = ৩ ৩ + ২ = ৫ ৫ + ৩ = ৮ ৮ + ৫ = ১৩ ১৩ + ৮ = ২১ ২১ + ১৩ = ৩৪ ৩৪ + ২১ = ৫৫ ৫৫ + ৩৪ = ৮৯ ∴ ১১ তম সংখ্যাটি ৮৯

Explanation:

A man spends 75% of his income. His income is increased by 20% and he increased his expenses by 10% . His saving are increased by Correct Answer 50% ধরি, বৃদ্ধির পর মাসিক আয় 100 টাকা বৃদ্ধির পর মাসিক খরচ করেন = ( 100 এর 75/100) টাকা = 75 টাকা বৃদ্ধির পর সঞ্চয় করেন = ( 100 - 75) = 25 টাকা 20% বৃদ্ধির পর মাসিক আয় = ( 100 + 100 এর 20/100) = 120 টাকা 10% বৃদ্ধির পর মাসিক খরচ ( 75 + 75 এর 10/100) = 82.5 টাকা মাসিক সঞ্চয় বৃদ্ধি পায় = 120 - 82.5 = 37.5 টাকা সুতরাং, মাসিক সঞ্চয় শতকরা 37.5% বৃদ্ধি পাবে।

Explanation:

A boat can travel with a speed of 13 km /hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream . Correct Answer 4 hours We know, Downstream = still water + stream = 13 + 4 = 17 ∴ Time 6817 = 4hours

Explanation:

If 323=2x, then X is equal to : Correct Answer 53 √32 = 2x 3 √ 8. 4 = 2x 2 3√4 = 2x 21 . 22/3 = 2x 25/3 = 2x x = 5/3

Explanation:

In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random . What is the probability of getting a prize ? Correct Answer 2/7 Total element = 10 + 25 = 35 Total event for A lottery = C135 = 35Event of getting A prize  = C110 = 10.'. probability  = 1035 = 27

Explanation:

2,4,8,16,32,..... 256 ধারাটি ...... । Correct Answer গুণোত্তর 4÷2 = 2 8÷2 = 2 16÷2 = 2 যা গুণোত্তর ধরার নির্দেশ করে । যার প্রত্যেকটি সাধারণ অনুপাত হবে 2 ।