২২৬৬১
If the length of a rectangle is 8 cm and its diagonal is 10 cm, find its area.
উত্তর
48 cm2
সমাধান
Using short cut technique
ABC is a right angled triangle
সমকোণী ত্রিভুজের তিন বাহুর অনুপাত হতে পারে
3 : 4 : 5 or 5 : 12 : 13
3 : 4 : 5 = 6 : 8 : 10
Area = 6 × 8 = 48 cm2
২২৬৬২
There ar 200 students in a class. 76% passed in Bangla and 54% passed in English. If 10% of the students failed in both the subjects then how many of them passed in both subjects?
উত্তর
80
সমাধান
Passed in Bangla = 76% of 200 = 152
Passed in English = 54% of 200 = 108
Failed in both subjects = 10% of 200 = 20
Passed in atleast one subject = 200 - 20 = 180
Passed in both subjects = 152 + 108 - 180 = 80
২২৬৬৩
In a certain country, a person is born in every 5 seconds and a person dies every 13 seconds. Therefore the birth and death and death rates account for a population growth rate of one person every-
উত্তর
8.125sec
২২৬৬৪
On dividing a number by 357, we get 39 as remainder. On dividing the same number by 17, what will be the remainder?
উত্তর
5
সমাধান
Let the number be n and initial divident be m.
Then, n = 357m + 39 = 21×17×m + 2×17 + 5
So, the final remainder will be 5.
২২৬৬৫
A man loses Tk. 55.50 yearly when the annual rate of interest falls from 11.5% to 10% his capital is:
উত্তর
Tk. 3700
সমাধান
Let, His capitat = x
x×11·5100 - x×10100 = 55·50⇒x·115 - ·10 = 55·50⇒x×·015 = 55·50∴x = 3700
২২৬৬৬
The population of a certain town increases by 50 percent every 50 years. If the population in 1950 was 810 , in year was the population 160?
উত্তর
1750
সমাধান
যেহেতু population 50% increase করে প্রতি 50 বছর, 1950 এর population 150% ছিল অথবা 32of1900 এর population অর্থাৎ 1900 এর population 1950 এর 23 গুণ, আমরা 23 দ্বারা গুণ করে যেতে থাকব যতক্ষণ পর্যন্ত 160 পাওয়া যায়।
1950:810×23 = 540 in 1900; 540×23 = 360 in 1850; 360×23 = 240 in 1800; 240×23 = 160 in 1750
২২৬৬৭
The average of three Numbers is U. If two numbers are x and y, which is the third number?
উত্তর
3 u - x - y
সমাধান
ধরি, third number হচ্ছে z
x + y + z3 = v⇒x + y + z = 3v⇒z = 3v - x - y
২২৬৬৮
the angles of a triangle are in the ratio 5: 4: 3 How many degrees are there in the largest angle?
উত্তর
75
সমাধান
5x + 4x + 3x = 180∘⇒12x = 180∘⇒x = 15∘∴5x = 15∘×5 = 75∘
২২৬৬৯
If m and p are positive integers and ( m +p) m is even , which of the following must be true?
উত্তর
If m is even , then p is even .
সমাধান
even এবং odd এর যোগফল odd এবং odd. odd এর গুণফল odd হয়। আবার odd কে even দিয়ে গুণ করলে সবসময় even হয়। তাই m even হতে হবে।
২২৬৭০
If xy = 2 and xy2= 8 , what is the value of x?
উত্তর
1/2
সমাধান
xy2xy = 82 = 4⇒y = 4x = 24 = 12