২১৮৫১
One pipe can fill a pool in 6 hours, and a second pipe can fill the same pool in 12 hours. If both pipes work together, how long will it take to fill the pool?
উত্তর
4 hours
সমাধান
First pipe can fill 1/6 of the pool in an hour
Second pool can fill 1/12 of the pool in an hour
Together they can fill (1/6 + 1/12) or 1/4 of the pool in an hour
So, they can fill the pool completely in 4 hours.
২১৮৫২
abc=120 হলে a এর মান কোনটি হতে পারে না?
উত্তর
0
সমাধান
দেওয়া আছে, abc = 120
বা, bc = 120/a
এখানে, a = 0 হতে পারে না।কারণ 0 দ্বারা কোনো সংখ্যাকে ভাগ করা যায় না।
২১৮৫৩
12 মিটার উঁচু একটি গাছ h উচ্চতায় এমনভাবে ভেঙে গেল যে, ভাঙ্গা অংশুটি মাটির সাথে 30 ডিগ্রি কোণে মিলিত হলো। গাছটি কত উঁচুতে ভেঙেছিল?
উত্তর
4 মিটার
সমাধান
The length of the broken part = 12 - h
So, h / (12 - h) = sin30°
or, h / (12 - h) = 1/2
or, 2h = 12 - h
or, 2h + h = 12
or, 3h = 12
So, h = 4 m.
২১৮৫৪
Shahin has purchased a square sheet of plywood of 169 square feet area. To cover a wall he must cut off two feet from a side. What is the area, in square feet, of the wall?
উত্তর
143
সমাধান
Side of the plywood = √169 = 13 feet
Cutting of 2 feet from a side will make it a rectangular sheet with a length of 13 feet and a width of 11 feet. Area of the wall is equal to the area of this sheet.
So, the area of the wall = 13 x 11 = 143 sq ft
২১৮৫৫
x+2y=7এবং 2x-3y=0 হলে x এবং y মান হবে-
উত্তর
3 ও 2
সমাধান
এখানে, x + 2y = 7
বা, x = 7 - 2y
আবার, 2x - 3y = 0
বা, 2(7 - 2y) - 3y = 0
বা, 14 - 4y - 3y = 0
বা, 7y = 14
বা, y = 2
বা, x = 7 - 2y = 7 - 2×2 = 7 - 4 = 3
সুতরাং, (x, y) = (3, 2)
২১৮৫৬
Two third of the faculty members of a department are female. Twelve of the male faculty members are unmarried, while 60% of them are married. The total number of faculty members in the department is:
উত্তর
90
সমাধান
Male members = 1 - 2/3 = 1/3
40% of the male members are married.
Married male members are 1/3 x 40% = 13.33% of all members.
13.33% = 12 members
100% = 12 x 100 / 13.33 ≈ 90 members
২১৮৫৭
A farmer has two rectangular fields. The larger has twice the length and four times the width of the smaller field. If the smaller field has area k, then the area of the larger field is greater than the area of the smaller field by what amount?
উত্তর
7k
সমাধান
Let the length and width of the smaller field be L & W respectively.
Area of the smaller field, k = L x W
Area of the larger field = 2L x 4W = 8(L x W) = 8k.
So, the area of the larger field is larger by (8k - k) = 7k than the smaller field.
২১৮৫৮
What are all the values of x that satisfy the equation x2+4x+3 = 0?
উত্তর
-3 and -1
সমাধান
Here, x2 + 4x + 3 = 0
or, x2 + 3x + x + 3 = 0
or, x(x + 3) + 1(x + 3) = 0
or, (x + 3)(x + 1) = 0
So, x + 3 = 0 or, x + 1 = 0
or, x = - 3, - 1
২১৮৫৯
City B is 5 miles east of city A. City C is 10 miles southeast of city B. Which of the following is the closer to the distance from City A to City C?
উত্তর
11 miles
সমাধান
so, Distance AC = √[(10)^2 + (5)^2]
= √(100 + 25) miles
= 11.2 miles
= 11 miles (ans)
২১৮৬০
A man 6 feet tall casts a shadow 4 feet long, at the same time a flagpole casts a shadow which is 50 feet long. How long is the flagpole?
উত্তর
75 feet