২২৭৬১
How many spokes are there in a wheel of a car, if any two spokes form an angle if 15 degree?
উত্তর
24
সমাধান
All the spokes will form a total angle of 360°. Two consecutive spokes form an angle of 15° but every spoke takes part in forming two such angles. So, the number of spokes will be equal to the number of 15° angles formed.
So, the number of spokes will be = 360/15 = 24
২২৭৬২
A line segment is drawn from point (8, -2) to point (4, 6). The coordinates of the midpoint of this line segment are ---
উত্তর
(6, 2)
সমাধান
Coordinates of the midpoint of a line segment made by joining two points are the averages of the respective coordinates of the two points.
So, coordinate of the midpoint is {(8 + 4)/2 , ( - 2 + 6)/2} = (6,2)
২২৭৬৩
Point P in on line segment AB, which of the following is always true?
উত্তর
AB>AP
সমাধান
6c1×1! + 6c2×2! + 6c3×3! + 6c4×4! + 6c5×5! + 6c6×6! = 1956
যেহেতু one or more at a time বলছে তাই নিজেদের মধ্যে ও factorial দিয়ে গুণ হয়েছে।
২২৭৬৪
To avoid paying a toll on a direct road, I drive west 10 miles, south 5 miles, west 30 miles and north 35 miles. What is the length of the toll road?
উত্তর
50
সমাধান
I drive west 10 miles, south 5 miles, west 30 miles, and north 35 miles = west 40 miles, north 30
so we get, (30)² + (40)² = n²
or,900 + 1600 = n²
or,2500 = n²
∴n = 50 or - 50
Throwing out the negative answer, we get the distance to be 50 miles
ans: 50 miles
২২৭৬৫
The average of 50 numbers is 38. If two numbers namely 45 and 55 are discarded, the average of the remaining number is:
উত্তর
37.50
সমাধান
Average for 50 number is 38.
The total is = 38×50 = 1900
The total of discarded number is = 45 + 55 = 100
Hence the total for 48 number is = 1900 - 100 = 1800
So, The new average is = 1800÷48 = 37.5
ans: 37.5
২২৭৬৬
A cricketer has a certain average for 9 innings. In the 10th innings he scores 100 runs, thus increasing his average by 8 runs. His new average is:
উত্তর
28
সমাধান
Let, initial average = x
So, total runs = 9x
And total runs scored in 10 innings = 9x + 100
So, new average = (9x + 100)/10
Since average increase by 8
ATQ,
x + 8 = (9x + 100)/10
10x + 80 = 9x + 100
x = 20
New average 20 + 8 = 28 (Ans)
২২৭৬৭
Masud has twice as much money as Selim has and Selim has 50% more money than what Bashir has. If the average money with them is Tk. 110, then Masud has:
উত্তর
180
সমাধান
Let Bashir has = x tk
Then selim has = 3x/2 tk
Then Masud has = 3x tk
Now ratio of Masud: Selim: Bashir = 6:3:2
They have total = 110 × 3 = 330 Taka
Then Masud share is 6/11 × 330 = 180 tk
২২৭৬৮
A man spends 75% of his income. his income is increased by 20% and he increased his expenditure by 10%. His savings are increased by:
উত্তর
50%
সমাধান
Let income = 100
Expenditure : 75
So, saving (100 - 75) = 25
New income = 100 + 20% of 100 = 120
New expenditure = 75 + 10% of 75 = 82.5
New saving = 120 82.5 = 37.5
Increase of saving = 37.5 25 = 12.5
% increase in saving = (12.5/25) × 100 = 50% (ans)
২২৭৬৯
If a commission of 10% is given on the marked price of a book, the publisher gains 20%. If the commission is increased to 15% the gain is:
উত্তর
13.33%
সমাধান
Let CP = 100
And Marked price = x
SP = x - 10% of x
x - 10% of x = 120
x - 10x/100 = 120
9x/100 = 120
9x = 1200
X = 133.33
If 15% Commission was given, then
SP = 133.33 - 15% of 133.33
SP = 133.33 - 20
SP = 113.33
Gain = 113.33 - 100 = 13.33% (ans)
২২৭৭০
The difference of two numbers is 7 and their product is 60 , then one of the two numbers must be -
উত্তর
5
সমাধান
x - y = 7; x = (y + 7)
xy = 60
or,(y + 7).y = 60
or,y2 + 7y - 60 = 0(y + 12) (y - 5) = 0So,Y = - 12,5So,the two number is 12 and 5