Job Solution - গণিত - Page 184 - Prothom Sir

1.

A depositor deposited Tk. 4,000 as x% simple interest and Tk. 5,000 at y % simple interest. received annual interest of Tk. 320 on his deposited amounts at the year end. If he could deposit Tk. 5,000 at x% simple interest and Tk. 4,000 at y% simple interest, he would recce annual interest of Tk. 310. Find the value of x and y.

2.

70 students are studying physics, mathematics and chemistry. 40 students study mathematics, 35 students study physics and 30 students study chemistry 15 students are studying all the subjects. How many students are studying exactly two of the subject?

3.

Find the value of $x^{6} + \frac{1}{x^{6}},$ if $x + \frac{1}{x} = 3$

4.

solve the equation: $\frac{3}{x + 2} + \frac{x + 1}{x - 5} = 2$

5.

simplify: $\frac{5 x + 2}{x^{2} - x - 20} + \frac{2 x - 1}{x^{2} - 4 x - 5}$

6.

In a survey at an airport, 55 travelers said that last year they had been to Spain, 53 to Fr and 79 to Germany, 18 had been to Spain and France, 17 to Spain and Germany and 2 France and Germany, while 10 had to all three countries. How many travelers took part survey?

7.

A shopkeeper sells two shirts at the same price. He makes 10% profit on one and loses 10 the other. How much in percentage does he gain or lose?

8.

The length of a tangent from a point A at distance 5cm from the center of the circle is 4cm. Find the radius of the circle

9.

Find the H.C.F. of $x^{3} - 16 x, 2 x^{2} + 9 x^{2} + 4 x, 2 x^{3} + x^{3} - 28 x$

10.

The sum of three numbers in Arithmetic Progression is 30, and the sum of their square 318.Find the numbers.

11.

Among 50 people, 35 can speak English, 25 can speak both English and Bangla and each can speak at least in one of the two languages. How many of them can speak only Bangla?

12.

Length of each equal side of an isosceles triangle is 10cm and the included angle between those two sides is 45°. Find the area of the triangle.

13.

What should be the values of a and b for which $64 x^{2} - 9 a x^{2} + 108 x - b$ will be a perfect cube?

14.

Price of 3 tables and 5 chairs is Tk. 2,000. Again, price of 5 tables and 7 chairs is 3200 Tk. What is the price of 1 table and 1 chair?

15.

A committee is to consist of three members. If there are seven men and five women available to serve on the committee, how many different committees can be formed?

16.

A and B started a business with capitals of Tk. 3,000 and Tk. 4,000 respectively. After 8 months, A invested Tk. 2,500 more in the business and 7 months after this, total profit becomes Tk. 980. Find the share of profit for each.

17.

Resolve into factors: $a^{2} + \frac{1}{a^{2}} + 2 - 2 a - \frac{2}{a}$

18.

A depositor deposited Tk. 4,000 at x% simple interest and Tk. 5,000 at y% simple interest. He received annual interest of Tk. 320 on his deposited amounts at the year end. If he could deposit Tk. 5,000 at x% simple interest and Tk. 4,000 at y % simple interest, he would receive annual interest of Tk. 310. Find the value of x and y.

19.

Selling 12 candies at a price of 1, 18 vids a loss of x% and selling 12 candies at a price of Tk. 12 yields a profit of x%. What is the value of x?

20.

In which bank the disbursement of loans was more than 25 percent of all banks in 2015?