গণিত

প্রশ্নসমূহ

১.

In the figure above, if the perimeter of Δ vzy is 17, what is the area of square region vwxy?

ক.

খ.

গ.

100

ঘ.

২.

In a mixture of 45 liters, the ratio of milk and water is 4 : 1. How much water must be added to make the mixture ratio 3 : 2?

ক.

20 liters

খ.

15 liters

গ.

25 liters

ঘ.

10 liters

৩.

Two trains of equal length are running on parallel lines in the same direction at 46km and 36km per hour. The faster train passes the slower train in 36 seconds. The length of each train is -

ক.

80m

খ.

72m

গ.

50m

ঘ.

82m

৪.

If the interest of Tk. M at M% in 4 years is Tk. M, then M = ?

ক.

খ.

গ.

ঘ.

৫.

The average of two numbers is 62. If 2 is added to the smaller number, the ratio between the numbers becomes 1 : 2. What is the smaller number?

ক.

খ.

গ.

ঘ.

৬.

A is twice as good a workman as B and together they finish a piece of work in 1 day. A alone can finish the work in -

ক.

28 days

খ.

24 days

গ.

25 days

ঘ.

21 days

ঙ.

Test Yourself

৭.

There are two squares S1 and S2 The ratio of their areas is 4 : 25. If the side of S1 is 6 cm. What is the side of S2 ?

ক.

20 cm

খ.

5 cm

গ.

15 cm

ঘ.

12 cm

৮.

The tax on a commodity is diminished by 10% and its consumption increases by 10%. Find the effects on revenue.

ক.

Increases by 2%

খ.

Decreases by 1%

গ.

Increases by 1%

ঘ.

Decreases by 2%

৯.

In the figure, AD and BC are lines intersecting at O. What is the value of a?

ক.

খ.

গ.

ঘ.

১০.

There are 3 green, 4 orange and 5 white colour bulbs in a bag. If a bulb is picked at random, what is the probability of having either a green green or a white bulb?

ক.

$\frac{3}{4}$

খ.

$\frac{2}{5}$

গ.

$\frac{1}{3}$

ঘ.

$\frac{2}{3}$

১১.

Which number is appropriate in place of question mark?

ক.

খ.

গ.

ঘ.

১২.

In a class 75% passed in English, 60% in Mathematics and 25% failed in both the subjects. What is the percentage who passed in both subjects?

ক.

60%

খ.

55%

গ.

50%

ঘ.

45%

১৩.

A man swimming in a stream which flows $1 \frac{1}{2} k m / h r$ finds that in a given time he can swim twice as far with the stream as he can against it. At what rate does he swim?

ক.

$4 \frac{1}{2} k m / h r$

খ.

$5 \frac{1}{2} k m / h r$

গ.

$7 \frac{1}{2} k m / h r$

ঘ.

$3 \frac{1}{2} k m / h r$

১৪.

The speed of three cars is in the ratio of 2 : 3 : 4 . The ratio of the times taken by these cars to travel the same distance is -

ক.

2 : 3 : 4

খ.

4 : 3 : 6

গ.

4 : 3 : 2

ঘ.

6 : 4 : 3

১৫.

At what profit percent must an article be sold so that by selling at half that price, there will be a loss of 30%?

ক.

25%

খ.

36%

গ.

42%

ঘ.

40%

১৬.

In a party 15 people shake their hands with each other. How many times did the handshakes take place?

ক.

120

খ.

105

গ.

135

ঘ.

165

১৭.

Which of the following is greater than 1 ?

ক.

$\frac{0.00004}{0.005}$

খ.

$\frac{0.01}{0.003}$

গ.

$\frac{0.003}{0.006}$

ঘ.

$\frac{0.001}{0.01}$

১৮.

1f 9 is $\frac{3}{4}$ of n, what number is $\frac{5}{6}$ of n?

ক.

খ.

গ.

ঘ.

12.5

১৯.

In the figure above, $\frac{a + b + c}{s + t + u} = ?$

ক.

$\frac{1}{2}$

খ.

$\frac{1}{3}$

গ.

$\frac{2}{3}$

ঘ.

২০.

$\frac{1}{3} + \frac{1}{3}$ equals how many twelfths?

ক.

খ.

গ.

ঘ.

২১.

If $3 x + \frac{3}{x} = 5 t h e n x^{3} + \frac{1}{x^{3}} = ?$

ক.

$\frac{260}{27}$

খ.

$\frac{85}{27}$

গ.

$- \frac{10}{27}$

ঘ.

$- \frac{90}{27}$

২২.

Denominator of a proper fraction is 3 more than the numerator. If the fraction is squared, its denominator will be 39 more than the numerator. The fraction is

ক.

$\frac{5}{8}$

খ.

$\frac{4}{7}$

গ.

$\frac{2}{5}$

ঘ.

$\frac{8}{11}$

২৩.

If $\frac{x}{y} + \frac{y}{z} = \sqrt{7}$ then what is the value of $\frac{x^{4}}{y^{4}} + \frac{y^{4}}{x^{4}} ?$

ক.

খ.

গ.

ঘ.

২৪.

A tank is $\frac{1}{3}$ parts full with water. If 8 liters of water is added, the tank becomes $\frac{5}{6}$ parts full. What is the capacity of the tauk?

ক.

খ.

গ.

ঘ.

None

২৫.

If the height of a triangle is increased by 60% and its base is decreased by 30%, what will be the effect on its area?

ক.

12% increase

খ.

12% decrease

গ.

112% increase

ঘ.

No change

২৬.

If A = {1, 4, 9, 16, 25} , the number of proper subsets of A is

ক.

খ.

গ.

ঘ.

২৭.

Solution set of the inequality: x - 5 > 4x + 7 is

ক.

(- ∞, - 4)

খ.

[- ∞, - 4)

গ.

(- ∞, - 4]

ঘ. [- ∞, - 4]

২৮.

If $\frac{\sqrt{x - 6} + \sqrt{x + 1}}{\sqrt{x - 6} - \sqrt{x + 1}} = - 7$ , the value of x is

ক.

খ.

গ.

ঘ.

None of these

২৯.

If log, $\frac{27}{64} = - 3$ then x = ?

ক.

$\frac{1}{3}$

খ.

$\frac{4}{3}$

গ.

$\frac{3}{4}$

ঘ.

$\frac{2}{3}$

৩০.

The average of a natural number and its cube is 13 times the number. The number is

ক.

খ.

-5

গ.

±5

ঘ.

৩১.

The distance between cities A and B is 120 miles. A car travels from A to B at 60 miles per hour and returns from B to A along the same route at 40 miles per hour. What is the average speed for the round trip?

ক.

খ.

গ.

ঘ.

৩২.

69% of the students of a certain class took Mathematics and 47% took Biology. If each student took Biology or Mathematics and 44 took both, what is the total number of students in the class?

ক.

150

খ.

250

গ.

300

ঘ.

275

৩৩.

${(289)}^{0.17} \times {(17)}^{0.16} = ?$

ক.

খ.

$\sqrt{7}$

গ.

$\sqrt{17}$

ঘ.

$\sqrt{19}$

৩৪.

In a tourist group of 100 people, 55 speak French, 40 speak Spanish, and 20 speak none of the languages. How many of them speak just one langunge?

ক.

খ.

গ.

ঘ.

৩৫.

At what rate of compound interest per annum will a sum of Tk. 1800 become Tk. 3042 in two years?

ক.

10%

খ.

15%

গ.

20%

ঘ.

30%

৩৬.

When the price of each book goes up by Tk. 5, the librarian purchases 20 books loss than the required number for Tk. 1200. The original price of the book was

ক.

15 Tk.

খ.

20 Tk.

গ.

25 Tk.

ঘ.

30 Tk.

৩৭.

A rectangular field is 3.2 yards long. A fence marking the boundary is 11.2 yards in longth. What is the pron of the field in square yards?

ক.

4.68

খ.

7.68

গ.

9.28

ঘ.

11.28

৩৮.

The sum of four consecutive multiples of 4 is 200. What is the largest number?

ক.

খ.

গ.

ঘ.

৩৯.

In the triangle, what is the value of x ?

ক.

খ.

গ.

ঘ.

৪০.

The average of 8 numbers is 8. If 4 is subtracted from each of 6 of these numbers, what is the new average?

ক.

3.5

খ.

গ.

ঘ.

6.5