Admission - উচ্চতর গণিত - Page 435 - Prothom Sir

Calculate sin ( $- 585 °$ ) .

1/4

1 / \sqrt{2}

১/৩

Try your self

1/4

1 / \sqrt{2}

১/৩

Try your self

2.

Find the value : $\frac{1 - \tan^{2} 60 °}{1 + \sin^{2} 60 °} + \sin^{2} 60 °$

\frac{3}{4}

\frac{7}{4}

\frac{5}{4}

Try your self

\frac{3}{4}

\frac{7}{4}

\frac{5}{4}

Try your self

3.

Express $0.2 ° 4 °$ into simple fraction:

\frac{3}{2}

\frac{1}{7}

\frac{8}{33}

\frac{9}{37}

\frac{3}{2}

\frac{1}{7}

\frac{8}{33}

\frac{9}{37}

4.

Two tailors X and Y are paid a total of Tk. 550 per week by their employer . If X is paid 120 percent of the sum paid to Y, how much is Y paid per Week?

Tk. 200

Tk. 250

Tk. 300

Tk. 400

Tk. 200

Tk. 250

Tk. 300

Tk. 400

5.

Two numbers A and B are such that the sum of 5% of A and 4% of B is two -third of the sum of 6% of A and 8% of B. What is A : B?

3: 3

1 : 3

২ :৩

4 : 3

3: 3

1 : 3

২ :৩

4 : 3

6.

A class of 50 girls and 60 boys sponsored a football game . If 52% of the girls and 30% of the boys attended the game, what percentage of the class went to the game?

৪৪%

৫৫%

40%

৩৫%

৪৪%

৫৫%

40%

৩৫%

7.

A man has Tk. 10,000 to invest . He invests TK. 4000 at 5% and Tk. 3500 at 4% . In order to have a yearly income of TK. 500 . he must invest the remainder at ____

৬%

6.3%

6.1%

6.4%

৬%

6.3%

6.1%

6.4%

8.

$11 - [3 + 5 o f (13 - 2 \times 6)] = ?$

2

3

5

10 Percent

2

3

5

10 Percent

9.

Two ships are sailing in the sea on the two sides

173 m

200 m

273 m

300 m

173 m

200 m

273 m

300 m

10.

What is the 200th term of the series , 2,5,8,11,14 ,..........?

496

599

705

৬০৩

496

599

705

৬০৩

11.

The velocity of a boat rowed downstrem is three times than that of the same boat rowed upstream . If the speed of the stream is 2.5 miles per hour, what is the speed of rowing in miles per hour?

5

6

৭

৪

5

6

৭

৪

12.

5+ 8+ 1+ 4 + .... if nth term is 383 , what is the value of n?

127

১৫০

২৭

Try your self

127

১৫০

২৭

Try your self

13.

The ratio of seats for Mathematics , Physics and Biology in a school is 5: 7: 8 . There is a proposal to increase these seats by 40% , 50% and 75% respectively. What will be the ratio of increased seats?

2 : 3: 4

6 : 7: 8

6: 8 : 9

7 : 8: 2

2 : 3: 4

6 : 7: 8

6: 8 : 9

7 : 8: 2

14.

$I f {\log^{\frac{1}{8}}}_{x} = \frac{- 3}{2}, t h e n x i s e q u a l t o___$

-4

৪

\frac{1}{2}

১০

-4

৪

\frac{1}{2}

১০

15.

The ratio between boys and girls in a class is 2 : 5 . If 2 boys leave and 4 girls join the class, the ratio of the boys to the girls becomes 1 :4 what is the original number of girls in the class?

১৫

20

১৮

25

১৫

20

১৮

25

16.

A number is 20 smaller than another $\frac{2}{3} r d o f s m a l l n u m b e r i s e q u a l t o \frac{1}{4} t h o f t h e l a r g e r n u m b e r . W h a t i s t h e l a r g e s t n u m b e r ?$

৩০

৩২

26

২৮

৩০

৩২

26

২৮

17.

যদি $x^{y}$ = $e^{x - y}$ হয়, তাহলে $\frac{d y}{d x}$ এর মান হবে-

\frac{1}{(1 + \ln x)^{2}}

\frac{\ln x}{(1 + \ln x)^{2}}

\frac{(1 + \ln x)^{2}}{\ln x}

\frac{(1 + \ln x)^{2}}{(\ln x)^{2}}

\frac{1}{\ln x}

\frac{1}{(1 + \ln x)^{2}}

\frac{\ln x}{(1 + \ln x)^{2}}

\frac{(1 + \ln x)^{2}}{\ln x}

\frac{(1 + \ln x)^{2}}{(\ln x)^{2}}

\frac{1}{\ln x}

18.

$\int \frac{e^{x}}{x} (1 + x \ln (x)) d x$ এর মান কোনটি?

e^{x} \ln (x) + c

\frac{1}{x} e^{x} + c

e^{x} + c

- \frac{1}{x^{2}} e^{x} + c

\ln (x) + c

e^{x} \ln (x) + c

\frac{1}{x} e^{x} + c

e^{x} + c

- \frac{1}{x^{2}} e^{x} + c

\ln (x) + c

19.

$I = \int^{π / 4} 0 \frac{\sin^{2} θ}{\sin^{4} θ + \cos^{4} θ} d θ$ এর মান কোনটি?

\frac{π}{3}

\frac{1}{4}

\frac{π}{5}

\frac{π}{4}

\frac{π}{6}

\frac{π}{3}

\frac{1}{4}

\frac{π}{5}

\frac{π}{4}

\frac{π}{6}

20.

কোন বিন্দুতে P এবং 2P মানের দু’টি বল ক্রিয়াশীল। প্রথমটিকে দ্বিগুণ করে দ্বিতীয়টির মান 8 এককক বৃদ্ধি করলে লব্ধির দিক অপরিবর্তিত থাকে। P এর মান কত?

4

একক

6

একক

12

একক

16

একক

8

একক

4

একক

6

একক

12

একক

16

একক

8

একক