Admission - উচ্চতর গণিত - Page 421 - Prothom Sir

1.

What is the greatest number of rectangles with integer side lengths and perimeter 10 that can be cut from a piece of paper with width 24 and length 60 ?

১২০

80

৩৬০

৯০

১২০

80

৩৬০

৯০

2.

The average of 3 numbers is 24. If 2 of the numbers are 21 & 23 , the third number is :

২৮

25

১৬

২৭

২৮

25

১৬

২৭

3.

The average of 5 five consecutive even numbers is 8. which is the smallest of the 5 numbers?

2

৮

6

৪

2

৮

6

৪

4.

Lenny's average score after 3 tests is 88 . What score on the 4th test would bring Lenny's average up to exactly 90 ?

৮৯

৯৬

97

92

৮৯

৯৬

97

92

5.

What is the average (arithmetic mean ) of 4x+5 7x -6 and -8x +2

x-1

2x+1

x

x+1

x-1

2x+1

x

x+1

6.

Sumi on three consecutive whole numbers is 5 then what is 1/3 of the middle number?

৪

5

6

৭

৪

5

6

৭

7.

If a number is divisible by 102 , then this is also divisible by :

12

23

১১

2

12

23

১১

2

8.

জটিল সংখ্যা $(1 + 2 i)^{- 1} এ র a + i b$ আকার হল-

\frac{1}{5} (1 - 2 i)

(1 - 2 i)

\frac{1}{5} (1 + 2 i)

\frac{1}{5} (2 + i)

\frac{1}{5} (1 - 2 i)

(1 - 2 i)

\frac{1}{5} (1 + 2 i)

\frac{1}{5} (2 + i)

9.

$(2 + \sqrt{3 i})$ মূল বিশিষ্ট দ্বিঘাত সমীকরণটি হল-

x^{2} + 4 x + 7

x^{2} - 4 x + 7 = 0

x^{2} + 4 x + 7 = 0

x^{2} - 7 x + 4 = 0

x^{2} + 4 x + 7

x^{2} - 4 x + 7 = 0

x^{2} + 4 x + 7 = 0

x^{2} - 7 x + 4 = 0

10.

$\log_{x} 324 = 4$ হলে x এর মান হল-

৪

3 \sqrt{4}

2 \sqrt{3}

4 \sqrt{2}

৪

3 \sqrt{4}

2 \sqrt{3}

4 \sqrt{2}

11.

$A = (\begin{matrix} 2 & - 3 \\ 1 & 5 \end{matrix})$ $B = (\begin{matrix} 1 & 3 \\ 2 & - 1 \end{matrix})$ হলে A,B হবে-

(\begin{matrix} - 4 & 9 \\ 10 & 5 \end{matrix})

(\begin{matrix} - 4 & 9 \\ - 11 & 2 \end{matrix})

(\begin{matrix} - 4 & 9 \\ 11 & - 2 \end{matrix})

(\begin{matrix} - 4 & 9 \\ 11 & 2 \end{matrix})

(\begin{matrix} - 4 & 9 \\ 10 & 5 \end{matrix})

(\begin{matrix} - 4 & 9 \\ - 11 & 2 \end{matrix})

(\begin{matrix} - 4 & 9 \\ 11 & - 2 \end{matrix})

(\begin{matrix} - 4 & 9 \\ 11 & 2 \end{matrix})

12.

PERMUTATION শব্দটির বর্ণগুলোর মধ্যে স্বরবর্ণের অবস্থান পরিবর্তন না করে বর্ণগুলোকে যত রকমে পুনরায় সাজানো যেতে পারে তার সংখ্যা-

৩৬০

359

361

৩ঃ৪ঃ৯

৩৬০

359

361

৩ঃ৪ঃ৯

13.

একটি বৃত্ত x=0, y=0, x=a এবং y=a সমীকরণগুলোকে স্পর্শ করে। বৃত্তটির সমীকরণ-

x^{2} + y^{2} - a x - a y = 0

x^{2} + y^{2} = a^{2}

4 (x^{2} + y^{2}) = a^{2}

4 (x^{2} + y^{2}) - 4 a (x + y) + a^{2} = 0

x^{2} + y^{2} - a x - a y = 0

x^{2} + y^{2} = a^{2}

4 (x^{2} + y^{2}) = a^{2}

4 (x^{2} + y^{2}) - 4 a (x + y) + a^{2} = 0

14.

c-এর মান কত হলে মূলবিন্দুতে y=cx(1+x) বক্ররেখার স্পর্শক x-অক্ষের সাথে $30^{\circ}$ কোণ উৎপন্ন করবে?

\sqrt{3}

\frac{1}{\sqrt{3}}

\frac{2}{\sqrt{3}}

\frac{\sqrt{3}}{2}

\sqrt{3}

\frac{1}{\sqrt{3}}

\frac{2}{\sqrt{3}}

\frac{\sqrt{3}}{2}

15.

তিনটি বল p, $\sqrt{3 p}$ , p সাম্যবস্থায় থাকলে প্রথম দুইটি বলের মধ্যবর্তী কোণ-

60^{\circ}

90^{\circ}

120^{\circ}

150^{\circ}

60^{\circ}

90^{\circ}

120^{\circ}

150^{\circ}

16.

এককের একটি কাল্পনিক ঘনমূল $ω$ হলে, $1 + ω^{2} + ω^{4} + . . . . . + ω^{16}$ এর মান হবে-

1

-1

ω^{2}

1

-1

ω^{2}

17.

$\cos (θ) = 0$ হলে, $θ$ এর সাধারণ মান হবে-

2 n π

n π

n Π + \frac{Π}{2}

2 n π \pm \frac{π}{4}

2 n π

n π

n Π + \frac{Π}{2}

2 n π \pm \frac{π}{4}

18.

what is a 'yes/no' question?

A question which can be answered simple with 'yes'

A question which can be answered simply with ' no'

A question which can be answered simply with either 'yes' or 'no'

None of of the above

A question which can be answered simple with 'yes'

A question which can be answered simply with ' no'

A question which can be answered simply with either 'yes' or 'no'

None of of the above

19.

Which of the following sentences is not properly punctuated?

Three important American composers are aron, scott and philip.

Beethoven was a musical genius, for the continued to compose major works after he had become completely deaf.

Have you read Gwendyn Brook's poem |"We Real Cool"?

"Groovy" was a popular expression that meant "terrific"

Three important American composers are aron, scott and philip.

Beethoven was a musical genius, for the continued to compose major works after he had become completely deaf.

Have you read Gwendyn Brook's poem |"We Real Cool"?

"Groovy" was a popular expression that meant "terrific"

20.

An abnormal rise in the level of the sea along a coast caused by the onshore winds of a winds of a severe cyclone is --- .

storm surge

coastline

onshore

Swamps

storm surge

coastline

onshore

Swamps