প্রশ্নঃ If P is the center of the given circle, what fraction of the circle is shaded?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Area covered by any angle to center of a corcle is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>θ</mi><msup><mn>360</mn><mo>∘</mo></msup></mfrac><mo>×</mo><msup><mi>πr</mi><mn>2</mn></msup><mspace linebreak="newline"/><mo>=</mo><mfrac><msup><mn>60</mn><mo>∘</mo></msup><msup><mn>360</mn><mo>∘</mo></msup></mfrac><mo>×</mo><msup><mi>πr</mi><mn>2</mn></msup><mspace linebreak="newline"/><mo>=</mo><mfrac><mn>1</mn><mn>6</mn></mfrac><mo>×</mo><msup><mi>πr</mi><mn>2</mn></msup></math>
প্রশ্নঃ ABCD is a square, EFGH is a rectangle, AB=3, EF=4, FG=6. Determine the area of the region outside of ABCD and inside of EFGH.
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Area of the square = <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>3</mn><mn>2</mn></msup><mo>=</mo><mn>9</mn></math>
Area of the rechangle = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>×</mo><mn>6</mn><mo>=</mo><mn>24</mn></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Area of region outside of ABCD & inside of EFGH = 24 - 9 = 15
প্রশ্নঃ If x+2y=4, and x/y=2 then determine the value of x and y.
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>x</mi><mi>y</mi></mfrac><mo>=</mo><mn>2</mn><mspace linebreak="newline"/><mo>⇒</mo><mi>x</mi><mo>=</mo><mn>2</mn><mi>y</mi><mspace linebreak="newline"/><mo>∴</mo><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>x</mi><mo>=</mo><mn>4</mn><mspace linebreak="newline"/><mo>⇒</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>4</mn><mspace linebreak="newline"/><mo>⇒</mo><mi>x</mi><mo>=</mo><mn>2</mn><mspace linebreak="newline"/><mo>∴</mo><mi>y</mi><mo>=</mo><mn>1</mn></math>
প্রশ্নঃ After x years Sujan will be y years old. After z years Sujan will be---
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Present age of Sujan= y-x years
After z years Sujan will be y-x+z years old
প্রশ্নঃ A bakery opened yesterday with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon, and 80% of the remaining rolls were sold between noon and closing time. How many dozen rolls had been sold when the bakery closed yesterday?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Sold by noon = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>40</mn><mn>2</mn></mfrac><mo>=</mo><mn>20</mn><mo> </mo><mi>d</mi><mi>o</mi><mi>z</mi><mi>e</mi><mi>n</mi><mo> </mo><mi>r</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>s</mi></math>
80% of remaining = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>×</mo><mn>80</mn><mo>%</mo><mo>=</mo><mn>16</mn><mo> </mo><mi>d</mi><mi>o</mi><mi>z</mi><mi>e</mi><mi>n</mi><mo> </mo><mi>r</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>s</mi></math> sold between noon & closing time
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> After closing <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>20</mn><mo>-</mo><mn>16</mn></mrow></mfenced><mo> </mo><mi>d</mi><mi>o</mi><mi>z</mi><mi>e</mi><mi>n</mi><mo>=</mo><mn>4</mn><mo> </mo><mi>d</mi><mi>o</mi><mi>z</mi><mi>e</mi><mi>n</mi><mo> </mo><mi>r</mi><mi>o</mi><mi>l</mi><mi>l</mi><mi>s</mi><mo> </mo><mi>a</mi><mi>r</mi><mi>e</mi><mo> </mo><mi>u</mi><mi>n</mi><mi>s</mi><mi>o</mi><mi>l</mi><mi>d</mi><mo>.</mo></math>
প্রশ্নঃ A 40 feet long rope is cut into two pieces. If one piece is longer than the other by 18 feet, what is the length, in feet, of the shorter piece?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Let, length of one piece be x. Then, another pieces lengh= x+10
Shorter piece= x+x+10= 40
2x=22
x=11
প্রশ্নঃ 2 bats and 2 balls cost Tk. 300. 5 bats and 5 balls cost Tk. 750.3 balls and 3 bats cost ----
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
2 bats & 2 balls cost Tk. 300
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> 1 " " 1 " " = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>300</mn><mn>2</mn></mfrac><mo>=</mo><mn>150</mn></math> Tk.
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> 3 " " 3 " " = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>150</mn><mo>×</mo><mn>3</mn><mo>=</mo><mn>450</mn></math> Tk.
প্রশ্নঃ The sum of 5 consecutive integers is 105. The sum of the first 2 is -----
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
x+(x-1)+(x+2)+(x+3)+(x+4)= 105
5x+10=105
5x=95
x=19
x+(x-1)19+20=39
প্রশ্নঃ The interest charged on a loan is Tk. p per Tk. 1,000 for the first month and Tk. q per Tk. 1,000 for each month after the first month. How much interest will be charged during the first three months on a loan of Tk. 10,000?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
For the first month interest of Tk 10000 =10p
For the second & third month interest of Tk 10000= 10q+10q= 20q
Total interest= 10p+20q
প্রশ্নঃ A man invests Tk. 9,00,000 in a share earning Tk. 9 as dividend per share, when a share of face value of Tk.100 is selling for Tk. 150. What is his annual income?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Total number of shares = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>9</mn><mo>,</mo><mn>00</mn><mo>,</mo><mn>000</mn></mrow><mn>100</mn></mfrac><mo>=</mo><mn>9</mn><mo>,</mo><mn>000</mn></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Total annual income = <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi>k</mi><mo>.</mo><mo> </mo><mn>9</mn><mo>,</mo><mn>000</mn><mo>×</mo><mn>9</mn><mspace linebreak="newline"/><mo>=</mo><mo> </mo><mi>T</mi><mi>k</mi><mo>.</mo><mo> </mo><mn>81</mn><mo>,</mo><mn>000</mn></math>
[Annual income শুধু dividend থেকে আসে। So selling price দিয়ে হিসাব করলে হবে না।]
প্রশ্নঃ =?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><msup><mi>y</mi><mn>2</mn></msup></mrow><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow></mfrac><mspace linebreak="newline"/><mo>=</mo><mfrac><mrow><mn>2</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow></mfenced><mo>+</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>-</mo><mi>y</mi></mrow></mfenced></mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow></mfenced></mfrac><mspace linebreak="newline"/><mo>=</mo><mfrac><mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow></mfenced><mstyle displaystyle="true"><mfenced><mrow><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mn>2</mn></mrow></mfenced></mstyle></mrow><mfenced><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow></mfenced></mfrac><mspace linebreak="newline"/><mo>=</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mn>2</mn></math>
[Answer is not given in the choice]
প্রশ্নঃ On Monday, a person mailed 8 packages weighing an average of pounds and on Tuesday, 4 packages weighing an average of pounds. What was the average weight, on pounds, of all the packages the person mailed on both days?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
Total weight of packages mailed on the 1st day = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mfrac><mn>3</mn><mn>8</mn></mfrac><mo>×</mo><mn>8</mn><mo>=</mo><mn>99</mn><mo> </mo><mi>p</mi><mi>o</mi><mi>u</mi><mi>n</mi><mi>d</mi><mi>s</mi></math>
Total weight of packages mailed on the 2nd day = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>×</mo><mn>4</mn><mo>=</mo><mn>61</mn><mo> </mo><mi>p</mi><mi>o</mi><mi>u</mi><mi>n</mi><mi>d</mi><mi>s</mi></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Average weight = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>99</mn><mo>+</mo><mn>61</mn></mrow><mrow><mn>8</mn><mo>+</mo><mn>4</mn></mrow></mfrac><mo>=</mo><mn>13</mn><mfrac><mn>1</mn><mn>3</mn></mfrac><mo> </mo><mi>p</mi><mi>o</mi><mi>u</mi><mi>n</mi><mi>d</mi><mi>s</mi></math>
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