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2012 Khagrachori Question

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Page 1: 2012 Khagrachori Question

���-����� ����� - �� ��� � �� ���� ��� ���� �� � �� � �� � � ����

������: �������� � �� � � ���� � �

�� ������ ����, ����� �� �� �� ������। 1

�������� : ����� (�� -� � ��) ��: � ��� �� �� �

�(������): � ��(���� ���):

Name (In English): Registration No:

[�� ������ �� � ���� ��� ���� ���। ����� ��� ���� ���� ������ ���� ��� ��� �� ��� ��� ���। ��� ����� ����� �� !��� ��"�#। ������ �� �� ���� ��� ��� ���।]

� ���� ��� � ���� �: �$ �% &� ����� &�

Write in numbers: twenty lacs two thousand and two

� ���� ����� �� '(�� ���)� ��� 42 ��� ����#। + '(��� �������$ �� ����% �� ��� ����#? Tamim Iqbal scored 42 runs in an over. How many runs did Bangladesh score at least in that over?

� !, ������� ���)� ��� ����' !�) ��� ���� ���� )��)� ����� ���। 33, 23432, 191 �-��� )��)� ������ �����.। /) 0���� ����� )��)� ����� ��� �" 0���� %12�� )��)� ������ ��3� ��� �� ��? If a number remains unchanged when reversed, it is called a palindrome. 33, 23432, 191 are examples of palindromes. What is the difference between the largest palindrome of 8 digits and smallest palindrome of 9 digits?

� a ��) �����।

3++++aa

(4��$) 107

� ����। a � ��� ��?

a is a number. The fraction 3++++a

ais equal to

107

. What is the value of a ?

� ��) 5���� #���� �� '�� 58 !��। + 5��� ��1� ���� #� ��� (� ����। ��� 5���� �� '�� !��� 59 !�� ����। ��1� ���� #��� !��) '�� 200 !�� ��� 5��� /�� ���� #� #�? Average weight of the students in a class is 58 kg. Three new students are admitted and the average weight becomes 59 kg. Total weight of those three students is 200 kg. What was the initial number of students in that class?

� �� 0���� %12�� !�6�� ����� ��� �� 0���� %12�� !�6�� ����� 7��� �(��� ���8�" !#�) �����) ��? What is the smallest number divisible by the smallest prime of one digit and the smallest prime of three digits?

� 0�1 ��� ��1 ����" &) ����� ����#। �� ����� &)� ���- ��� 0�1� !��� �����)� ���- 30। /��� !�� ���- ' ��1� !��� �����)� ���- 40। 0�1 ��� ��1� !��� �����&)� !,��9� ��? Each of Opu and Topu has written a number. The GCD of the number written by Opu and the LCM of these numbers is 30. The GCD of the number written by Topu and the LCM of these numbers is 40. What is the sum of these two numbers?

���$� 8�, AO !����$ DO �� ��� �:। ∠∠∠∠AOC ���

∠∠∠∠DOC � 7 -.। ∠∠∠∠DOB � ��� ��? In this diagram, AO is perpendicular on DO. ∠∠∠∠AOC is 7 times of ∠∠∠∠DOC. What is the value of ∠∠∠∠DOB?

Page 2: 2012 Khagrachori Question

���-����� ����� - �� ��� � �� ���� ��� ���� �� � �� � �� � � ����

������: �������� � �� � � ���� � �

�� ������ ����, ����� �� �� �� ������। 2

� 5 7��� �(��� ��) !����� ������ 0��-���� !,��9� 15। ���� ���8�" !#�) �����)� ���8�" �� !�6��

�������� ��? The sum of the digits of an odd number is 15. The number is divisible by 5. What is the largest prime factor of the smallest such number?

��

���$� 8�, ABCD �� �� 16) ���� !#�) !#�) ��� (�� ��� !������ �����। ABCD �� !%9� 32 �� ��� ��� PQRS �� !%9� �� �� ���? In this diagram, the square ABCD is divided in 16 equal parts. Area of ABCD is 32 square units. What is the area of PQRS?

Page 3: 2012 Khagrachori Question

���-����� ����� - �� ��� � �� ���� ��� ���� �� � �� � �� � � ����

������: �������� � �� � � ���� � �

�� ������ ����, ����� �� �� �� ������। 3

��������: ��� �� (�� -� � ��) ��: � ��� �� �� �

�(������): � ��(���� ���):

Name (In English): Registration No:

[�� ������ �� � ���� ��� ���� ���। ����� ��� ���� ���� ������ ���� ��� ��� �� ��� ��� ���। ��� ����� ����� �� !��� ��"�#। ������ �� �� ���� ��� ��� ���।] � ���� ��� � ���� ����� �� '(�� ���)� ��� 42 �� �� ��। � ���� �������$ �� ����% �� ��� ����#?

Tamim Iqbal scored 42 runs in an over. How many runs did Bangladesh score at least in that over?

� 0�1 ��� ��1 ����" &) ����� ����#। �� ����� &)� ���- ��� 0�1� !��� �����)� ��- 51। !�� !�� "��- ' ��1� !��� �����)� ��- 33। 0�1 ��� ��1� !��� �����&)� !,��9� ��? Each of Opu and Topu has written a number. The LCM of the number written by Opu and the GCD of these numbers is 51. The LCM of the number written by Topu and the GCD of these numbers is 33. What is the sum of these two numbers?

8�, AD⊥⊥⊥⊥BC �!� E ��; AD �� �3��<1। ,� CD = 6 �!�

∆∆∆∆BDE �� !%9� ∆∆∆∆ABC � �� ���" �� ��" �� ���� BC � =�> � �� ���? In the diagram, AD⊥⊥⊥⊥BC and E is the midpoint of AD. If CD = 6 and the area of ∆∆∆∆BDE is one sixth of the area of ∆∆∆∆ABC, then find the length of BC.

��!�� ∠∠∠∠x + ∠∠∠∠y = 2300 । ∠∠∠∠A !��.)� ��� ��?

In this diagram, ∠∠∠∠x + ∠∠∠∠y = 2300. Find the angle ∠∠∠∠A.

���$� 8�, ABCD �� �� 16) ���� !#�) !#�) ��� (�� ��� !������ �����। ABCD �� !%9� 16 �� ��� ��� PQRS �� !%9� �� �� ���? In this diagram, the square ABCD is divided in 16 equal parts. Area of ABCD is 16 square units. What is the area of PQRS?

Page 4: 2012 Khagrachori Question

���-����� ����� - �� ��� � �� ���� ��� ���� �� � �� � �� � � ����

������: �������� � �� � � ���� � �

�� ������ ����, ����� �� �� �� ������। 4

� ���� 5 � ���� ���� �� । ���� ���� � � ���� � ! ������� "��#� �� । �! 5 �

������ ���� ���� �� �$�� ������ %��& ��� '��� ? You have 5 points. No three of them fall on the same line. How many lines can you draw using these points?

���$� 8�, BD = DE = EC। F, AB �� �3��<1। FI||BC,

GHED �� !%9� 18 ��� (1� ABC �� !%9� ��? In this diagram, BD = DE = EC. F is the midpoint of AB. If FI||BC and the area of GHED is 18, what is the area of triangle ABC?

� # n ��) 3��?� �@. �����। �� 0���� !��� %12�� ����� n2 �!� (n + 3)2 �� ��3� ��� �� ��� $ ���� ��� ? Let, n is a positive integer. What is the smallest three digit number that qualifies to be the difference between n2 and (n + 3)2?

�� 8� ���������� ��) �A� 0�$ !������ ��"�#। 8B� �<1-��� ��" ���� ���� C�� ����� ��� $ ��� ��;। ����� x � ��� ��? This diagram shows a fragment of the number line. Here the dotted points are equally spaced and represent successive integers. What is the value of x?

�� ∆∆∆∆ABC � AC ��D�� F �, E �3 � ��� ���� !,� AF = AB ��। A �<1�� ∠∠∠∠ABC � ���� �� ����

!��. ∠∠∠∠FAE $�� ��� !,� AE, BC !� G �<1�� !#� ���। ∠∠∠∠AFE = ∠∠∠∠BAC �!� B �<1 ��" AE �� ���E��� ��� /F�� !����$ �3 � FE !� D �<1�� !#� ���। BGED ��) ����E��, BC = 4GC

�!� ∆∆∆∆ABC �� !%9� 1549

�� BDFC �� !%9��� ba16

/���� !��� ,�"। a + b � ���

��? In ∆∆∆∆ABC, AC is extended upto F so that AF = AB. An angle ∠∠∠∠FAE is drawn at point A so that it is equal to ∠∠∠∠ABC and AE meets BC at G. ∠∠∠∠AFE = ∠∠∠∠BAC and the line parallel to AE drawn from B meets extended FE at D. BGED is a parallelogram, BC = 4GC and

the area of ∆∆∆∆ABC is 1549

. The area of BDFC can be written as ba16

. Find the value

of a + b.

Page 5: 2012 Khagrachori Question

���-����� ����� - �� ��� � �� ���� ��� ���� �� � �� � �� � � ����

������: �������� � �� � � ���� � �

�� ������ ����, ����� �� �� �� ������। 5

��������: ��������(�-�� � ��) ��: � ��� �� �� �

�(������): � ��(���� ���):

Name (In English): Registration No:

[�� ������ �� � ���� ��� ���� ���। ����� ��� ���� ���� ������ ���� ��� �!� �� %�� ���� ��!। ��� ����� ����� �� !��� ��"�#। ������ �� �� ���� ��� ��� ���।] � ���� ��� � ���� ����� �� '(�� ���)� ��� 42 ��� ����#। + '(��� �������$ �� ����% �� ��� ����#?

Tamim Iqbal scored 42 runs in an over. How many runs did Bangladesh score at least in that over?

8�, ∠∠∠∠A � ��� 450 । ∠∠∠∠X + ∠∠∠∠Y + ∠∠∠∠W + ∠∠∠∠Z � ��� ��?

In the given diagram, the value ∠∠∠∠A is 300. What is the value of ∠∠∠∠X + ∠∠∠∠Y + ∠∠∠∠W + ∠∠∠∠Z ?

8�, AD⊥⊥⊥⊥BC �!� E ��; AD �� �3��<1। ,� CD = 6 �!�

∆∆∆∆BDE �� !%9� ∆∆∆∆ABC � �� ���" �� ��" �� ���� BC �� =�> � �� ���? In the diagram, AD⊥⊥⊥⊥BC and E is the midpoint of AD. If CD = 6 and the area of ∆∆∆∆BDE is one sixth of the area of ∆∆∆∆ABC, then find the length of BC.

� &) ������ ���� �� ����� -.9� ��? �����&)� 0E� ��? Square of average of two numbers is equal to their product. What is their difference?

� # n ��) 3��?� �@. �����। n �� !��� %12�� ����� ��� n2 �!� (n + 3)2 �� ��3� ��� �� �� 0�� �$� ��) ����� �"? Let, n is a positive integer. What is the smallest value of n so that that the difference between n2 and (n + 3)2 is a three digit number?

�� 8� ���������� ��) �A� 0�$ !������ ��"�#। 8B� �<1-��� ��" ���� ���� C�� ����� ��� $ ��� ��;। ����� x � ��� ��? This diagram shows a fragment of the number line. Here the dotted points are equally spaced and represent successive integers. What is the value of x?

� 3643 ======== ba ��

ba12 ++++ � ��� ��?

What is the value of ba12 ++++ if 3643 ======== ba ?

Page 6: 2012 Khagrachori Question

���-����� ����� - �� ��� � �� ���� ��� ���� �� � �� � �� � � ����

������: �������� � �� � � ���� � �

�� ������ ����, ����� �� �� �� ������। 6

� ���� ��� �

���$� 8�, BD = DE = EC। F, AB �� �3��<1। FI||BC,

HIEC �� !%9� 13 ��� (1� ABC � !%9� ��? In this diagram, BD = DE = EC. F is the midpoint of AB. If FI||BC and the area of HIEC is 18, what is the area of triangle ABC?

� 522 ++++++++ xx ��&�� qpxx ++++++++ 24 ��& ���� ������ �� q � ��� ��?

The polynomial 522 ++++++++ xx divides the polynomial qpxx ++++++++ 24 . What is the value of q?

�� ∆∆∆∆ABC � AC ��D�� F �, E �3 � ��� ���� !,� AF = AB ��। A �<1�� ∠∠∠∠ABC � ���� �� ����

!��. ∠∠∠∠FAE $�� ��� !,� AE, BC !� G �<1�� !#� ���। ∠∠∠∠AFE = ∠∠∠∠BAC �!� B �<1 ��" AE �� ���E��� ��� /F�� !����$ �3 � FE !� D �<1�� !#� ���। BGED ��) ����E��, BC = 4GC

�!� ∆∆∆∆ABC �� !%9� 1549

�� BDFC �� !%9��� ba16

/���� !��� ,�"। a + b � ���

��? In ∆∆∆∆ABC, AC is extended upto F so that AF = AB. An angle ∠∠∠∠FAE is drawn at point A so that it is equal to ∠∠∠∠ABC and AE meets BC at G. ∠∠∠∠AFE = ∠∠∠∠BAC and the line parallel to AE drawn from B meets extended FE at D. BGED is a parallelogram, BC = 4GC and

the area of ∆∆∆∆ABC is 1549

. The area of BDFC can be written as ba16

. Find the value

of a + b.

Page 7: 2012 Khagrachori Question

���-����� ����� - �� ��� � �� ���� ��� ���� �� � �� � �� � � ����

������: �������� � �� � � ���� � �

�� ������ ����, ����� �� �� �� ������। 7

��������: ����� �������� (� �!"-����-�#$����) ��: � ��� �� �� �

�(������): � ��(���� ���):

Name (In English): Registration No:

[�� ������ �� � ���� ��� ���� ���। ����� ��� ���� ���� ������ ���� ��� ��� �� ��� ��� ���। ��� ����� ����� �� !��� ��"�#। ������ �� �� ���� ��� ��� ���।] � ���� ��� � ���� ����� �� '(�� ���)� ��� 42 ��� ����#। + '(��� �������$ �� ����% �� ��� ����#?

Tamim Iqbal scored 42 runs in an over. How many runs did Bangladesh score at least in that over?

8�, AD⊥⊥⊥⊥BC �!� E ��; AD �� �3��<1। ,� CD = 6 �!�

∆∆∆∆BDE �� !%9� ∆∆∆∆ABC � �� ���" �� ��" �� ���� BC � =�> � �� ���? In the diagram, AD⊥⊥⊥⊥BC and E is the midpoint of AD. If CD = 6 and the area of ∆∆∆∆BDE is one sixth of the area of ∆∆∆∆ABC, then find the length of BC.

� 5 7��� �(��� ��) !����� ������ 0��-���� !,��9� 15। ���� ���8�" !#�) �����)� ���8�" �� !�6�� �������� ��? The sum of the digits of an odd number is 15. The number is divisible by 5. What is the largest prime factor of the smallest such number?

� &) ������ ���� �� ����� -.9� ��? �����&)� 0E� ��? Square of average of two numbers is equal to their product. What is their difference?

� !, ������� ���)� ��� ����' !�) ��� ���� ���� )��)� ����� ���। 33, 23432, 191 �-��� )��)� ������ �����.। �� 0���� ����� )��)� ����� �. " �� !,� ��� 0��-���� !,��9� ��) !�6�� ����� �"। If a number remains unchanged when reversed, it is called a palindrome. 33, 23432, 191 are examples of palindromes. Find the largest three digit palindrome whose sum of digits is a prime.

� ��) !��$��� 50% #� 91)�� !���� �#< ���, 45% #� C��) !���� �#< ��� ��� 5% &�)� !���� �#< ���। G31 3 �� #� !��� !���� �#< ��� ��। + !��$�� �� �� #� /�#? In a given section, 50% students like to play football, 45% like to play cricket and 5% like to play both. Only 3 students don’t like to play any of these games. What is the total number of students in that section?

� x + 2y – 6z = 5 2x + y + 2z = 6 3x + by – 4z = 11

���$� ��H !�'"� �� ��.-��� x, y �!� z �� 0� � ����� ����� ��� ��� �"। ����� b � ��� ��? The given set of equations has infinitely many solutions for real x, y and z. What is the value of b?

Page 8: 2012 Khagrachori Question

���-����� ����� - �� ��� � �� ���� ��� ���� �� � �� � �� � � ����

������: �������� � �� � � ���� � �

�� ������ ����, ����� �� �� �� ������। 8

���$� 8�, BD = DE = EC। F, AB �� �3��<1। FI||BC,

∆∆∆∆AGH �� !%9� 3 ��� (1� ABC �� !%9� ��? In this diagram, BD = DE = EC. F is the midpoint of AB.

If FI||BC and the area of ∆∆∆∆AGH is 3, what is the area of triangle ABC?

� 722 ++++−−−− xx ��&�� qpxx ++++++++ 24 ��& ���� ������ �� q � ��� ��?

The polynomial 722 ++++−−−− xx divides the polynomial qpxx ++++++++ 24 . What is the value of q?

�� ∆∆∆∆ABC � AC ��D�� F �, E �3 � ��� ���� !,� AF = AB ��। A �<1�� ∠∠∠∠ABC � ���� �� ����

!��. ∠∠∠∠FAE $�� ��� !,� AE, BC !� G �<1�� !#� ���। ∠∠∠∠AFE = ∠∠∠∠BAC �!� B �<1 ��" AE �� ���E��� ��� /F�� !����$ �3 � FE !� D �<1�� !#� ���। BGED ��) ����E��, BC = 4GC

�!� ∆∆∆∆ABC �� !%9� 1549

�� BDFC �� !%9��� ba16

/���� !��� ,�"। a + b � ���

��? In ∆∆∆∆ABC, AC is extended upto F so that AF = AB. An angle ∠∠∠∠FAE is drawn at point A so that it is equal to ∠∠∠∠ABC and AE meets BC at G. ∠∠∠∠AFE = ∠∠∠∠BAC and the line parallel to AE drawn from B meets extended FE at D. BGED is a parallelogram, BC = 4GC and

the area of ∆∆∆∆ABC is 1549

. The area of BDFC can be written as ba16

. Find the value

of a + b.