9 वी - महाराष्ट्र बोर्ड - गणित भाग - 2 - टेस्ट - चॅप्टर 1 - Basic Concepts of Geometry
9 वी - महाराष्ट्र बोर्ड - गणित भाग - 2 - टेस्ट - चॅप्टर 1 - Basic Concepts of Geometry
2) Distance काढत असतांना दोन्ही point च्या co-ordinate मधील जो co-ordinate मोठा असेल, त्यातनं छोट्या co-ordinate ला वजा करायचे, येणारं उत्तर म्हणजेच त्या दोन point मधील अंतर असेल.
3) याच पद्धतीने काही प्रश्नांमध्ये एखाद्या segment चा midpoint दिलेला असेल आणि आपल्याला त्या segment च्या एका section चं distance काढायला सांगितलेलं असेल.
4) उदाहरणार्थ एखादा segment जर का 8 cm चा असेल, तर midpoint पासून end point पर्यंतच अंतर हे 8 च्या निम्मे म्हणजेच 4 cm च असेल.
5) काही प्रश्नांमध्ये if आणि then या स्वरूपात काही वाक्य लिहायला सांगितलेली आहेत. यामध्ये एक वाक्य किंवा एक statement आपल्याला दिलेलं असेल आणि त्या statement मधील दोन भाग, पहिला भाग if आणि then च्या मध्ये, तर दुसरा भाग then नंतर असा वापरायचा आहे.
6) अशाच पद्धतीने statement जर का conditional form मध्ये म्हणजेच if... then च्या स्वरूपामध्ये दिलेलं असेल, तर त्याचा converse लिहायला सांगितलेला आहे.
7) Converse लिहत असताना then नंतरचा part आधी लिहायचा if नंतर आणि जो original if पासून तर then पर्यंतचा भाग होता, त्याला आता then नंतर लिहायचं.
8) अशाच पद्धतीने दिलेले point collinear आहेत की नाही, collinear जर का असतील तर त्यांचा sequence कसा असेल, त्यांचा क्रम कसा असेल, या पद्धतीचे प्रश्न सुद्धा विचारलेली आहेत.
9) त्यानंतर segment आणि ray हे दिलेले असतील, यांचा आपल्याला union set किंवा intersection set काय असेल, याबद्दलची प्रश्न सुद्धा या प्रकरणामध्ये विचारली गेलेली आहेत.
10) तसेच theorem काय असतात, postulates काय असतात, Direct proof काय असते, indirect proof काय असते, याबद्दलचे प्रश्न सुद्धा विचारले गेलेले आहेत.
9 वी - महाराष्ट्र बोर्ड - गणित भाग - 2 - टेस्ट
चॅप्टर 1 - Basic Concepts of Geometry
Questions
Q1. On a number line, if the co-ordinate of point A is 2 and point B is 7,
what is d(A, B)?
(A) 9
(B) 5
(C) -5
(D) 7
Q2. If the co-ordinate of point P is -3 and point Q is -8, find d(P, Q).
(A) 5
(B) -11
(C) -5
(D) 11
Q3. Distance between two distinct points on a number line is always a _____
real number.
(A) Negative
(B) Non-negative positive
(C) Zero
(D) Fractional
Q4. If d(A, B) = 0, what can be concluded about points A and B?
(A) They are on opposite sides of origin
(B) They are collinear
(C) They are the same point
(D) They are endpoints of a line segment
Q5. If the co-ordinates of X and Y are 4 and -4 respectively, find d(X, Y).
(A) 0
(B) 4
(C) 8
(D) -8
Q6. If d(P, Q) = 7, d(Q, R) = 3, and d(P, R) = 10, which point is between
the other two?
(A) Point P
(B) Point Q
(C) Point R
(D) Points are non-collinear
अजून वाचून पहा : 9 वी - महाराष्ट्र बोर्ड - गणित भाग 1 टेस्ट - चॅप्टर 1 - Sets
Q7. If points A, B, and C are collinear such that A-B-C, and d(A, C) = 15, d(A, B) = 9, find d(B, C).
(A) 24
(B) 6
(C) 12
(D) 9
Q8. Which condition satisfies that point Y is between X and Z (X-Y-Z)?
(A) d(X, Y) + d(Y, Z) = d(X, Z)
(B) d(X, Z) + d(Y, Z) = d(X, Y)
(C) d(X, Y) - d(Y, Z) = d(X, Z)
(D) d(X, Y) \times d(Y, Z) = d(X, Z)
Q9. Given three distinct points A, B, and C. If d(A, B) = 5, d(B, C) = 8, and d(A, C) = 11, are the points collinear?
(A) Yes, with A-B-C
(B) Yes, with B-A-C
(C) No, they form a triangle
(D) Cannot be determined
Q10. Points L, M, and N are collinear. If d(L, M) = 11, d(M, N) = 4, and L-N-M, find d(L, N).
(A) 15
(B) 7
(C) 8
(D) 11
Q11. The set union of segment AB and ray AB is:
(A) Segment AB
(B) Ray AB
(C) Line AB
(D) Point A
Q12. The intersection of Ray AB and Ray BA is:
(A) Line AB
(B) Empty set
(C) Segment AB
(D) Point A
Q13. Opposite rays have a common origin and their union forms a:
(A) Segment
(B) Angle
(C) Straight line
(D) Triangle
Q14. If point M is the midpoint of seg AB, and AB = 9 cm , what is the length of AM?
(A) 4.5 cm
(B) 9 cm
(C) 18 cm
(D) 3 cm
Q15. If length of segment AB = 7 cm and length of segment CD = 7 cm , then seg AB and seg CD are:
(A) Parallel
(B) Perpendicular
(C) Congruent
(D) Opposite
Q16. If l(AB) = 5 cm , l(CD) = 3.5 cm , and l(EF) = 6 cm , which statement is true?
(A) seg AB > seg EF
(B) seg CD < seg AB
(C) seg EF < seg CD
(D) seg AB = seg CD
Q17. How many midpoints can a single line segment have?
(A) Infinite
(B) Two
(C) Exactly one
(D) Depends on its length
Q18. If P is the midpoint of seg CD and CP = 6.4 cm , find l(CD).
(A) 3.2 cm
(B) 12.8 cm
(C) 6.4 cm
(D) 9.6 cm
Q19. Perpendicularity between two segments means the angle formed at their intersection is:
(A) 180 degree
(B) 45 degree
(C) 90 degree
(D) 60 degree
Q20. If AB Congruent CD and CD Congruent EF, then AB Congruent EF. This property of congruence is called:
(A) Reflexivity
(B) Symmetry
(C) Transitivity
(D) Betweenness
Q21. A statement which is written in the "If... then..." form is called a:
(A) Postulate
(B) Conditional statement
(C) Proof
(D) Theorem
Q22. The part of a conditional statement following "if" is called the:
(A) Antecedent (Given)
(B) Consequent (To prove)
(C) Converse
(D) Corollary
Q23. What is the converse of: "If a quadrilateral is a rhombus, then its diagonals are perpendicular bisectors"?
(A) If diagonals are perpendicular bisectors, then the quadrilateral is a rhombus.
(B) If a quadrilateral is not a rhombus, its diagonals are not perpendicular.
(C) All rhombuses have equal diagonals.
(D) Diagonals of a square are always perpendicular.
Q24. Self-evident basic truths which are accepted without proof are called:
(A) Theorems
(B) Postulates
(C) Proofs
(D) Premises
Q25. Which of the following is a Euclid postulate?
(A) Two points determine a unique line.
(B) A circle can be drawn with any center and any radius.
(C) All right angles are congruent to one another.
(D) All of the above.
Q26. A statement proved using logical reasoning based on postulates and defined terms is called a:
(A) Definition
(B) Theorem
(C) Postulate
(D) Hypothesis
Q27. Vertically opposite angles formed by two intersecting lines are always:
(A) Complementary
(B) Supplementary
(C) Congruent (Equal)
(D) Adjacent
Q28. If two angles form a linear pair, then the sum of their measures is:
(A) 90 degree
(B) 180 degree
(C) 360 degree
(D) 120 degree
Q29. In a direct proof, we start with the _____ and logically arrive at the conclusion.
(A) Negation
(B) Given (Antecedent)
(C) Converse
(D) False assumption
Q30. In an indirect proof, we begin by assuming that the statement to be proved is:
(A) True
(B) False
(C) Partially true
(D) A postulate
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