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Difficult Questions

Mathematics Class 7

43 of 43 questions

43
Selected Questions
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Easy
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Medium
43
Hard

🏆 Difficult Questions: Challenge yourself with the hardest questions available.

Q1
hardExpression Building
Find two different expressions to get 5072 using Creative Chitti’s buttons.
A.(50×100)+(7×10)+(2×1) and (3×1000)+(20×100)+(72×1)
B.(5×1000)+(72×1) and (507×10)+(2×1)
C.(5072×1) and (0)
D.Both expressions are the same
Q2
hardOptimization
What is the smallest number of button presses to get 8300 on Systematic Sippy?
A.13 presses (+1000×8, +100×3)
B.830 presses
C.83 presses
D.8 presses
Q3
hardNumber Names
Read 4050678 in Indian place value notation and write its name in the American system.
A.Four million fifty thousand six hundred seventy-eight
B.Forty lakh fifty thousand six hundred seventy-eight
C.Four million fifty lakh sixty thousand
D.None of the above
Q4
hardSubtraction
Convert 14,63,128 – 4,90,020 exactly.
A.9,73,108
B.9,63,108
C.9,73,008
D.9,63,008
Q5
hardNumber Patterns
What pattern is observed when multiplying 1111 × 1111?
A.1234321
B.1111111
C.1110000
D.Wrong pattern
Q6
hardFascinating Facts
The average Amazon discharge per second is given by 6400 × 62,500. What is this product?
A.400,000,000
B.380,000,000
C.420,000,000
D.360,000,000
Q7
hardCreative Thinking
Starting from 42,019 (23 sticks), adding two sticks yields 42,078. What is another valid bigger number?
A.42,091
B.42,029
C.42,019
D.42,000
Q8
hardCombinatorics
Using digits 0–9 once, what is the largest multiple of 5?
A.9876543120
B.9876543210
C.9876543102
D.9876543012
Q9
hardRounding
Write the seven nearest neighbours (thousand to crore) for 3,87,69,957: what is the nearest crore?
A.4,00,00,000
B.3,00,00,000
C.3,80,00,000
D.3,90,00,000
Q10
hardOptimization
Which button combination gives the fewest presses for 20,800 on Systematic Sippy?
A.+10,000×2 + +1,000×0 + +100×8
B.+10,000×2 + +1,000×1 + +100×8
C.+10,000×2 + +1,000×0 + +100×80
D.+10,000×2 + +1,000×0 + +100×80
Q11
hardCounting
How many stick segments to write 5108 in toothpick digits?
A.20
B.19
C.21
D.22
Q12
hardEvaluation
Evaluate 48 – 10 × 2 + 16 ÷ 2 using order of operations.
A.54
B.28
C.36
D.32
Q13
hardReasoning
Without calculating, which has greater value: (8 – 3) × 29 or (3 – 8) × 29?
A.First is greater
B.Second is greater
C.They are equal
D.Cannot tell
Q14
hardWord Problems
Melvin reads 2 pages daily except Tuesdays and Saturdays. In 8 weeks how many pages?
A.5 × 2 × 8
B.7 × 2 × 8
C.(7 – 2) × 2 × 8
D.(7 – 2) × 8
Q15
hardReasoning
Which pair of expressions are equal without calculation?
A.(6 + 10) – 2 and 6 + (10 – 2)
B.(16 – 8) – 3 and 16 – (8 – 3)
C.Both A and B
D.Neither
Q16
hardEvaluation
Evaluate 6 × 3 – 4 × 5 using order of operations.
A.–2
B.–14
C.–8
D.2
Q17
hardEvaluation
Evaluate 39 – 2 × 6 + 11 without brackets.
A.28
B.42
C.38
D.36
Q18
hardComparison
Which is the correct ascending order of values: 67 – 19, 67 – 20, 35 + 25, 5 × 11, 120 ÷ 3?
A.47, 48, 60, 55, 40
B.48, 47, 60, 55, 40
C.40, 47, 48, 55, 60
D.47, 48, 55, 60, 40
Q19
hardWord Problems
Which story situation matches the expression 89 + 21 – 10?
A.Queen gives coins and loses some
B.Buying items and getting change
C.Group forming game
D.Rice packets problem
Q20
hardReasoning
Which two expressions are equal by reasoning, not calculation?
A.(34 – 28) × 42 and 34 × 42 – 28 × 42
B.15 + 9 × 18 and (15 + 9) × 18
C.23 × (17 – 9) and 23 × 17 + 23 × 9
D.All of the above
Q21
hardPaper Folding
In paper folding activity how many parallel lines do you get after two horizontal folds on a square sheet
A.Two
B.Three
C.Four
D.Five
Q22
hardNotations
Which notation denotes two sets of parallel lines in a figure
A.Single arrow marks for both sets
B.Double arrow marks for second set
C.Square mark for parallelism
D.Arrowheads on endpoints
Q23
hardParallel Lines
What property of corresponding angles is both necessary and sufficient to establish parallelism
A.They are supplementary
B.They are equal
C.They are complementary
D.They are right angles
Q24
hardTransversals
What is the maximum number of distinct angle measures formed when a transversal intersects two lines
A.Four
B.Six
C.Eight
D.Two
Q25
hardAlternate Angles
Which angles are called alternate exterior angles
A.Angles outside the two lines on opposite sides of transversal
B.Angles inside the two lines on opposite sides of transversal
C.Angles inside on the same side
D.Angles outside on the same side
Q26
hardAlternate Angles
Which angle is the alternate interior of angle e in figure five point twenty five
A.Angle c
B.Angle d
C.Angle f
D.Angle g
Q27
hardApplications
Which discipline is not mentioned as an application of geometry in the chapter introduction
A.Art
B.Engineering
C.Biology
D.Physics
Q28
hardChallenges
In the figure it out questions why might it be challenging to draw lines parallel to inclined segments on rectangular dot sheet
A.Lack of ruler
B.Eye strain
C.Different orientation makes intuition harder
D.Dots are unevenly spaced
Q29
hardTriangle Inequality
Which case describes circles touching at exactly one point during triangle construction?
A.No intersection
B.Touching externally
C.Touching internally
D.Intersecting at two points
Q30
hardTriangle Inequality
Which construction case leads to no triangle formation?
A.Circles intersecting
B.Circles touching internally
C.Circles not intersecting
D.Circles coincident
Q31
hardAngle Properties
Which pair of angles cannot be adjacent angles of a triangle if their sum ≥ 180°?
A.40° and 100°
B.30° and 130°
C.60° and 70°
D.50° and 120°
Q32
hardConstructions
Which pair of given sides and included angle can sometimes fail to construct a triangle?
A.3 cm, 5 cm, 60°
B.4 cm, 7 cm, 140°
C.5 cm, 6 cm, 30°
D.2 cm, 3 cm, 45°
Q33
hardConstructions
What does the construction ‘ASA’ guarantee in triangle formation?
A.Unique triangle up to congruence
B.Multiple triangles
C.No triangle
D.Infinite triangles
Q34
hardAngle Sum Property
Which method uses paper folding to demonstrate angle sum property?
A.Compass arcs
B.Fold all three vertices to meet
C.Fold parallel line
D.Fold base in half
Q35
hardConstructions
Which construction cannot determine a triangle uniquely?
A.SSS
B.SAS
C.ASA
D.SSA
Q36
hardAngle Properties
Which pair of angles can always form a triangle with some side length?
A.90° and 95°
B.100° and 85°
C.120° and 70°
D.140° and 30°
Q37
hardConstructions
What is the least value of external angle B that prevents triangle formation with angle A fixed at 40°?
A.90°
B.100°
C.140°
D.180°
Q38
hardConstructions
What is proven by constructing full circles in triangle side-side cases?
A.Altitude length
B.Intersection existence
C.Angle sum
D.Parallel lines
Q39
hardTriangle Inequality
Which condition ensures two circles intersect at two points internally?
A.Sum of radii = base
B.Sum of radii < base
C.Sum of radii > base
D.Difference of radii = base
Q40
hardWord Problems
How much did Somu keep after giving to children? (5/6 −5/12−5/18)
A.5/36
B.1/6
C.5/12
D.1/3
Q41
hardHistorical Context
Who first stated the general rule for fraction multiplication?
A.Brahmagupta
B.Aryabhata
C.Bhāskara II
D.Umasvati
Q42
hardHistorical Context
In which work did Brahmagupta state fraction multiplication?
A.Brāhmasphuṭasiddhānta
B.Līlāvatī
C.Āryabhaṭīyabhāṣhya
D.Śhulbasūtra
Q43
hardHistorical Context
Who wrote Līlāvatī?
A.Bhāskara II
B.Brahmagupta
C.Śhrīdharāchārya
D.Caturveda
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