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Q1. Mark against the correct answer: The supplement of 35° is: 55° 65° 145° 165°
1 Mark
Ans: 145° Solution: Supplement of 35° = 180° - 35° = 145°
Q2. If three cubes each of edge 4cm are placed end to end, then the dimensions of resulting solid are: 12cm × 4cm × 4cm 4cm × 8cm × 4cm 4cm × 8cm × 12cm 4cm × 6cm × 8cm
1 Mark
Ans: 12cm × 4cm × 4cm Solution: When three cubes are placed end to end then the dimensions of the resulting solid would be more than the cube. The new cuboid will be having the following dimensions: 12cm × 4cm × 4cm So the correct answer is A.
Q3. Mark against the correct answer. In the given figure, what value of x will make AOB a straight line?
x = 50 x = 100 x = 60 x = 80
1 Mark
Ans: x = 80 Solution: In the figure, AOB is a straight line
Q4. The order of rotational symmetry in the figure given below is: 1 Mark
∠AOC + ∠COD + ∠DOB = 180∘
⇒ 55∘^ + x + 45∘^ = 180∘
⇒ x + 100∘^ = 180∘
⇒ x = 180∘^ − 100∘^ = 80∘
Infinitely many
Ans: 2 Solution: The number of times a figure fits into itself in one full turn is called as order of rotational symmetry. So for the given figure the order of rotational symmetry is two. So the correct answer is B.
Q5. Mark against the correct answer: In a If A B 33° and B C 18°, then 35° 45° 45° 57°
1 Mark
Ans: 55° Solution:
A + B + C = 180° .....(i) Given, A - B = 33° A = 33° + B .....(ii) B - C = 18° C = B + 18° .....(iii) Putting the values of A and B in equation (i): ⇒ B + 33° + B + B - 18° = 180° ⇒ 3B = 180° - 15
Q6. Mark against the correct answer. In the given figure, two straight lines AB and CD intersect at a point O and. Then,
1 Mark
Ans: 50° Solution: AB and CD intersect each other at O and Vertically opposite angles)
Q7. Mark against the correct answer: In side BC has been produced to D such that and Then :
1 Mark
△ABC, ∠B =?
In △ABC :
⇒ B = 165 = 55∘
∘ 3
∠AOC = 50∘
∠BOD =?
∠AOC = 50∘
∠BOD = ∠AOC = 50∘
△ABC, ∠ADC = 125∘^ ∠BAC = 60∘
∠ABC =?
Solution:
Q10. Mark against the correct answer. In AB = 5cm and AC = 13cm. Then, BC ?
8cm. 18cm. 12cm. None of these.
1 Mark
Ans: 12cm. Solution: In But AC = AB + BC By Pythagoras Theoram) ⇒ 13 = 5 + BC ⇒ 169 = 25 + BC ⇒ BC = 169 - 25 = 144 = 12 BC = 12cm
Q11. Mark against the correct answer. The sum of any two sides of a triangle is always: Equal to the third side. Less than the third side. Greater than or equal to the 3rd side. Greater than the 3rd side.
1 Mark
Ans: Greater than the 3rd side. Solution: Sum of any two sides of a triangle is always greater than the third side.
Q12. Mark against the correct answer. is right angled at A. If AB = 24cm and AC = 7cm, then BC =? 31cm. 17cm. 25cm. 28cm.
1 Mark
Ans: 25cm. Solution:
△ABC, ∠B = 90∘,
△ABC, ∠B = 90∘
2 2 2 2 2 2 2 2 2
△ABC
is a right angled, AB = 24cm, AC = 7cm but BC = AB + AC ⇒ BC = 24 + 7 = 576 + 49 = 625 = 25 BC = 25cm.
Q13. Mark against the correct answer. In if and then 25° 30° 35° 40°
1 Mark
Ans: 30° Solution: In
But Angles of a triangle)
Q14. Which of the following nets is a net of a cylinder?
1 Mark
Ans:
Solution: A net is 2 D figure which when folded in a particular axis gives a 3 D figure.
△ABC, ∠A = 90∘
2 2 2 2 2 2
△ABC ∠A = 65∘^ ∠C = 85∘^ ∠B =?
△ABC
∠A = 65∘, ∠C = 85∘
∠A + ∠B + ∠C = 180∘
⇒ 65∘^ + ∠B + 85∘^ = 180∘
⇒ 150∘^ + ∠B = 180∘
⇒ ∠B = 180∘^ − 150∘^ = 30∘
and
(alternate angles) But Ext.
Q18. A triangle can be constructed by taking two of its angles as: 110°, 40° 70°, 115° 135°, 45° 90°, 90°
1 Mark
Ans: 110°, 40° Solution: We know that, the sum of all the angles of a triangle is equal to 180°. So, sum of any two angles of a triangle should be less than 180°. 110° + 40° = 150° i.e. less than 180°. 70° + 115° = 185° i.e. greater than 180°. 135° + 45° = 180° i.e. equal to 180°. 90° + 90° = 180° i.e. equal to 180°. Hence, (a) is the correct option.
Q19. All faces of a pyramid are always: Triangular Rectangular Congruent None of these
1 Mark
Ans: None of these Solution: The faces of pyramid can be triangular or rectangular. But we have to choose only one correct option.
So the correct answer is D.
Q20. Mark against the correct answer. In the given figure, AOB is a straight line, and. The value of x is:
1 Mark
Ans: 112 Solution: In the figure But Linear pair)
PQ ∥ RS,
∠PAB = 60∘^ ∠ACS = 100∘
PQ ∥ RS
∠ABC = ∠PAB 60 ∘
∠ACS = ∠BAC + ∠ABC
⇒ 100∘∠BAC + 60∘
⇒ ∠BAC = 100∘^ − 60∘^ = 40∘
∠AOC = 68∘^ ∠BOC = x∘
∠AOC = 68∘
∠AOC + ∠BOC = 180∘
68 ∘^ + x = 180∘
⇒ x = 180∘^ − 68∘^ = 112∘
Q21. Mark against the correct answer. In side BC has been produced to D. If and then
1 Mark
Ans: 78° Solution: In side BC is produced to D and Ext.
Q22. If we rotate a right-angled triangle of height 5cm and base 3cm about its base, we get: Cone of height 3cm and base 3cm Cone of height 5cm and base 5cm Cone of height 5cm and base 3cm Cone of height 3cm and base 5cm
1 Mark
Ans: Cone of height 3cm and base 5cm Solution: When a right angled triangle of height 5cm and base 3cm is rotated about its base in full turn, then we will get a cone of height 3cm and base of radius 5cm. So the correct answer is D.
Q23. If we rotate a right-angled triangle of height 5cm and base 3cm about its height a full turn, we get: Cone of height 5cm, base 3cm Triangle of height 5cm, base 3cm Cone of height 5cm, base 6cm Triangle of height 5cm, base 6cm
1 Mark
Ans: Cone of height 5cm, base 3cm Solution: If we rotate a right-angled triangle of height 5cm and base 3cm about its height a full turn, then we get a cone of height 5cm and base 3cm.
Q24. In which of the following cases, a unique triangle can be drawn: AB = 4cm, BC = 8cm and CA = 2cm BC = 5.2cm, and XY = 5 cm, and An isosceles triangle with the length of each equal side 6.2cm.
1 Mark
Ans: XY = 5 cm, and Solution: Let us draw the triangle according to measurement given in respective options. As we can see, triangle cannot be drawn.
Triangle cannot be formed.
△ABC, ∠ACD = 132∘^ ∠A = 54∘^ ∠B =?
△ABC,
△ACD = 132∘^ ∠A = 54∘
∠ACD = ∠A + ∠B
⇒ 132∘^ = 54∘^ + ∠B
⇒ ∠B = 132∘^ − 54∘^ = 78∘
∠B = 90∘^ ∠C = 110∘
∠X = 45∘^ ∠Y = 60∘
∠X = 45∘^ ∠Y = 60∘
Ans: Cone Solution: The cone is the shape, that has only one vertex. Hence, (c) is the correct option.
Q29. Mark against the correct answer. A ladder is placed in such a way that its foot is 15 m away from the wall and its top reaches, a window 20 m above the ground. The length of the ladder is: 35m. 25m. 18m. 17.5m.
1 Mark
Ans: 25m. Solution:
Let AB is a ladder and A is the window BC = 15m, AC = 20m Now in right AB = BC + AC = 15 = 20 = 225 + 400 = 625 = 25 AB = 25m
Q30. Mark against the correct answer. Two supplementary angles are in the ratio 3 : 2. The smaller angle measures: 108° 81° 72° None of these.
1 Mark
Ans: 72° Solution: Two supplementary angle are in the ratio = 3 : 2 Let first angle = 3x Second angle = 2x But 3x + 2x = 180° ⇒ 5x = 180° ⇒ x = 36° Smaller angle = 2x = 2 36° = 72°
Q31. Mark against the correct answer. In the adjoining figure, what of x will make AOB a straight line?
x = 30 x = 35 x = 25 x = 40
1 Mark
Ans: x = 35 Solution: In the figure,
△ABC
2 2 2 2 2 2
AOB is a straight line Linear pair)
Q32. Mark against the correct answer. The angles of a triangle are in the ratio 2 : 3 : 7. The measure of the largest angle is: 84° 98° 105° 91°
1 Mark
Ans: 105° Solution: The ratio of angles of a triangle is 2 : 3 : 7 But sum of angles of a triangle = 180° Measure of largest angle
Q33. Mark against the correct answer. is an isosceles triangle with and AC = 5cm. then, AB =? 2.5cm. 5cm. 15m.
1 Mark
Ans: Solution:
is an isosceles triangle
AC = 5cm BC = AC = 5cm In right AB = AC + BC = 5 + 5 = 25 + 25 = 50 = 2 25
Q34. Mark against the correct answer. In a if and Then, 35° 55° 45° 57°
1 Mark
Ans: 55° Solution: In and and But
∠AOC + ∠BOC = 180∘
⇒ 2x − 10∘^ + 3x + 15∘^ = 180∘
5x = 180∘^ + 10∘^ − 15∘^ = 175∘
⇒ x = 35∘
x = 35
∘× 2+3+
∘× 2+3+
△ABC ∠C = 90∘
5√2cm.
5√2cm.
△ABC
∠C = 90∘
△ABC
2 2 2 2 2
AB = √2 × 25 = 5√2cm
△ABC, ∠A − ∠B = 33∘^ ∠B − ∠C = 18∘. ∠B =?
△ABC,
∠A − ∠B = 33∘^ ∠B − ∠C = 18∘.
∠A = 33∘^ + ∠B ∠C = ∠B − 18∘
∠A + ∠B + ∠C = 180∘
⇒ 33∘^ + ∠B + ∠B + ∠B − 18∘^ = 180∘
⇒ 3∠B = 180∘^ − 33∘^ + 18∘^ = 165∘
⇒ ∠B = 55∘
Ans: 1.5cm, 3.6cm, 3.9cm Solution: The sides of right-angled triangle must satisfy Pythagoras theorem. Hypotenuse) = Base) + Perpendicular) Note: Hypotenuse is the largest side of all the sides. So, check all options by putting the values in above formula. Let us check all the options. 6 = 3 + 4 36 = 9 + 16 36 ≠ 25 26 = 16 + 9 = 676 = 256 + 81 676 ≠ 337 3.9 = 1.5 + 3.6 = 15. = 2.25 + 12. = 15. = 15.21 (satisfied) 26 = 7 + 24 = 676 = 49 + 576 = 676 ≠ 625 Clearly, option (c) is correct.
Q39. Total number of edges a cylinder has: 0 1 2 3
1 Mark
Ans: 2 Solution: The total number of edges of a cylinder are two. The figure of cylinder is as follows:
So the correct answer is C.
Q40. Mark against the correct answer. An angle is 32° less than its supplement. The measure of the angle is: 37° 74° 148° None of these.
1 Mark
Ans: 74° Solution: Let required angle = x Then its supplement angle = x + 32 But x + x + 32° = 180° ⇒ 2x = 180° 32 = 148° x = 74° Required angle = 74°
Q41. Take a square piece of paper as shown in figure 1 . Fold it along its diagonals as shown in figure 2 . Again fold it as shown in figure 3 . Imagine that you have cut off 3 pieces of the form of congruent isosceles right-angled triangles out of it as shown in figure 4.
1 Mark
2 2 2
2 2 2
2 2 2
2 2 2
2 2 2
On opening the piece of paper which of the following shapes will you get?
Ans:
Q45. Mark against the correct answer. In the given figure, AOB is a straight line, , and. The value of x is:
1 Mark
Ans: 32 Solution: AOB is a straight line
⇒ 3x 8° + 50° + x + 10° = 180° ⇒ 4x = 180° + 8° 50° 10° ⇒ 4x = 128° ⇒ x = 32°
Q46. Mark against the correct answer. In the given figure, , and Then,
1 Mark
Ans: 30° Solution: In the figure,
and
Similarly
But
Q47. The order of rotational symmetry in the Fig given below is: 1 Mark
⇒ x = 150∘
∠AOC = (3x-8)∘^ ∠COD = 50∘^ ∠BOD = (x+10)∘
∠AOC + ∠COD+∠DOB = 180∘
AB∥CD ∥ EF, ∠ABG = 110∘, ∠GCD = 100∘^ BCG = x∘^ x =?
PQ∥RS∥EF
∠ABG = 110∘^ ∠GCD = 100∘
∠BGC = x∘
AB ∥ EF
∠ABG + ∠BGE = 180∘
⇒ 110∘^ + ∠BGE = 180∘
⇒ ∠BGE = 180∘^ − 110∘^ = 70∘
CD ∥ EF
∠GCD + ∠CGF = 180∘
⇒ 100∘^ + ∠CGF = 180∘
∠BGE + ∠BGC + ∠CGF = 180∘
⇒ 70∘^ + x + 80∘^ = 180∘
⇒ x = 180∘^ − 150∘^ = 30∘
Infinitely many
Ans: 6 Solution: Since, the number of times a figure fits onto itself in one full turn is called order of rotational symmetry. Therefore, the given figure has rotational symmetry of order 6.
Q48. Mark against the correct answer. In a it is given that and Then, 86° 66° 114° 57°
1 Mark
Ans: 114° Solution: In But (angles of a triangle)
Q49. Mark against the correct answer. An angle is one-fifth of its supplement. The measure of the angle is: 30° 15° 75° 150°
1 Mark
Ans: 30° Solution: The angle is one-fifth of its supplement Let angle be x, then ⇒ x + 5x = 180° ⇒ 6x = 180° x = 30° Angle is 30°
Q50. When a torch is pointed towards one of the vertical edges of a cube, you get a shadow of cube in the shape of: Square Rectangle but not a square Circle Triangle
1 Mark
Ans: Rectangle but not a square Solution: When a torch is pointed towards one of the vertical edges of a cube, you get a shadow of cube in the shape of rectangle but not a square.
Q51. Mark against the correct answer. In the given figure, and Then,
1 Mark
△ABC ∠B = 37∘^ ∠C = 29∘^ ∠A =?
△ABC, ∠B = 90∘, ∠G = 29∘
∠A + ∠B + ∠C = 180∘
⇒ ∠A + 37∘^ + 29∘^ = 180∘
⇒ ∠A + 66∘^ = 180∘
⇒ ∠A = 180∘^ − 66∘^ = 114∘
∠A = 50∘, CE∥BA ∠ECD = 60∘. ∠ACB =?
Ans: 10° Solution: Complement of 80° is 10° 10° + 80° = 90°
Q55. The number of lines of symmetry in Fig is:
Infinitely many
1 Mark
Ans: 3 Solution: The given figure has 3 lines of symmetry.
Q56. Which of the following letters of English alphabets have more than 2 lines of symmetry?
1 Mark
Ans:
Solution: The letter 0 has more than two lines of symmetry.
Q57. Mark against the correct answer. An angle is 24° more than its complement. The measure of the angle is: 47° 57° 53° 66°
1 Mark
Ans: 57° Solution: Let angle is x Then its complement angle = x - 24° But x + x - 24° = 90° ⇒ 2x = 90° + 24° = 114° x = 57° The required angle is 57°
Q58. Mark against the correct answer. The supplement of 45° is: 45° 75° 135° 155°
1 Mark
Ans: 135° Solution: Supplement of 45° is 135° 135° + 45° = 180°
Q59. The number of lines of symmetry in the figure given below is:
Infinitely many
1 Mark
Ans: 6 Solution: Line of symmetry is the line which divides a figure into two equal halves which are mirror image of each other. So for the given figure, it has six grooves or inside edge through which we can draw three lines of symmetry. The figure also has six outside edge through which we can draw three lines of symmetry.
