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Question 1 of 12
1. Question
3 pointsSOLVE:
5(2 – 3x) – 17(2x – 5) = 16
Correct
Incorrect
10 – 15x – 34x + 85 = 16
10 + 85 – 34x – 15x = 16
95 – 49x = 16
-49x = -79
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Question 2 of 12
2. Question
3 pointsSOLVE:
Correct
Incorrect
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Question 3 of 12
3. Question
3 pointsFind the greatest number where three consecutive natural numbers such that the sum of the first and second is 15 more than the third.
Correct
Incorrect
Let the first number be ‘x’. Hence, the second number = x + 1 and the third number = x + 2.
=> Sum of first and second numbers = (x) + (x + 1).
According to question:
(x) + (x + 1) = 15 + (x + 2)
=> 2x + 1 = 17 + x
Transposing x to LHS and 1 to RHS, we get
=> 2x – x = 17 – 1
=> x = 16
So, first number = x = 16, second number = x + 1 = 16 + 1 = 17 and third number = x + 2 = 16 + 2 = 18
Thus, the required consecutive natural numbers are 16, 17 and 18.
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Question 4 of 12
4. Question
3 pointsMrs. Jain is 27 years older than her daughter Nilu. After 8 years she will be twice as old as Nilu. Find their present ages.
Correct
Incorrect
Let the present age of Nilu = ‘x’ years.
Therefore, the present age of Nilu’s mother, Mrs. Jain = (x + 27) years.
So, after 8 years,
Nilu’s age = (x + 8), and Mrs. Jain’s age = (x + 27 + 8) = (x + 35) years
=> x + 35 = 2(x + 8)
Expanding the brackets, we get
=> x + 35 = 2x + 16
Transposing x to RHS and 16 to LHS, we get
=> 35 – 16 = 2x – x
=> x = 19
So, the present age of Nilu = x = 19 years, and the present age of Nilu’s mother = x+ 27 = 19 + 27 = 46 years.
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Question 5 of 12
5. Question
3 pointsThe length of a rectangular field is twice its breadth. If the perimeter of the field is 228 metres, find the dimensions of the field.
Correct
Incorrect
2 (2x + x) = 228
=> 2 (3x) = 228
=> 6x = 228
Dividing both sides by 6, we get
=> 6x/6 = 228/6
=> x = 38
So, the breadth of the rectangle = x = 38 metres,
and the length of the rectangle = 2x = 2(38) = 76 metres.
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Question 6 of 12
6. Question
3 pointsAndy has twice as many marbles as Pandy, and Sandy has half as many has Andy and Pandy put together. If Andy has 75 marbles more than Sandy. How many does sandy have?
Correct
Incorrect
Let the number of marbles with Pandy = ‘x’.
So, the number of marbles with Andy = ‘2x’.
Thus, the number of marbles with Sandy =
According to the question,
x = -150
Since, no. of marbles cannot be negative.
Therefore, x = 150
So, Pandy has 150 marbles, Andy has 2x = 2(150) = 300 marbles, and Sandy has 3x/2 = 225 marbles.
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Question 7 of 12
7. Question
3 pointsIn ∆ABC, ∠ABC = 100°, ∠BAC = 35° and BD perpendicular to AC meets side AC in D. If BD = 2 cm, find ∠C, and length DC.
Correct
Incorrect
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Question 8 of 12
8. Question
3 pointsIn Figure, AD and CF are respectively perpendiculars to sides BC and AB of ∆ABC. If ∠FCD = 50°, find ∠BAD
Correct
Incorrect
∠FCB + ∠CBF + ∠BFC = 180°
50° + ∠CBF + 90°= 180°
Or,
∠CBF = 180° – 50°– 90° = 40° … (i)
Using the above rule for ∆ABD, we can say that:
∠ABD + ∠BDA + ∠BAD = 180°
∠BAD = 180° – 90°– 40° = 50° [from (i)]
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Question 9 of 12
9. Question
3 pointsThe side BC of ∆ABC is produced to a point D. The bisector of ∠A meets side BC in L. If ∠ABC= 30° and ∠ACD = 115°, find ∠ALC
Correct
Incorrect
ACD+ ∠ACB = 180°
115° + ∠ACB =180°
∠ACB = 180°– 115°
∠ACB = 65°
We know that the sum of all angles of a triangle is 180°.
Therefore, for ∆ABC, we can say that:
∠ABC + ∠BAC + ∠ACB = 180°
30° + ∠BAC + 65° = 180°
Or,
∠BAC = 85°
∠LAC = ∠BAC/2 = 85/2
Using the above rule for ∆ALC, we can say that:
∠ALC + ∠LAC + ∠ACL = 180°
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Question 10 of 12
10. Question
3 pointsTwo poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, the distance between their tops is
(a) 13 m
(b) 14 m
(c) 15 m
(d) 12.8 mCorrect
Incorrect
Suppose AB and CD are two poles.The is distance between AB and CD is 12 m.
In right traingle BDE,
BD2 = DE2 + BE2
⇒ BD2 = (5)2 + (12)2
⇒ BD2 = 25 + 144
⇒ BD2 = 169
⇒ BD2 = (13)2(52√)2
⇒ BD = 13 m
Hence, the correct answer is option (a). -
Question 11 of 12
11. Question
3 pointsA 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
(a) 35 m
(b) 25 m
(c) 18 m
(d) 17.5 mCorrect
Incorrect
Suppose BC is the ladder which is placed againts the wall OA. The foot of the ladder C is 15 m away from the foot O of the wall and its top reaches the window which is 20 m above the ground.
In right traingle BOC,
BC2 = OC2 + OB2
⇒ BC2 = (15)2 + (20)2
⇒ BC2 = 225 + 400
⇒ BC2 = 625
⇒ BC2 = (25)2
⇒ BC = 25 m
Hence, the correct answer is option (b). -
Question 12 of 12
12. Question
3 pointsIn Fig. 68, the values of x and y are
(a) x = 120, y = 150
(b) x = 110, y = 160
(c) x = 150, y = 120
(d) x = 110, y = 160
Correct
Incorrect
In △DEF
∠DEF + ∠DFE + ∠EDF = 180° [Angle sum property of triangle]
⇒ 110° + 40° + ∠EDF = 180°
⇒ ∠EDF = 30°
Now, ∠EDF + ∠FDA = 180° [Linear pair angles]
⇒ 30° + x° = 180°
⇒ x = 150
Now, ∠EDF = ∠ADB = 30° [Vertically opposite angles]
Now, In △ABD
∠ADB + ∠DAB + ∠ABD = 180° [Angle sum property of triangle]
⇒ 30° + 90° + ∠ABD = 180°
⇒ ∠ABD = 60°
Now, ∠ABD + ∠DBC = 180° [Linear pair angles]
⇒ 60° + y° = 180°
⇒ y = 120
Hence, the correct answer is option (c).