TEST - MATHEMATICS
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Time allowed : 1 hours
Maximum marks: 40
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General Instructions:
(i) The question paper comprises three sections A, B, and C . There are 42 questions in
the question paper. All questions are compulsory
(ii) All questions and parts there of are of one mark each.
1. A mother is three times as old as her daughter . Ten years later the mother will be
two times as old as her daughter . Find the sum of their present ages in years
(a) 25
(b) 30
(c) 40
(d) 35
2. If the point (𝑥, 4) lies on a circle whose centre is at the origin and radius is 5 then 𝑥 =
(a) ±5
(b) ±3
(c) 0
(d) ±4
3. If 𝑎 = 23 × 3, 𝑏 = 2 × 3 × 5, c = 3𝑛 × 5 and LCM (a, b, c) = 23 × 32 × 5 Then 𝑛 =
(a) 1
(b) 2
(c)3
(d) 4
4. If 𝑥 + 2 is a factor of 𝑥 2 + 𝑎𝑥 + 2𝑏 and 𝑎 + 𝑏 = 4, then
(a) 𝑎 = 1, 𝑏 = 3
(c) 𝑎 = −1, 𝑏 = 5
(b) 𝑎 = 3, 𝑏 = 1
(d) 𝑎 = 5, 𝑏 = −1
5. The hour hand of a clock is 6 cm long. The area swept by it between 11.20 am and
11.55 am is
(a) 2.75 𝑐𝑚2
(b) 5.5 𝑐𝑚2
(c) 11 𝑐𝑚2
(d) 10 𝑐𝑚2
6. 𝑠𝑒𝑐 4𝐴 − 𝑠𝑒𝑐 2𝐴 is equal to
(a) 𝑡𝑎𝑛2 𝐴 − 𝑡𝑎𝑛4 𝐴
(c) 𝑡𝑎𝑛4 𝐴 + 𝑡𝑎𝑛2 𝐴
(b) 𝑡𝑎𝑛4 𝐴 − 𝑡𝑎𝑛2 𝐴
(d) 𝑡𝑎𝑛2 𝐴 + 𝑡𝑎𝑛4 𝐴
7. If 3 is the least prime factor of number a and 7 is the least prime factor of number b,
then the least prime factor of a +b, is
(a) 2
(b) 3
8. If the system of equations
3𝑥 + 𝑦 = 1
(2𝑘 – 1) 𝑥 + (𝑘 – 1) 𝑦 = 2𝑘 + 1
is inconsistent, then k =
(c) 5
(d) 10
(a) 1
(b) O
(c)−1
(d) 2
9. Two dice are rolled simultaneously . The probability that they show different faces is
(a)
2
(b)
3
1
(c)
6
1
3
(d)
5
6
10. The LCM and HCF of two rational numbers are equal, then the numbers must be
(a) prime
11.
(a)
𝑠𝑖𝑛𝜃
1+𝑐𝑜𝑠𝜃
(b) co-prime
(c) composite
(d) equal
is equal to
1+𝑐𝑜𝑠𝜃
𝑠𝑖𝑛𝜃
(b)
1−𝑐𝑜𝑠𝜃
(c)
𝑐𝑜𝑠𝜃
1−𝑐𝑜𝑠𝜃
𝑠𝑖𝑛𝜃
(d)
1−𝑠𝑖𝑛𝜃
𝑐𝑜𝑠𝜃
12. If ∆𝐴𝐵𝐶~ ∆ DEF such that AB=9.1 cm and DE=6.5cm . If the perimeter of ∆ DEF is
25 cm , then the perimeter of ∆ ABC is
(a) 36 cm
(b) 30 cm
(c) 34 cm
(d) 35 cm
13. A line segment is of length 10 units. If the coordinates of its one end are (2, − 3) and
the abscissa of the other end is 10, then its ordinate is
(a) 9, 6
(b) 3,−9
(c) − 3, 9
(d) 9,−6
1
14. The smallest rational number by which should be multiplied so that its decimal
3
expansion terminates after one place of decimal, is .
(a)
3
10
(b)
1
10
(c) 3
(d)
3
100
15. In a family of three children , the probability of having at least one boy is
(a)
7
8
(b)
1
8
(c)
5
8
(d)
3
4
16. If the centroid of the triangle formed by the points (a, b), (b, c) and (c, a) is at the
origin, then 𝑎3 + 𝑏3 + 𝑐 3 =
(a) 𝑎𝑏𝑐
(b) 0
(c) 𝑎 + 𝑏 + 𝑐
(d) 3 𝑎𝑏𝑐
17. The area of incircle of an equilateral triangle is 154 𝑐𝑚2. The perimeter of the
triangle is
(a) 71.5 cm
(b) 71.7 cm
(c) 72.3 cm
(d) 72.7 cm
18. In given figure ||𝐷𝐵||𝑃𝑄 . If CP=PD=11 cm and DR=RA=3 cm. Then the values of x
and y are respectively
(a) 12 , 10
(b) 14 , 6
(c) 10, 7
(d) 16, 8
19. From a pack of playing cards , all cards whose numbers are multiple of 3 are
removed . A card is now drawn at random . Then the probability that the card drawn is
an even numbered red card , is
(a)
10
52
(b)
1
4
(c)
1
(d)
5
3
13
20. A vertical stick 20 m long casts a shadow 10 m long on the ground . At the same
time , a tower casts a shadow 50 m long on the ground . The height of the tower is :
(a) 100 m
(b) 120 m
(c) 25 m
(d) 200 m
21. The value of (1 + 𝑐𝑜𝑡𝜃 − 𝑐𝑜𝑠𝑒𝑐𝜃) (1 + 𝑡𝑎𝑛𝜃 + 𝑠𝑒𝑐𝜃)
(a) 1
(b) 2
(c)4
(d) 0
22. In an isosceles triangle ABC if AC = BC and 𝐴𝐵 2 = 2𝐴𝐶 2, then ∠𝐶 =
(a) 30°
(b) 45°
(c) 90°
(d) 60°
23. The ratio in which the x-axis divides the segment joining (3, 6) and (12, −3) is
(a) 2:1
(b) 1:2
(c) − 2:1
(d) 1:-2
24. (𝑐𝑜𝑠𝑒𝑐𝜃 − 𝑠𝑖𝑛𝜃) (𝑠𝑒𝑐𝜃 − 𝑐𝑜𝑠𝜃)(𝑡𝑎𝑛𝜃 + 𝑐𝑜𝑡𝜃) is equal to
(a) 0
(b) 1
(c) -1
(d) None of these
25. The area of the triangle formed by the lines 𝑦 = 𝑥, 𝑥 = 6 and 𝑦 = 0 is
(a) 36 sq. units
(c) 9 sq. units
(b) 18 sq. units
(d) 72 sq. units
26. A jar contains 24 marbles , some are green and others are blue. If a marble is drawn
at random from the jar , the probability that it is green is 2/3 , the number of blue
marbles in the jar is
(a) 12
(b) 8
(c) 10
(d) 14
27. The coordinates of the fourth vertex of the rectangle formed by the points (0, 0),
(2,0), (0, 3) are
(a) (3, 0)
(b) (0, 2)
(c) (2, 3)
(d) (3, 2)
28. If 𝑎 𝑐𝑜𝑡𝜃 + 𝑏 𝑐𝑜𝑠𝑒𝑐𝜃 = 𝑝 and 𝑏 𝑐𝑜𝑡𝜃 + 𝑎 𝑐𝑜𝑠𝑒𝑐𝜃 = 𝑞 then 𝑝 2 − 𝑞2 =
(a) 𝑎2 − 𝑏 2
(b) 𝑏2 − 𝑎2
(c) 𝑎2 + 𝑏2
(d) 𝑏 − 𝑎
29. The coordinates of the fourth vertex of the rectangle formed by the points (0, 0),
(2,0), (0, 3) are
(a) (3, 0)
(b) (0, 2)
(c) (2, 3)
(d) (3, 2)
30. If 𝐴𝐵𝐶 is a right triangle right angled at B and M,N are the mid points of AB and BC
respectively, then 4(𝐴𝑁 2 + 𝐶𝑀2 ) =
(a) 4 𝐴𝐶 2
(b) 5 𝐴𝐶 2
5
(c) 𝐴𝐶 2
31. If α, β are the zeros of the polynomial 𝑓(𝑥) = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐, then
(a)
𝑏2 −2𝑎𝑐
𝑎2
(b)
𝑏2 −2𝑎𝑐
𝑐2
(d) 6 𝐴𝐶 2
4
(c)
𝑏2 +2𝑎𝑐
𝑎2
1
𝛼2
+
1
𝛽2
=
(d)
𝑏2 +2𝑎𝑐
𝑐2
32. If the system of equations
2𝑥 + 3𝑦 = 7
2𝑎𝑥 + (𝑎 + 𝑏) 𝑦 = 28
has infinitely many solutions, then
(a)𝑎 = 2𝑏
(c) 𝑎 + 2𝑏 = 0
(b) 𝑏 = 2𝑎
(d) 2𝑎 + 𝑏 = 0
SECTION-C
Case study-based questions are compulsory. Attempt any 4 sub parts from each
question. Each question carries 1 mark.
CASE STUDY-1
Ramkishan is a landlord. He borrowed some amount from the bank as an agriculture
loan and repaid the said loan at 10% p.a. He spent ₹2800𝑥 on fertilizers and pesticides,
₹400 𝑥 2 on wages and cultivation and ₹4800 on seeds for the production of soyabean.
He also spent ₹3300 𝑡 on fertilizers and pesticides, ₹300𝑡 2 on wages and cultivation
and ₹9000 on seeds for the production of cotton and urad crop.
Based on above information, answer the following questions.
33. The polynomial represented by total expenses on soyabean is
(a) 200 𝑥 2 + 4000 𝑥 + 2800 𝑥
(b) 400 𝑥 2 – 2800 𝑥 + 200
(c) 400𝑥 2 + 2800 𝑥 + 4800
(d) 400𝑥 2 – 2800 𝑥 – 4800
34. Zeroes of the polynomial represented by expenses on soyabean are
(a) 3,4
(b) −3,−4
(c) 3,−4
(d) −3,4
35. The polynomial represented by total expenses on cotton and urad crops is
(a) 300 𝑡 2 + 3300 𝑡 + 9000
(b) 300 𝑡 2 − 3300 𝑡 − 9000
(c) 300 𝑡 2 + 3300 𝑡 − 9000
(d) 300𝑡 2 − 3300 𝑡 + 9000
36. Zeroes of the polynomial represented by expenses on cotton and urad crops are
(a) 5, −6
(b) −5, 6
(c) 5,6
(d) −5, −6
37. If the value of 𝑥 is 2, then the total expenses on soyabean is
(a) ₹10000
(b) ₹20000
(c) ₹12000
(d) ₹15000
CASE STUDY-2
ENTRANCE OF BANQUET HALL
Binesh goes to the marriage function of his friend Arun, arranged at the banquet hall.
He observes the entrance door of banquet hall closely and sees that door is semicircular and decorated by flowers as shown below. If the semi-circle, centred at O, has a
1
diameter 6 m, the chord BC is parallel to AD and BC = AD, then answer the following
3
questions.
38. Find the height, OE of the door.
(a) 2 m
(b) 2√2 m
(c) 3 m
(d) 3√2 m
(c) 3√2 𝑚2
(d) 2√2 𝑚2
39. Find the area of ∆AOB.
(a) 3 𝑚2
(b) 2 𝑚2
40. Find the area of ∆BOC.
(a) 3 𝑚2
(b) 2√2 𝑚2
(c) 3√2 𝑚2
(d) 2 𝑚2
(c) 12.14 𝑚2
(d) 14.143 𝑚2
(c) 4 𝑚2
(d) 3.62 𝑚2
41. Find the area of semi-circle.
(a) 12 𝑚2
(b) 13.41 𝑚2
42. Find the area covered by flowers .
(a) 2.863 𝑚2
(b) 3.2 𝑚2