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Previous year question paper with solutions for Mathematics Mar-2018
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Question paper 1
SECTION – A
1. The relation between LCM and HCF of two positive integers will be :
(A) HCF > LCM (B) HCF = LCM
(C) LCM > HCF (D) None of these
Answer:
(C) LCM > HCF
2. Which one is polynomial ?
(A)
(B) 
(C)
(D) 
Answer:
(D)
3. If in equations
then which of the following is true ? (A) Coincident lines (B) Intersecting lines
(C) Parallel lines (D) None of thes
Answer:
(C) Parallel lines
4. Which one is an A. P. series ?
(A) .
(B) 
(C) a, 2a, 3a, 4a, …… (D) 1, 3, 9, 27, ……
Answer:
(C) a, 2a, 3a, 4a, ……
5. In an A. P. 2, 7, 12, …. 10th term is :
(A) −47 (B) 47
(C) 57 (D) None of these
Answer:
(B) 47
6. Which one pair of the triangles is not similar triangles ?
Answer:
(D)
7. Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio :
(A) 2 : 3 (B) 4 : 9
(C) 81 : 16 (D) 16 : 81
Answer:
(D) 16 : 81
8. How many tangents are drawn from a point on the circle ?
(A) 1 (B) 2
(C) Infinitely many (D) None of these
Answer:
(C) Infinitely many
9. The tangent at any point of a circle makes an angle to the radius through the point of contact :
(A) 45° (B) 90°
(C) 180° (D) 60
Answer:
(B) 90°
10. Point P(3, 4) lies in which quadrant ?
(A) First (B) Second
(C) Third (D) Fourth
Answer:
(A) First
11. Coordinate of mid point of line joining two points
are : (A) (5, −3) (B)
(C) (0, 0) (D) None of these
Answer:
(C) (0, 0)
12. State whether the following statement is true or false :
"The value of sec A is always lies between −1 and 1"
Answer:
False Statement
13. State whether the following statement is true or false :
"cosec A is the product of cosec and A
Answer:
False
14. Area of major sector of angle θ° of a circle with radius R will be:
(A)
(B) 
(C)
(D) None of theseAnswer:
(C)
15. CSA of hemisphere having radius 4 cm will be :
(A) 32π
(B) 16π (C) 64π
(D) None of theseAnswer:
Ans=D16. Probability of getting 3 in a single throw of a die is :
(A)
(B) 
(C) 1 (D) 0
Answer:
(A)
SECTION-B
17. Prove that
is an irrational number. Answer:
3
18. Find a quadratic polynomial with the given number as the sum and product of its zeroes respectively are 3 and 2.
Answer:
Sum of zeroes =3
Product=2
19. A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.
Answer:
20. Find the value of cos 48° − sin 42°.
Answer:
21. Cost of ploughing at the rate of Rs. 10 per 2 m is Rs. 1,540. Find the radius of circular field.
Answer:
Let Radius of field=r
SECTION-C
22. Solve the following equations :
Answer:
23. The altitude of a right angled triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Answer:
24. How many two-digit numbers are divisible by 3 ?
Answer:
25. PQ is a chord of length 8 cm of a circle of radius 5 cm tangents at P and Q intersect at a point T. Find the length TP, if O is the centre of a circle
Answer:
Let TR=y
26 One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting the Jack of hearts
Answer:
Total cards in deck=52
No of jack of Hearts=1
Probability of Jack =
27. Find the area of a triangle whose vertices are (1, −1), (−4, 6) and (−3, −5).
Answer:
SECTION-D
28. Is it possible to design a rectangular park of perimeter 80 m and area 400 m2 ? If so, find its length and breadth.
Answer:
Perimetr of rectangular park=80m
Rectangular park is not possible l=b
29. Prove that
, using the identity 
Answer:
OR
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.
Answer:
let h be the height of tree.
30. Draw a triangle ABC with sides BC = 6 cm, AB = 5 cm and ABC = 60°, then construct a triangle whose sides are
of the corresponding sides of the triangle ABC. Give the justification of the construction alsoAnswer:
31. A 20 m deep well with diameter 7 m is dug and the earth taken out of it has been spread evenly in the shape of a platform 22 m × 14 m. Find the height of the platform.
Answer:
32. 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows
Number of letters
1-4
4-7
7-10
10-13
13-16
16-19
Numbers of surnames
6
30
40
16
4
4
Find the median numbers of letters in the surnames.
Answer:
No of letters
No of surname
c.f
1-4
6
6
4-7
30
36
7-10
40
76
10-13
16
92
13-16
4
96
16-19
4
100
OR
Consider the distribution of daily wages of 50 workers of a factory :
Daily wages(in Rs)
100-120
120-140
140-160
160-180
180-200
Number of workers
12
14
8
6
10
Find the mean daily wages of the workers of the factory by using an appropriate method.
Answer:
Daily wages
No of Wagers
100-120
12
110
-40
-2
-24
120-140
14
130
-20
-1
-14
140-160
8
150
0
0
0
160-180
6
170
20
1
6
180-200
10
190
40
2
20
50 12
Question paper 2
SECTION – A
1. If a and b are two positive integers, then the relation between their LCM
and HCF will be :(A) LCM > HCF (B) HCF > LCM
(C) HCF = LCM (D) None of these
Answer:
(A) LCM > HCF
2. Which one is polynomial?
(A)
(B) 
(C)
(D) 
Answer:
(C)
3. If in equations
and 
then which of the following is true ?
(A) Intersecting lines (B) Coincident lines
(C) Parallel lines (D) None of theseAnswer:
(C) Parallel lines
4. Which one is A. P. series ?
(A) 2, 4, 8, 12, … (B) 0.2, 0.22, 0.222,…………
(C) -10, -6, -2, 2, …… (D) 1, 3, 9, 27, ……
Answer:
(C) -10, -6, -2, 2, ……
5. In an A. P. -10, -6, -2, 2, …., 20th term is :
(A) 66 (B) -66
(C) 77 (D) None of theseAnswer:
(D) None of these
6. Which one pair of the triangles is not similar triangles ?
Answer:
(c)
7. If the ratio of the sides of two similar triangles is 3 : 2, then the ratio of their areas is :
(A)
(B) 2 : 3
(C) 9 : 4 (D) None of theseAnswer:
(C) 9 : 4
8. Number of tangents drawn from a point inside the circle is :
(A) 1 (B) 2
(C) 0 (D) None of these
Answer:
(C) 0
9. How many tangents can a circle have ?
(A) 1 (B) 2
(C) Infinitely many (D) 0
Answer:
(C) Infinitely many
10. Point Q(-3, –4) lies in which quadrant ?
(A) First (B) Third
(C) Second (D) Fourth
Answer:
(B) Third
11. Coordinate of mid point of line joining two points (-5, 7) and (5, -7) are:
(A) (5, 7) (B) (0, 0)
(C) (0, 7) (D) (5, 0)
Answer:
Give two points (-5, 7) and (5, -7)
Let mid point of AB is C
Then C is given by
Mid point C=
Ans12. State whether the following statement is true or false : "The value of tan A is always lies in between -1 and 1"
Answer:
Statement is false
13. State whether the following statement is true or false : "cot A is not defined for A = 0°"
Answer:
Statement is false
14. Length of an arc of a sector of angle
° of a circle with radius r will be :(A)
(B)
(C)
(D) None of theseAnswer:
(C)
15. The radius of the base of a cone is 4 cm and slant height is 5 cm. Its CSA is :
(A)
(B) 
(C)
(D) 
Answer:
radius of the base of a cone r = 4 cm
slant height l =5 cm
Curved surface area CSA =
=
ans.16. Probability of getting 6 in a single throw of a die is :
(A) 1 (B) 0(C)
(D) None of theseAnswer:
(C)
SECTION-B
17. Prove that
is an irrational numberAnswer:
suppose that
is a rational number then it can be written in the form 
Where a, b are co-prime numbers
Continue a=
bBy squaring
=
is divisible by 7 : a is an multiple of 7: a=7c
Put the value in
=
is divisible by 7 .
From
and we conclude that and have common factor 7 this is contradiction, as a, b are co-prime numbers is wrong 18. Find a quadratic polynomial with the given number as the sum and product of its zeroes respectively are
and 4.Answer:
Sum of roots =
product of roots = 4
quadratic equation is
product = 0
19. CM and RN are respectively the medians of
ABC and PQR. If ABC ~ PQR, prove that AMC ~ PNRAnswer:
AMC ~ PNR
But AB=2AB, PQ=2PN : CM and RN are Median
from and
from 2 4From
and 
20. Find the value of :
Answer:
=1
ans21. Find the cost of ploughing the circular field having diameter 10 meter and rate of ploughing is Rs. 1.50 per square meter.
Answer:
Diameter of circular field d
Area =
Now cost of ploughing
= 117.857 Rs Ans
SECTION-C
22. Solve the following equations :
3x - y = 3
x - y = 4Answer:
---------
---------Multiply
by 3 and subtract from We get
.
Put this value in
23. Find two numbers whose sum is 27 and product is 182.
Answer:
Here
Multiple of 4 between 10 and 250 are 21Ans
24. How many multiples of 4 lie between 10 and 250 ?
Answer:
Here
Multiple of 4 between 10 and 250 are 21Ans
25. Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.
Answer:
Let o be the center of two concentric circles C1 Aand C2
Let AB are chord of the C2 which is tangent the smaller circles C1 at the point of D npw we have to prove that chord XY is bisected at D that is XD = DY
Join OD
Now OD is radius of C1 and XY is tangent to C1 at D
So OP XY[Tangent at any point of circle to radius at the point of contact ]
XD=DY
Hence tthe prove ]
26. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting a face card.
Answer:
Total cards = 52
Total face cards=12
Probability of face card=
=
27. Find the value of k, if the points A(8, 1), B(k, -4) and C(2, -5) are collinear.
Answer:
ABC are collinear
A(8, 1)
B(k, -4)
C(2, -5)
AB=BC
AB=
= 
=
SECTION-D
28. Is the following situation possible ? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Answer:
Let age of first friend = x years
Let age of 2nd friend = x-20
Four year ago
Let age of first friend = x-4
Let age of 2nd friend =
This eq. cannot be solved became value of x should be whole no.This situation doesn’t occurs
29. Prove that
Answer:
Div both side by sin A,we get
PUT 1 = 
=
=
=
R.H.SOR
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45°, respectively. If the bridge is at a height of 3 m from the banks, find the width of the river.
Answer:
Let AB be a river and CD is a Bridge. E be any point on Bridge
In ∆ AEF,
°
= FB=3
Breath of River =
30. Construct triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are
of the corresponding sides of the first triangle. Give the justification of the construction also.Answer:
Step1= Draw a line segment AB = 4cm
Take A,B as center, draw arcs of 6cm, 5cm
Let these arcs intersects at C,
ABC is required having sides 4,5,6 cm respectively
Step2= Draw a ray AX making acute angle with AB on opposite side of vertex C
Step3= Locate 3 points A1,A2,A3 on AX as in 2/3, 3is greater. Now join A3 With point B a draw a line thorough A2
to A3 BStep4= Draw a line through B1
BC ABC is required 31. A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
Answer:
radius of sphere = 4.2 cm
volume=
=
Vol. of cylinder = Vol of sphere
=
= 2.75 ans
32. The lengths of 40 leaves of a plant are measured correct to the nearest millimetre and the data obtained is represented in the following table :
Length
(in mm)117.5-
126.5126.5-
135.5135.5-
144.5144.5-
153.5153.5-
162.5162.5-
171.5171.5-
180.5Number of
Leaves3
5
9
12
5
4
2
Find the median length of the leaves
Answer:
Length
No of Leaves
C.F
117.5-126.5
3
3
126.5-135.5
5
8
135.5-144.5
9
17
144.5-153.5
12
29
153.5-162.5
5
34
162.5-171.5
4
38
171.5-180.5
2
40
n = 40
C.F=29, l = 144.5
h = 9
median =
=
=
74= 137.75 ans
Or
The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs. 18. Find the missing frequency f
:Daily Pocket Allowance (in Rs.)
11-13
13-15
15-17
17-19
19-21
21-23
23-25
Number of Children
7
6
9
13
f
5
4
Answer:
Allowance
No. of Children
Mid point x
fixi
11-13
7
12
8 4
13-15
6
14
8 4
15-17
9
16
14 4
17-19
13
18
23 4
19-21
20
20f
21-23
5
22
110
23-25
4
24
96
44+
752+20
Mean =
18 =
Question paper 3
1. If g and l are LCM and HCF of two positive integers, then the relation will be :
(A) g > l (B) g < l
(C) g = l (D) None of these
Answer:
(B) g < l
2. Which one is polynomial ?
(A)
(B) 
(C)
(D) 
Answer:
(B)
3. If in equations
then which of the following is true ? (A) Parallel lines (B) Intersecting lines
(C) Coincident lines (D) None of these
Answer:
(B) Intersecting lines
4. Which one is an A. P. series ?
(A)
…. (B) 
….(C)
…… (D) a, 2a, 3a, 4a, ……Answer:
(D) a, 2a, 3a, 4a, ……
5. In an A. P. 2, 7, 12, …. 20th term is :
(A) −47 (B) 47
(C) 57 (D) 97
Answer:
(D) 97
6.Which one pair of the triangles is not similar triangles ?
Answer:
(D)
7. Ratio of corresponding median of two similar triangles are 4 : 9. Then areas of these triangles are in the ratio :
(A) 2 : 3 (B) 4 : 9
(C) 16 : 81 (D) 81 :16
Answer:
(C) 16 : 81
8. How many tangents are drawn from a point on the circle ?
(A) 1 (B) 2
(C) Infinitely many (D) None of these
Answer:
(C) Infinitely many
9. How many parallel tangents are drawn on a circle at the most ?
(A) 1 (B) 2
(C) 3 (D) None of these
Answer:
(B) 2
10. Point P(−3, –4) lies in which quadrant ?
(A) First (B) Second
(C) Third (D) Fourth
Answer:
(C) Third
11. Coordinates of point which divide the line joining two points (−1, 7) and (4, –3) in the ratio 2 : 3 are :
(A) (1, 3) (B) (−1, 3)
(C) (1, −3) (D) (−1, −3)
Answer:
(A) (1, 3)
12. State whether the following statement is true or false :
"The value of cosec θ lies ≥ 1 and ≤ −1"
Answer:
False
13. State whether the following statement is true or false :
"
for some angle θ"Answer:
False
14. Area of a sector of angle P ° of a circle with radius r will be :
(A)
(B) 
(c )
(D) 
Answer:
(c )
15. Base area of hemisphere having base radius r cm will be :
(A)
(B) 
(C) 2πr (D)
Answer:
(B)
16. Probability of getting 7 in a single throw of a die will be :
(A)
(B) 1(C) 0 (D)
Answer:
(C) 0
SECTION-B
17. Prove that
is an irrational number.Answer:
18. Find a quadratic polynomial with the given number as the sum and product of its zeroes respectively are 5 and 3.
Answer:
Sum of roots =5,
Product=3
Equation is
19. A ladder is placed against a wall such that its foot is at a distance of 2.5 m from the wall and its top reaches a window 6 m above the ground. Find the length of the ladder.
Answer:
20. Express cot 85° + cos 75° in terms of trigonometric ratios of angles between 0° and 17°.
Answer:
21. Cost of ploughing at the rate of Rs. 10 per 2 m is Rs. 1,540. Find the radius of the circular field.
Answer:
SECTION – C
22. Solve the following equations :
Answer:
23. Find the root of the quadratic equation by factorization method
Answer:
24. How many two-digit numbers are divisible by 4 ?
Answer:
25. PQ is a chord of length 8 cm of a circle of radius 5 cm. Tangents at P and Q intersect at a point T. Find the length TP, if O is the centre of a circle.
Answer:
Now
26. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting the queen of diamonds.
Answer:
27. Find the area of a triangle whose vertices are (−1.5, 3), (6, −2) and (−3, 4).
Answer:
SECTION – D
28. Find the value of k for the quadratic equation
so that they have two equal rootsAnswer:
D=k2-4.2.3=0
29. Prove that sinθ-
, using the identity 
Answer:
OR
A man 1.5 m tall is 28.5 m away from a Chimney. The angle of elevation of the top of the Chimney from her eyes is 45°. What is the height of the Chimney ?
Answer:
30. Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°, then construct a triangle whose sides are
times the corresponding sides of ∆ABC. Give the justification of the construction alsoAnswer:
31. Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.
Answer:
32. The distribution below gives the weights of 30 students of a class. Find the median weight of the students :
Weight(in kg)
40-45
45-50
50-55
55-60
60-65
65-70
70-75
Number of students
2
3
8
6
6
3
2
Answer:
40-45
2
45-50
3
50-55
8
55-60
6
60-65
6
65-70
3
70-75
2
30
OR
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate :
Literacy rate (in%)
45-55
55-65
65-75
75-85
85-95
Number of cities
3
10
11
8
3
Answer:
Literacy rate
No of
xi
di
fidi
45-55
3
50
20
60
55-65
10
60
10
100
65-75
11
70
0
0
75-85
8
80
10
80
85-95
3
90
20
60
35 300
