MATHEMATICS
Previous year question paper with solutions for MATHEMATICS Mar-2018
Our website provides solved previous year question paper for MATHEMATICS Mar-2018. Doing preparation from the previous year question paper helps you to get good marks in exams. From our Math question paper bank, students can download solved previous year question paper. The solutions to these previous year question paper are very easy to understand.
These Questions are downloaded from www.brpaper.com You can also download previous years question papers of 10th and 12th (PSEB & CBSE), B-Tech, Diploma, BBA, BCA, MBA, MCA, M-Tech, PGDCA, B-Com, BSc-IT, MSC-IT.
Print this page
Question paper 1
1. Select the corect ansrver in the following:
Arca of a sector of angle p (in degrees) of a circle rvith radius R is :
a) \({P\over180}*2nR\) b)\({P \over 180} * nR^2 \) c) \({P\over360}*2nR\) d) \({P \over 360} * 2nR^2 \)
Answer:
c) \({P\over360}*2nR\)
2. Which of the following cannot be the probability of an event :
a) \( {2\over3}\) b)-1.5 c)15% d) 0.7
Answer:
-1.5 cannot be the probability of an event
Probability never be neagtive
3. Every composite number can be expressed (factorized) as a product of prirnes, (True/False)
Answer:
True
4. Find the first term a and the conrmon difference d of A.P: - 5, - I, 3 7,______
Answer:
First Term = -5
Common difference = -1 -(-5) = -1 + 5 = 4
5. Write the formula for finding volume of a firustum of a cone.
Answer:
volume of a firustum of a cone
V = \({\pi \over 3 }( R^2 + Rr + r^2)\)
6. If the area of a triangle is O square units then the vertices of a triangle are _______
Answer:
Collinear
7. sin (A+B)=sinA+sinB (Write Ture/False)
Answer:
False
8. A polynomial of degree _______ is called a linear polynomial.
Answer:
one
9. If tangents PA and PB from a point P to a circle with centre 0 are inclined to each other at angle of 800. then find the valne of POA
Answer:
Angle POA = ?
Sun of angle of triangle is = 1800
LP + LO + LA = 1800
40 + 90 + LPOA = 1800
LPOA = 180 -130
= 500
10. A child has a die whose six faces shorw the letters as given below :
A B C D E A
The die is tlrown once. What is tlre probability of getting
(i) A? (ii) D ?
Answer:
P(A) = 2 / 6 = 1/ 3
P(D) = 1/ 6
11. Use Euclid's division algorithm to find the H.C.F. of 420 and 130'
Answer:
12. Solve the pair of lirrear equation 2x + 3y = 11 and 2x - 4y = -24
Answer:
The wickets taken by a bowler in l0 cricket matches are as follows :
2 6 4 5 0 2 1 3 2 3
Find the mode of the data
Answer:
2 6 4 5 0 2 1 3 2 3
Mode = 2
2 occur three times which is greater than Every Number
14. Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their top
Answer:
Let AC and BE Two towers 12m apart
In CED , DC2 = CE2 + DE2
= 122 + 52
= 144 + 25
= 169
DC = 13
Distance between their Poles = 13 m
15. Find the discriminant of the quadratic equation 2x2 6x + 3 = 0. and hence find the nature of its roots
Answer:
2x2 6x + 3 = 0
Here a = 2 b = 6 c = 3
D = b2 - 4ac (-6)2 - 4. 2. 3
= 36 -24 =12
16. Divide the polynomial p (x) = x3 - 3x2 + 5x - 3 by the polynomial g(x) = x2 -2 Find the quotient and remainder.
Answer:
17. The angle of elevation of the top of a tower from a point on the ground. which is 30 m away front the foot of the tower, is 300. Find fhe heiglrt of the tower
Answer:
BC be a tower with hight R
In Triangle ABC ,
Tan30 = R/AB
\(1 \over \sqrt 3\) = R/ 30
h = \({30 \over \sqrt 3} * {\sqrt3 \over \sqrt 3} = { 30 \sqrt 3 \over 3}\)
h = \(10\sqrt 3\)
18. In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 crn, find tlre area of the
(i) Quadrant OACB (ii) Shaded region.
Answer:
19. Prove that opposite sides ofn quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
or
D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that : AE2 + BD2 = AB2 + DE2
Answer:
20. In a class test, the sum of Shefali's rnarks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.
Answer:
Let Marks in Math = x
Marks in English = y
given x + y = 30
(x+2) * (y-3) = 210
From x + y = 30
y = 30 - x
(x+2)(30-x-3) = 210
(x+2)(27-x) = 210
27x - x2 + 54 -2x =210
- x2 +25x = 156
x2 -25x +156 = 0
x2 -13x - 12x + 156 = 0
(x-12) (x-13) = 0
x = 12 , x = 13
y = 30-12 = 18
y = 30-13 = 17
21. Consider TringleACB , right-angled at C. in which AB = 29 units, BC = 21 units and ZABC = 0 (see figure). Detemrine the value of sin2 0 + cos2 0
or
Prove that :
\({l+sec \over sec} = {sin2 A \over 1-cosA}\)
Answer:
\({l+sec \over sec} = {sin2 A \over 1-cosA}\)
\({l+secA \over secA} \) = \(1 + {1 \over cosA} \over {1 \over cosA}\) = \(cos A + 1 \over cos A\)* \(cosA \over 1\) = 1 + cos A
By Rationalizing
\({l+secA \over secA} \) = \(1 + cos A \over 1\)* \((1 - cosA )\over (1-cos A)\)
= \(1^2 - cos ^2 A \over 1- cos A\)
\(Sin^2A \over 1- cos A\)
LHS = RHS
22. An A.P. consists of 50 terms of which Srd term is 12 and the last term is 106. Find the 29th term
Answer:
Given n = 50
a3 = 12
a50 = 106
a29 = ?
an = a + (n-1)d
a3 = a + (3-1)d
12 = a + 2d
-47d = -94
d = 97/47 =2
put
a + 2d = 12
a+ 2(2) = 12
a = 12-4 = 8
a =8
a29 = a + (29-1)d
= 8 + (28)2
= 8 + 56
a29 = 64
23. If A and B are (-2, -2) and (2, -4), respectively, find the coordinates of P such that AP = \({3\over7}\) AB and P lies on the line segment AB
Answer:
Given A(-2, -2) , B(2 -4) be
two Points
AB be line joinin those points P be any Point on line Let coordinate of P be (x,y)
given AP = 3/7 AB
\({AP \over AB} = {3 \over 7}\)
\({AP \over PB} = {3 \over 4}\)
Here \((x_1 y_1) = (-2 , -2) , (x_2 y_2) = (2, -4)\)
\(m_1 = 3, m_2 = 4\)
By Section Formula
x = \({m_1 x_2 + m_2 x_1 \over m_1 + m_1 } = {3(2) + 4(-2) \over 3+4} \)
x = \({6 - 8 \over 7} = {-2 \over 7}\)
y = \({m_1 y_2 + m_2 y_1 \over m_1 + m_1 } = {3(-4) + 4(-2) \over 3+4} \)
y = \({-12 - 8 \over 7} = {-20 \over 7}\)
P = (\({-2\over 7} , {-20 \over 7}\))
24. A well of diameter 3 m is dug 14 m cleep. The earth taken ont of it has been spreacl evenly all arouud it in the slrape of a circular ring of rvidth 4 nr to fonrr an embanklrrent. Fincl the height of the embankment.
Answer:
Diameter of well = 3m
Radius = 1.5 m
depth H = 14m
Vol of well = \(\pi r^2 H\)
= \(\pi * (1.5)^2 * 14\)
Volume of inner embankment = \(\pi r^2 h\)
= \(\pi * (1.5)^2 * h \)
Volume of outter embankment = \(\pi * (5.5)^2 * h \)
Volume of well = Volume of inner embankment - Volume of outter embankment
\(\pi * (1.5)^2 * 14\) = \(\pi * (1.5)^2 * h \)- \(\pi * (5.5)^2 * h \)
h = \({(1.5)^2 * 14 \over (5.5)^2 - (1.5)^2} = {2.25 * 14 \over 30.25 - 2.25} = 1.125 m\)
Height of the embankment = 1.125m
Question paper 2
Part-A
1. Find the first term a and the conrmon difference d of A.P: - 5, - 1, 3 7,______
Answer:
First Term = -5
Common difference = -1 -(-5) = -1 + 5 = 4
2. sin (A + B) = sin A +sin B (Write True/False)
Answer:
False
3. Which of the following cannot be the probability of an event :
a) \( {2\over3}\) b)-1.5 c)15% d) 0.7
Answer:
-1.5 cannot be the probability of an event
Probability never be neagtive
4. Every composite number can be expressed (factorized) as a product of primes. (True/False)
Answer:
True
5. If the area of a triangle is 0 square units then the vertices of a triangle are _________ (Fill in the blanks)
Answer:
Collinear
6. Write the formula for finding volume of a frustum of a cone
Answer:
volume of a firustum of a cone
V = \({\pi \over 3 }( R^2 + Rr + r^2)\)
7. A polynomial of degree is called a linear polynomial (Fill in the blanks)
Answer:
One
8. Select the corect ansrver in the following:
Arca of a sector of angle p (in degrees) of a circle rvith radius R is :
a) \({P\over180}*2nR\) b)\({P \over 180} * nR^2 \) c) \({P\over360}*2nR\) d) \({P \over 360} * 2nR^2 \)
Answer:
c) \({P\over360}*2nR\)
Part-B
9. Find the discriminant of the quadratic equation 2x2 - 6x + 3 = 0, and hence find the nature of its roots.
Answer:
2x2 6x + 3 = 0
Here a = 2 b = 6 c = 3
D = b2 - 4ac (-6)2 - 4. 2. 3
= 36 -24 =12
10. If tangents PA and PB from a point P to a circle with centre o are inclined to each other at angle of 80°, then find the value of LPOA.
Answer:
Angle POA = ?
Sun of angle of triangle is = 1800
LP + LO + LA = 1800
40 + 90 + LPOA = 1800
LPOA = 180 -130
= 500
11. A child has a die whose six faces shorw the letters as given below :
A B C D E A
The die is tlrown once. What is tlre probability of getting
(i) A? (ii) D ?
Answer:
P(A) = 2 / 6 = 1/ 3
P(D) = 1/ 6
12. Use Euclid's division algorithm to find the H.C.F. of 420 and 130.
Answer:
13. Solve the pair of linear equation 2x + 3y = 11 and 2x - 4y = -24,
Answer:
14. The wickets taken by a bowler in 10 cricket matches are as follows:
2 6 4 5 0 2 1 3 2 3
Find the mode of the data.
Answer:
2 6 4 5 0 2 1 3 2 3
Mode = 2
2 occur three times which is greater than Every Number
15. Divide the polynomial p(x) = x 3x +5x-3 by the polynomial g(x)= x2 -2. Find the quotient and remainder.
Answer:
16. Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops
Answer:
Let AC and BE Two towers 12m apart
In CED , DC2 = CE2 + DE2
= 122 + 52
= 144 + 25
= 169
DC = 13
Distance between their Poles = 13 m
Part-C
17. If A and B are (-2,-2) and (2,-4), respectively, find the coordinates of P such that AP= 3/7 AB and P lies on the line segment AB.
Answer:
Given A(-2, -2) , B(2 -4) be
two Points
AB be line joinin those points P be any Point on line Let coordinate of P be (x,y)
given AP = 3/7 AB
\({AP \over AB} = {3 \over 7}\)
\({AP \over PB} = {3 \over 4}\)
Here \((x_1 y_1) = (-2 , -2) , (x_2 y_2) = (2, -4)\)
\(m_1 = 3, m_2 = 4\)
By Section Formula
x = \({m_1 x_2 + m_2 x_1 \over m_1 + m_1 } = {3(2) + 4(-2) \over 3+4} \)
x = \({6 - 8 \over 7} = {-2 \over 7}\)
y = \({m_1 y_2 + m_2 y_1 \over m_1 + m_1 } = {3(-4) + 4(-2) \over 3+4} \)
y = \({-12 - 8 \over 7} = {-20 \over 7}\)
P = (\({-2\over 7} , {-20 \over 7}\))
18. The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.
Answer:
BC be a tower with hight R
In Triangle ABC ,
Tan30 = R/AB
\(1 \over \sqrt 3\) = R/ 30
h = \({30 \over \sqrt 3} * {\sqrt3 \over \sqrt 3} = { 30 \sqrt 3 \over 3}\)
h = \(10\sqrt 3\)
19. Consider TringleACB , right-angled at C. in which AB = 29 units, BC = 21 units and ZABC = 0 (see figure). Detemrine the value of sin2 0 + cos2 0
or
Prove that :
\({l+sec \over sec} = {sin2 A \over 1-cosA}\)
Answer:
\({l+sec \over sec} = {sin2 A \over 1-cosA}\)
\({l+secA \over secA} \) = \(1 + {1 \over cosA} \over {1 \over cosA}\) = \(cos A + 1 \over cos A\)* \(cosA \over 1\) = 1 + cos A
By Rationalizing
\({l+secA \over secA} \) = \(1 + cos A \over 1\)* \((1 - cosA )\over (1-cos A)\)
= \(1^2 - cos ^2 A \over 1- cos A\)
\(Sin^2A \over 1- cos A\)
LHS = RHS
20. In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 crn, find tlre area of the
(i) Quadrant OACB (ii) Shaded region.
Answer:
21. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle
orD and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that : AE? + BD = ABS + DE
Answer:
22. Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.
Answer:
23. In a class test, the sum of Shefali's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.
Answer:
Let Marks in Math = x
Marks in English = y
given x + y = 30
(x+2) * (y-3) = 210
From x + y = 30
y = 30 - x
(x+2)(30-x-3) = 210
(x+2)(27-x) = 210
27x - x2 + 54 -2x =210
- x2 +25x = 156
x2 -25x +156 = 0
x2 -13x - 12x + 156 = 0
(x-12) (x-13) = 0
x = 12 , x = 13
y = 30-12 = 18
y = 30-13 = 17
24. An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.
Answer:
Given n = 50
a3 = 12
a50 = 106
a29 = ?
an = a + (n-1)d
a3 = a + (3-1)d
12 = a + 2d
-47d = -94
d = 97/47 =2
put
a + 2d = 12
a+ 2(2) = 12
a = 12-4 = 8
a =8
a29 = a + (29-1)d
= 8 + (28)2
= 8 + 56
a29 = 64
Part-D
25. In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. Prove it.
or
The lengths of the tangents drawn from an external point to a circle are equal. Prove it.Answer: