Board Paper of Class 10 2017 Maths - Solutions
(1) Check the question paper for fairness of printing. If there is any lack of fairness, inform the Hall Supervisor immediately.(2) Use Blue or Black ink to write and underline and pencil to draw diagrams.Note : This question paper contains four sections.
- Question 1
If
f (
x) =
x2 + 5, then
f(−4) =
(a) 26
(b) 21
(c) 20
(d) −20
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- Question 2
If
k + 2, 4
k − 6, 3
k − 2 are the three consecutive terms of an A.P., then the value of k is :
(a) 2
(b) 3
(c) 4
(d) 5
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- Question 3
If the product of the first four consecutive terms of a G.P. is 256 and if the common ratio is 4 and the first term is positive, then its 3
rd term is:
(a) 8
(b)
(c)
(d) 16
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- Question 4
The remainder when
x2 − 2
x + 7 is divided by
x + 4 is :
(a) 28
(b) 29
(c) 30
(d) 31
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- Question 5
The common root of the equations
x2 −
bx + c = 0 and
x2 +
bx −
a = 0 is :
(a)
(b)
(c)
(d)
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- Question 6
If
, then the matrix B =
(a)
(b)
(c)
(c)
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- Question 7
Slope of the straight line which is perpendicular to the straight line joining the points (−2, 6) and (4, 8) is equal to :
(a)
(b) 3
(c) –3
(d)
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- Question 8
If the points (2, 5), (4, 6) and (a, a) are collinear, then the value of ‘
a’ is equal to :
(a) −8
(b) 4
(c) −4
(d) 8
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- Question 9
The perimeters of two similar triangles are 24 cm and 18 cm respectively. If one side of the first triangle is 8 cm, then the corresponding side of the other triangle is :
(a) 4 cm
(b) 3 cm
(c) 9 cm
(d) 6 cm
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- Question 10
ΔABC is a right angled triangle where ∠B = 90° and BD ⊥ AC. If BD = 8 cm, AD = 4 cm, then CD is :
(a) 24 cm
(b) 16 cm
(c) 32 cm
(d) 8 cm
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- Question 11
In the adjoining figure ∠ABC =
(a) 45°
(b) 30°
(c) 60°
(d) 50°
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- Question 13
If the surface area of a sphere is 100 π cm
2, then its radius is equal to :
(a) 25 cm
(b) 100 cm
(c) 5 cm
(d) 10 cm
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- Question 14
Standard deviation of a collection of a data is
. If each value is multiplied by 3, then the standard deviation of the new data is :
(a)
(b)
(c)
(d)
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- Question 15
A card is drawn from a pack of 52 cards at random. The probability of getting neither an ace nor a king card is :
(a)
(b)
(c)
(d)
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- Question 16
Given, A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6} and C = {5, 6, 7, 8}, show that A⋃ (B ⋃ C) = (A ⋃ B) ⋃ C.
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- Question 17
The following table represents a function from A = {5, 6, 8, 10} to B = {19, 15, 9, 11} where
f(
x) = 2
x − 1. Find the values of
a and
b.
x |
5 |
6 |
8 |
10 |
f(x) |
a |
11 |
b |
19 |
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- Question 18
If
are in G.P., find the values of
m.
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- Question 19
Solve by elimination method : 13
x + 11
y = 70, 11
x + 13
y = 74.
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- Question 21
Construct a 2 × 2 matrix A = [
aij] whose elements are given by
aij = 2
i − j.
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- Question 22
Let
. Find the matrix C, if C = 2A + B.
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- Question 23
Find the coordinates of the point which divides the line segment joining (−3, 5) and (4, −9) in the ratio 1 : 6 internally.
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- Question 24
“The points (0,
a),
a > 0 lie on
x-axis for all
a”. Justify the truthness of the statement.
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- Question 25
In ΔPQR, AB || QR. If AB is 3 cm, PB is 2 cm and PR is 6 cm, then find the length of QR.
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- Question 26
The angle of elevation of the top of a tower as seen by an observer is 30°. The observer is at a distance of 30
m from the tower. If the eye level of the observer is 1.5 m above the ground level, then find the height of the tower.
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- Question 27
The total surface area of a solid right circular cylinder is 1540 cm
2. If the height is four times the radius of the base, then find the height of the cylinder.
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- Question 28
The smallest value of a collection of data is 12 and the range is 59. Find the largest value of the collection of data.
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- Question 29
In tossing a fair coin twice, find the probability of getting :
(i) Two heads
(ii) Exactly one tail
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- Question 30
(a) If the volume of a solid sphere is
cu. cm, then find its radius.
OR
(b) If
x =
a sec θ +
b tan θ and
y =
a tan θ +
b sec θ, then prove that
x2 −
y2 =
a2 −
b2.
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- Question 31
Let A = {
a,
b,
c,
d,
e,
f,
g,
x,
y,
z}, B = {1, 2,
c,
d,
e} and C = {
d,
e,
f,
g, 2,
y}. Verify A\(B ⋃ C) = (A\B) ⋂ (A\C).
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- Question 32
Let A={6, 9, 15, 18, 21}; B = {1, 2, 4, 5, 6} and
f : A → B be defined by
. Represent
f by :
(i) an arrow diagram
(ii) a set of ordered pairs
(iii) a table
(iv) a graph
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- Question 33
Find the sum of the first 2
n terms of the series 1
2 − 2
2 + 3
2 − 4
2 + ...
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- Question 34
Find the sum of first
n terms of the series 7 + 77 + 777 +...
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- Question 35
The speed of a boat in still water is 15 km/hr. It goes 30 km upstream and return downstream to the original point in 4 hrs 30 minutes. Find the speed of the stream.
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- Question 36
Find the values of
a and
b if 16
x4 − 24
x3 + (
a − 1)
x2 + (
b + 1)
x + 49 is a perfect square.
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- Question 38
Find the area of the quadrilateral formed by the points (−4, −2), (−3, −5), (3, −2) and (2, 3).
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- Question 40
A flag post stands on the top of a building. From a point on the ground, the angles of elevation of the top and bottom of the flag post are 60° and 45° respectively. If the height of the flag post is 10 m, find the height of the building.
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- Question 41
The perimeter of the ends of a frustum of a cone are 44 cm and 8.4 π cm. If the depth is 14 cm, then find its volume.
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- Question 42
The length, breadth and height of a solid metallic cuboid are 44 cm, 21 cm and 12 cm respectively. It is melted and a solid cone is made out of it. If the height of the cone is 24 cm, then find the diameter of its base.
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- Question 43
Find the coefficient of variation of the following data.
18, 20, 15, 12, 25
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- Question 44
If a die is rolled twice, find the probability of getting an even number in the first time or a total of 8.
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- Question 45
(a) Find the GCD of the following polynomials 3
x4 + 6
x3 − 12
x2 − 24
x and 4
x4 + 14
x3 + 8
x2 − 8
x.
OR
(b) A straight line cuts the coordinate axes at A and B. If the mid point of AB is (3, 2), then find the equation of AB.
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- Question 46
(a) Draw the two tangents from a point which is 10 cm away from the centre of a circle of radius 6 cm. Also, measure the lengths of the tangents.
OR
(b) Construct a cyclic quadrilateral ABCD, given AB = 6 cm, ∠ABC = 70°, BC = 5 cm and ∠ACD=30°.
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- Question 47
(a) Solve graphically 2
x2 +
x − 6 = 0.
OR
(b) Draw the graph of
xy = 20,
x, y > 0. Use the graph to find
y when
x = 5, and to find
x when
y = 10.
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