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CBSE X | Mathematics
Board Paper – 2015
CBSE Board
Class X Mathematics
Board Paper – 2015
Time: 3 hours
Total Marks: 90
General Instructions:
(i) All questions are compulsory
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(iii) Section A contains 4 questions of 1 mark each
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(iv) Use of calculators is not permitted
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1
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2
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Find the Sun’s altitude
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Two different dice are tossed together
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4
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If
∠QPT = 60˚, find ∠PRQ
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CBSE X | Mathematics
Board Paper – 2015
SECTION B
Question numbers 5 to 10 carry 2 marks each
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In the following figure, two tangents RQ and RP are drawn from an external point R to
the circle with centre O, If ∠PRQ = 120˚, then prove that OR = PR + RQ
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In Figure 4, a ∆ABC is drawn to circumscribe a circle of radius 3 cm, such that the
segments BD and DC are respectively of lengths 6 cm and 9 cm
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7
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In an AP, if S5 + S7 = 167 and S10 = 235, then find the A
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, where Sn denotes the sum of
its first n terms
9
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10
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CBSE X | Mathematics
Board Paper – 2015
SECTION C
Question numbers 11 to 20 carry 3 marks each
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The 14th term of an A
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is twice its 8th term
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12
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The angle of elevation of an aeroplane from point A on the ground is 60°
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If the aeroplane is flying at a constant
height of 1500 3 m, find the speed of the plane in km/hr
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If the coordinates of points A and B are (-2, -2) and (2, -4) respectively, find the
3
coordinates of P such that AP = AB , where P lies on the line segment AB
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The probability of selecting a red ball at random from a jar that contains only red, blue
1
and orange balls is
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If the jar contains 10 orange balls, find the total number of balls in the jar
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Find the area of the minor segment of a circle of radius 14 cm, when its central angle is
22
60˚
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[Use
]
7
17
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If the lower
part of each tent is of the form of a cylinder of diameter 4
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8 m, and the canvas to be used costs
Rs
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m, find the amount, the associations will have to pay
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A hemispherical bowl of internal diameter 36 cm contains liquid
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Find the height of each bottle, if 10% liquid
is wasted in this transfer
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A cubical block of side 10 cm is surmounted by a hemisphere
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5 per sq
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[Use π = 3
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topperlearning
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504 cones, each of diameter 3
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22
[Use
]
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SECTION D
Question numbers 21 to 31 carry 4 marks each
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The diagonal of a rectangular field is 16 metres more than the shorter side
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22
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, if it has a total of 60 terms and hence find the
sum of its last 10 terms
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A train travels at a certain average speed for a distance of 54 km and then travels a
distance of 63 km at an average speed of 6 km/h more than the first speed
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Prove that the lengths of the tangents drawn from an external point to a circle are equal
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Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the
chord joining the end points of the arc
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Construct a ∆ ABC in which AB = 6 cm, ∠A = 30° and ∠B = 60°, Construct another ∆AB’C’
similar to ∆ABC with base AB’ = 8 cm
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At a point A, 20 metres above the level of water in a lake, the angle of elevation of a
cloud is 30°
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Find the distance of the cloud from A
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A card is drawn at random from a well-shuffled deck of playing cards
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a card of spade or an ace
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a black king
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neither a jack nor a king
iv
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29
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units
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topperlearning
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In the following figure, PQRS is square lawn with side PQ = 42 metres
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Find the total area of the two flower beds (shaded parts)
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From each end of a solid metal cylinder, metal was scooped out in hemispherical from
of same diameter
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2 cm
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4 cm
22
thickness
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[Use
]
7
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