Maths | RJ Board | Grade 10 | 2014
Q. Write the distance of the point (3, 2) from y-axis
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Q. In the figure, CD and RS are respectively the medians of ABC and PQR. If ABCPQR, prove that
(ii) CDRS=ABPQ

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Q. If the sum of zeroes of the quadratic polynomial kx2+5x+3k is equal to their product, find the value of k
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Q. Two cubes each of volume 27 cm3 are joined end to end to form a solid. Find the surface area (cm2) of the resulting cuboid.
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Q. An express train takes 2 hour less time than a passenger train to travel 400 km between two stations (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 10 km/h more than of the passenger train, find the average speed of the two trains
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Q. BE and CF are medians of a triangle ABC right angles at A. Prove that 4(BE2+CF2)=5BC2.
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Q. In the figure, a quadrilateral PQRS is drawn to circumscribe a circle. Prove that PQ+RS=PS+QR

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Q. Find the L.C.M. of the numbers 180, 72 and 252.
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Q. From the top of a 10 m high building, the angle of elevation of a tower is 60 and the angle of depression of its foot at 45. Determine the height of the tower.
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Q. Find the co-ordinates of the points of trisection of the line segment joining the points P(3, 4) and Q(4, 5)
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Q. Show that tan36tan17tan54tan73=1
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Q. If the median of the distribution given below is 28.5, find the values of x and y.
 Class-interval 0−10 10−20 20−30 30−40 40−50 50−60 Total Frequency 5 x 20 15 y 5 60
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Q. Write the area of a sector of a circle with radius r and angle with degree measure θ.
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Q. Find the value of cos212+cos278
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Q. Find the area of the shaded region in the figure, if AB=5 cm, AC=12 cm and O is the centre of the circle

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Q. A box contains 30 discs which are numbered 1 to 30. If one disc is drawn at random from the box, find the probability that it bears
(i) a two digit number
(ii) a perfect square number
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Q. Write the next two terms of A.P.4, 1, 2, 5, .....
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Q. A hemispherical tank full of water is emptied by a pipe at the rate of 5 litres per second. How much time will it take to empty half of the tank, if it is 3.5 m in diameter?
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Q. If the probability of solving a problem by a student is 23, then find the probability of not solving the problem by the student.
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Q. If tangents TA and TB from a point T to a circle with centre O are inclined to each other at an angle of 70, then find AOB (in degrees).
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Q. If the sum of the first 12 terms of an A.P. is 468 and its common difference is 6, find the 10th term
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Q. Find the area of a circle whose circumference is 44 cm44 cm in sq cm.
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Q. The mean of the following frequency table is 50. Find the values of x and y.
 Class-interval 0−20 20−40 40−60 60−80 80−100 Total Frequency 17 x 32 y 19 120
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Q. Write the solution of the pair of linear equations 3x+4y=0 and 2xy=0
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Q. A boy 2 m long casts a shadow 1 m long on the plane ground. At the same time, a tower casts a shadow 5 m long on the ground. Find the height of the tower (in m).
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Q. Number 3625 is a terminating decimal or a non-terminating repeating decimal? Write it in decimal form.
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Q. If M(4, 5) is the mid-point of the line segment AB and co-ordinates of A are (3, 4), then find the co-ordinates of point B.
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Q. Prove that 1+cosA1cosA=cosecA+cotA
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Q. If sinθ=12, then find the value of 12sin2θsinθ
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Q. Construct a tangent to any point on the circle of radius 3 cm.
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