Maths | CBSE Board | Grade 10 | 2013
Q. The sum of first n terms of an AP is 3n2n. Find the 25th term of this AP.
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Q. A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the volume of wood in the toy. [Useπ=227]
1. 425
2. 290
3. 474.83
4. 205.33
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Q. Solve that following for x:
12a+b+2x=12a+1b+12x
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Q. Water is flowing through a cylindrical pipe, of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m/s. Determine the rise in level of water in the tank in half hours.
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Q. In fig., a circle is inscribed in triangle ABC touches its sides AB, BC and AC at points D, E and F respectively. If AB=12 cm, BC=8 cm and AC=10 cm, then find the length of AD, BE and CF.

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Q. Find the ratio in which the yaxis divides the line segment joining the points (4, 6) and (10, 12). Also, find the coordinates of the point of division.
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Q. In fig., l and m are two parallel tangents to a circle with centre O, touching the circle at A and B respectively. Another tangent at C intersects the line l at D and m at E. Prove that DOE=90o

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Q. Sum of the areas of two squares is 400 cm2. If the difference of their perimeters is 16 cm, find the sides of the two squares.
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Q. Show that the points (2, 3), (8, 3) and (6, 7) are the vertices of a right triangle.
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Q. In fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively, If AB=29 cm, AD=23 cm, B=90o and DS=5 cm, then the radius of the circle (in cm) is:

1. 11
2. 18
3. 6
4. 15
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Q. How many three-digit natural numbers are divisible by 7?
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Q. For what values of k, the roots of the quadratic equation (k+4)x2+(k+1)x+1=0 are equal?
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Q. Solve the following quadratic equation for x: 43x2+5x23=0
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Q. A Group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is (i) extremely patient (ii) extremely kind or honest. Which of the above values you prefer more?
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Q. A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability that the drawn card is neither a king nor a queen.
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Q. Prove that the parallelogram circumscribing a circle is a rhombus.
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Q. In fig., the area of triangle ABC (in sq. units) is:

1. 15
2. 7.5
3. 2.5
4. 10
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Q. The horizontal distance between two poles is 15 m. The angle of depression of the top of first pole as seen from the top of second pole is 30o. If the height of the second pole is 24 m, find the height of the first pole. [Use3=1.732]
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Q. A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears a prime-number less than 23, is:
1. 790
2. 1090
3. 445
4. 989
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Q. If the difference between the circumference and the radius of a circle is 37cm, then using π=227, the circumference (in cm) of the circle is:
1. 154
2. 44
3. 14
4. 7
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Q. Given A.P is 13q, 16q3q, 112q3q. Find the common difference
1. 2
2. 1
3. 1
4. 2
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Q. A bucket opens at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs 10 per 100 cm2. [Use π=3.14].Insert answer in nearest integer.

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Q. The probability of getting an even number, when a die is thrown once, is:
1. 12
2. 13
3. 16
4. 56
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Q. In a circle of radius 21 cm, an arc subtends an angle of 60o at the centre. Find the sum of the length of the arc and area of the sector formed by the arc. [Useπ=227]
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Q. Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm.
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Q. In fig., PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4cm. If PA PB, then the length of each tangent is:

1. 4 cm
2. 3 cm
3. 5 cm
4. 6 cm
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Q. The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30o. The distance of the car from the base of the tower (in m.) is:
1. 253
2. 503
3. 753
4. 150
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Q. In Fig., AB and CD are two diameters of a circle with centre O, which are perpendicular to each other. OB is the diameter of the smaller circle. If OA=7 cm, find the area of the shaded region. [Useπ=227]

1. 60.5 cm2
2. 63.5 cm2
3. 66.5 cm2
4. 56.5 cm2
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Q. Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions 14 cm×7 cm. Find the area of the remaining card board. [Useπ=227]
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Q. A vessel is in the form of hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the total surface area of the vessel. [Useπ=227]
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