Board Paper of Class 10 2012 Maths (SET 1) - Solutions
1. All questions are compulsory.
2. The question paper consists of 34 questions divided into four sections A, B, C and
3. Section A contains 10 questions of 1 mark each, which are multiple choices type
questions, Section B contains 8 questions of 2 marks each, Section C contains 10
questions of 3 marks each, Section D contains 6 questions of 4 marks each.
4. There is no overall choice in the paper. However, internal choice is provided in one
question of 2 marks, 3 questions of 3 marks each and two questions of 4 marks each.
5. Use of calculators is not permitted.
- Question 1
If 1 is a root of the equations ay2 + ay + 3 = 0 and y2 + y + b = 0 then ab equals:
- Question 2
The sum of first 20 odd natural numbers is:
- Question 3
In Fig. 1, the sides AB, BC and CA of a triangle ABC, touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, then the length of BC (in cm) is:
- Question 4
In Fig 2, a circle touches the side DF of ΔEDF at H and touches ED and EF produced at
K and M respectively. If EK = 9 cm, then the perimeter of ΔEDF (in cm) is:
- Question 5
If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:
A. 1 : 2
B. 2 : 1
C. 1 : 4
D. 4 : 1
- Question 6
If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, then the diameter of the larger circle (in cm) is:
D. 14VIEW SOLUTION
- Question 7
The length of shadow of a tower on the plane ground is times the height of the tower.
The angle of elevation of sun is:
- Question 8
If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5), then the coordinates of the other end of the diameter are:
A. (−6, 7)
B. (6, −7)
C. (6, 7)
D. (−6, −7)VIEW SOLUTION
- Question 9
The coordinates of the point P dividing the line segment joining the points A (1, 3) and B (4, 6) in the ratio 2 : 1 are:
A. (2, 4)
B. (3, 5)
C. (4, 2)
D. (5, 3)
- Question 10
Two dice are thrown together. The probability of getting the same number on both dice is:
- Question 11
Find the value(s) of k so that the quadratic equation x2 − 4kx + k = 0 has equal roots.
- Question 12
Find the sum of all three digit natural numbers, which are multiples of 11.
- Question 13
Tangents PA and PB are drawn from an external point P to two concentric circles with centre O and radii 8 cm and 5 cm respectively, as shown in Fig. 3. If AP = 15 cm, then find the length of BP.
- Question 14
In Fig. 4, an isosceles triangle ABC, with AB = AC, circumscribes a circle. Prove that the point of contact P bisects the base BC.
In Fig. 5, the chord AB of the larger of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC = CB.
- Question 15
The volume of a hemisphere is . Find its curved surface area.
- Question 16
In Fig. 6, OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region.
- Question 17
If a point A (0, 2) is equidistant from the points B (3, p) and C (p, 5), then find the value of p.
- Question 18
A number is selected at random from first 50 natural numbers. Find the probability that it is a multiple of 3 and 4.
- Question 19
Solve for x: 4x2 − 4ax + (a2 − b2) = 0
Solve for x:
- Question 20
Prove that the parallelogram circumscribing a circle is a rhombus.
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.VIEW SOLUTION
- Question 21
Construct a right triangle in which the sides, (other than the hypotenuse) are of length 6 cm and 8 cm. Then construct another triangle, whose sides are times the corresponding sides of the given triangle.
- Question 22
In Fig. 7, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and
3.5 cm and centre O. If ∠POQ = 30°, then find the area of the shaded region.
- Question 23
From a solid cylinder of height 7 cm and base diameter 12 cm, a conical cavity of same height and same base diameter is hollowed out. Find the total surface area of the remaining solid.
A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, then find the radius and slant height of the heap.VIEW SOLUTION
- Question 24
The angles of depression of two ships from the top of a light house and on the same side of it are found to be 45° and 30°. If the ships are 200 m apart, find the height of the light house.
- Question 25
A point P divides the line segment joining the points A (3, −5) and B (−4, 8) such that
. If P lies on the line x + y = 0, then find the value of K.
- Question 26
If the vertices of a triangle are (1, −3), (4, p) and (−9, 7) and its area is 15 sq. units, find the value(s) of p.
- Question 27
A box contains 100 red cards, 200 yellow cards and 50 blue cards. If a card is drawn at random from the box, then find the probability that it will be (i) a blue card (ii) not a yellow card (iii) neither yellow nor a blue card.
- Question 28
The 17th term of an AP is 5 more than twice its 8th term. If the 11th term of the AP is 43, then find its nth term.
- Question 29
A shopkeeper buys some books for Rs 80. If he had bought 4 more books for the same amount, each book would have cost Rs 1 less. Find the number of books he bought.
The sum of two numbers is 9 and the sum of their reciprocals is. Find the numbers.
- Question 30
Sum of the first 14 terms of an AP is 1505, and its first term is 10. Find its 25th term.
- Question 31
Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.
- Question 32
A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them being 3.5 cm and the total height of solid is 9.5 cm. Find the volume of the solid.
- Question 33
A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, find the height of the bucket.VIEW SOLUTION
- Question 34
The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of depression from the top of the tower to the foot of the hill is 30°. If the tower is 50 m high, find the height of the hill.