(i) All questions are compulsory.
(ii) The question paper consists of 31 questions divided into four sections – A, B, C and D.
(iii) Section A contains 4 questions of 1 mark each, Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions of 4 marks each.
(iv) Use of calculated is not permitted.
- Q1VIEW SOLUTION
- Q2VIEW SOLUTION
A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and these are equally likely outcomes. Find the probability that the arrow will point at any factor of 8.VIEW SOLUTION
- Q4VIEW SOLUTION
- Q5VIEW SOLUTION
- Q6VIEW SOLUTION
Solve for x :VIEW SOLUTION
- Q8VIEW SOLUTION
- Q9VIEW SOLUTION
- Q10VIEW SOLUTION
- Q11VIEW SOLUTION
- Q12VIEW SOLUTION
- Q13VIEW SOLUTION
A bag contains 18 balls out of which x balls are red.VIEW SOLUTION
(i) If one ball is drawn at random from the bag, what is the probability that it is not red?
(ii) If 2 more red balls are put in the bag, the probability of drawing a red ball will be times the probability of drawing a red ball in the first case. Find the value of x.
From the top of a tower of height 50 m, the angles of depression of the top and bottom of a pole are 30° and 45° respectively. FindVIEW SOLUTION
(i) how far the pole is from the bottom of a tower,
(ii) the height of the pole. (Use )
- Q16VIEW SOLUTION
- Q17VIEW SOLUTION
A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weight, a conical hole is drilled in the cylinder. The conical hole has a radius of cm and its depth is cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape.VIEW SOLUTION
In Figure 3, ABCD is a trapezium with AB || DC, AB = 18 cm, DC = 32 cm and the distance between AB and DC is 14 cm. If arcs of equal radii 7 cm have been drawn, with centres A,B, C and D, then find the area of the shaded region.VIEW SOLUTION
A solid right-circular cone of height 60 cm and radius 30 cm is dropped in a right-circular cylinder full of water of height 180 cm and radius 60 cm. Find the volume of water left in the cylinder, in cubic metres.VIEW SOLUTION
- Q21VIEW SOLUTION
- Q22VIEW SOLUTION
The total cost of a certain length of a piece of cloth is Rs 200. If the piece was 5 m longer and each metre of cloth costs Rs 2 less, the cost of the piece would have remained unchanged. How long is the piece and what is its original rate per metre ?VIEW SOLUTION
- Q24VIEW SOLUTION
In Figure 4, O is the centre of the circle and TP is the tangent to the circle from an external point T. If ∠PBT = 30°, prove that BA : AT = 2 : 1.
- Q26VIEW SOLUTION
Two poles of equal heights are standing opposite to each other on either side of the road which is 80 m wide. From a point P between them on the road, the angle of elevation of the top of a pole is 60° and the angle of depression from the top of another pole at point P is 30°. Find the heights of the poles and the distances of the point P from the poles.VIEW SOLUTION
A box contains cards bearing numbers from 6 to 70. If one card is drawn at random from the box, find the probability that it bears(i) a one digit number.
(ii) a number divisible by 5.(iii) an odd number less than 30.
(iv) a composite number between 50 and 70.VIEW SOLUTION
The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of point C are (0, −3). The origin is the mid-point of the base. Find the coordinates of the points A and B. Also find the coordinates of another point D such that BACD is a rhombus.VIEW SOLUTION
A vessel full of water is in the form of an inverted cone of height 8 cm and the radius of its top, which is open, is 5 cm. 100 spherical lead balls are dropped into the vessel. One-fourth of the water flows out of the vessel. Find the radius of a spherical ball.VIEW SOLUTION
Milk in a container, which is in the form of a frustum of a cone of height 30 cm and the radii of whose lower and upper circular ends are 20 cm and 40 cm respectively, is to be distributed in a camp for flood victims. If this milk is available at the rate of Rs 35 per litre and 880 litres of milk is needed daily for a camp, find how many such containers of milk are needed for a camp and what cost will it put on the donor agency for this. What value is indicated through this by the donor agency ?VIEW SOLUTION
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