(i) All questions are compulsory.
(ii) The question paper consists of 34 questions divided into four sections A, B, C and D.
(iii) Sections A contains 8 questions of one mark each, which are multiple choice type questions, section B contains 6 questions of two marks each, section C contains 10 questions of three marks each, and section D contains 10 questions of four marks each.
(iv) Use of calculators is not permitted.
- Q1VIEW SOLUTION
- Q2VIEW SOLUTION
- Q3VIEW SOLUTION
- Q4VIEW SOLUTION
- Q5VIEW SOLUTION
In Figure 1, a quadrilateral ABCD is drawn to circumscribe a circle such that its sides AB, BC, CD and AD touch the circle at P, Q, R and S respectively. If AB = x cm, BC = 7 cm, CR = 3 cm and AS = 5 cm, find x.VIEW SOLUTION
- Q7VIEW SOLUTION
- Q8VIEW SOLUTION
- Q9VIEW SOLUTION
- Q11VIEW SOLUTION
- Q12VIEW SOLUTION
- Q13VIEW SOLUTION
- Q14VIEW SOLUTION
- Q17VIEW SOLUTION
- Q10VIEW SOLUTION
In Figure 4, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside the region. Find the area of the shaded region.VIEW SOLUTION
- Q16VIEW SOLUTION
- Q18VIEW SOLUTION
- Q19VIEW SOLUTION
A girl empties a cylindrical bucket, full of sand, of base radius 18 cm and height 32 cm, on the floor to form a conical heap of sand. If the height of this conical heap is 24 cm, then find its slant height correct upto one place of decimal.VIEW SOLUTION
Two ships are approaching a light-house from opposite directions. The angles of depression of the two ships from the top of the light-house are 30° and 45°. If the distance between the two ships is 100 m, find the height of the light-house.VIEW SOLUTION
- Q22VIEW SOLUTION
- Q23VIEW SOLUTION
- Q24VIEW SOLUTION
The angle of elevation of the top of a chimney from the foot of a tower is 60° and the angle of depression of the foot of the chimney from the top of the tower is 30°. If the height of the tower is 40 m, find the height of the chimney. According to pollution control norms, the minimum height of a smoke emitting chimney should be 100 m. State if the height of the above mentioned chimney meets the pollution norms. What value is discussed in this question?VIEW SOLUTION
- Q26VIEW SOLUTION
The mid-point P of the line segment joining the points A(−10, 4) and B(−2, 0) lies on the line segment joining the points C(−9, −4) and D(−4, y). Find the ratio in which P divides CD. Also find the value of y.VIEW SOLUTION
A hemispherical depression is cut out from one face of a cubical block of side 7 cm, such that the diameter of the hemisphere is equal to the edge of the cube. Find the surface area of the remaining solid.VIEW SOLUTION
[Use π = ]
- Q29VIEW SOLUTION
A metallic bucket, open at the top, of height 24 cm is in the form of the frustum of a cone, the radii of whose lower and upper circular ends are 7 cm and 14 cm respectively. Find :VIEW SOLUTION
(i) the volume of water which can completely fill the bucket.
(ii) the area of the metal sheet used to make the bucket.
[Use π = ]
- Q31VIEW SOLUTION
- Q32VIEW SOLUTION
A piggy bank contains hundred 50 p coins, fifty Rs 1 coins, twenty Rs 2 coins and ten Rs 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, find the probability that the coin which fellVIEW SOLUTION
(i) will be a 50 p coin.
(ii) will be of value more than Rs 1.
(iii) will be of value less than Rs 5.
(iv) will be a Rs 1 or Rs 2 coin.
- Q34VIEW SOLUTION
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