

10th Class Mathematics Pre Board Examination Paper 
The paper consists of 30 questions divided into 4 sections... 

Pre Board Exam Class X Mathematics Time : 3 hours  Maximum marks: 80  General Instructions (i)  All questions are compulsory.  (ii)  The paper consists of 30 questions divided into 4 sections: Section A comprises of 10 questions of 1 marks each. Section B comprises of 5 questions of 2 marks each and has 1 internal choice. Section C comprises of 10 questions of 3 marks each and has 3 internal choices. Section D comprises of 5 questions of 6 marks each and has 2 internal choices.  (iii)  Use of calculators is not permitted.  Section A Q.1  Show that 3  √5 is irrational.  Q.2  In figure, the graph of some polynomial P(x) is given. Find the zeroes of the polynomial.  Q.3  The length of tangent from a point A at a distance of 7 cm from the centre is 2√6 cm. What will be the radius of the circle?  Q.4  Two dice are thrown simultaneously. What is the probability of getting multiple of 3 as the sum?  Q.5  For what values of k, the quadratic equation 2x^{2}  kx +1 = 0 has equal roots?  Q.6  In the following figure, the length of an arc AB = 20 cm is a sector of a circle. Find the radius of the circle if AOB = 144^{o}.  Q.7  For what value of 'p' the following pair of linear equation has infinitely many solutions? 2x  3y = 7 (p+2)x  (2p +1)y = 21  Q.8  If AB, AC, PQ are tangents in the given figure. AB  7cm and XQ = 2cm, find the length of AQ.  Q.9  If the sum of n terms of an AP be 3n^{2}  n and its common difference is 6, then find the first term.  Q.10  If tanθ = 5/6 and θ+ = 90^{o}, then what is the value of cot?  Section B Q.11  Prove that: (1 + cotθ  cosecθ) ( 1 + tanθ + secθ) = 2 Or If cos(3y  2x) = and cos (x +y) = √3 / 2, 0^{o} < x +y < 90^{o} and x  Q.12  Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre of the circle.  Q.13  Find all zeroes of 2x^{4}  3x^{3}  3x^{2} + 6x  2, if you know two of its zeroes are √2 and √2.  Q.14  Find the value of 'a' for which the points A(5, 1), B (1, a) and C(4, 2) are collinear.  Q.15  Find the roots of the quadratic equation, if they exist, using the quadratic formula. 3x^{2}  5x + 2 = 0  Section C Q.16  A piggy bank contains hundred 50 p coins, fifty Re 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, what is the probability that coins. (i) will be a 50 p coin. (ii) will not be a Rs 5 coin. Or A carton consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major defects. Jimmy, a trader, will only accept the shirts which are good, but Sujatha, another trader, will only rejects the shirts which have major defects, one shirt drawn at random. What is the propability that (i) it is acceptable to Jimmy? (ii) it is acceptable to Sujatha?  Q.17  The diagonals of a quadrilateral ABCD intersect each other at the point O such that Show that ABCD is a trapezium.  Q.18  Evaluate : + 2cot8^{o} cot17^{o} cot45^{o} cot 73^{o} cot 82^{o}  3 (sin^{2} 38^{o} + sin^{2} 52^{o})  Q.19  If the second term of an AP is 4 and seventh is  11. Find the 16th term.  Q.20  If ( 2, 1), B(x , 0), C (4, y) and D (1, 2) are the vertices of a parallelogram taken is order, find x & y. Or The coordinates of the centroid of a triangle are (1, 3) and its two vertices are (7, 6) and (8, 5). Find the third vertex. Also, find the coordinates of the centroid of the triangle when the third vertex is (2, 4).  Q.21  A hemispherical tank full of water is emptied by a pipe at the rate of 3 4/7 litres per second. How much time will it take to empty half the tank. if it is 3 m in diameter? ( Take = 22/7)  Q.22  A manufacturer of T. V sets produced 600 sets in the third year and 700 sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find: (a) the production in the first year (b) the production in the tenth year (c) the total production is first 7 years  Q.23  The line joining the points (2, 1) and (5, 8) is trisected at the points P and Q. If point P lies on the line 2x  y + k= 0 find the value of k.  Q.24  Prove that the square of any positive integer is of the form 5q, 5q +1, 5q +4 for some integer q.  Q.25  Construct a triangle of sides 4 cm. 5 c and 6 cm and then a triangle similar to it whose sides are 2/3 of the corresponding sides of the firs triangle. Justify your construction. Or Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60^{o}.  Section C Q.26  Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60o and 30o respectively. Find the height of the pole and the distance of the point from the poles. Or A vertical flagstaff stands on the top of a building. The height of the flagstaff above the building is 6 cm. The angle of the elevation of the top and bottom of the flagstaff at a point on the level ground are 45o and 30o respectively. Find the height of the building.  Q.27  A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs. 1000 as hostel charges whereas a student B, who takes food for 26 days pays Rs. 1180 as hostel charges. Find the fixed charges and the cost of food per day.  Q.28  A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. the ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.  Q.29  Prove that the ratio of the areas of two similar triangles is equal to the ration of the square of their corresponding sides. Using the above result, solve: The areas of two similar triangles ABC and PQR are 64 cm^{2} and 121 cm^{2} respectively. If QR 15.4 cm. Find BC.  Q.30  If the mean of the following distribution is 19.92. Find the missing frequencies F_{1} and F_{2} Class  4  8  8  12  12  16  16  20  20  24  24  28  28  32  32  36  Total  No. of Students  2  F_{1}  15  25  18  12  F_{2}  3  100  Or During the medical check up of 35 students of a class, their weights were recorded as follows: Weights ( in kg)  No. of Students  Less than 38  0  Less than 40  3  Less than 42  5  Less than 44  9  Less than 46  14  Less than 48  28  Less than 50  32  Less than 52  35  Draw a less than type ogive for the given data. Hence, obtain the median weight from the graph and verify the result by using formula.  

Related Words: 
Polynomial, Tangent, Radius of Circle, Probability, Quadratic Equation, Parallel Tangents, Quadratic Formula, Trader, Trapezium, Parallelogram, Circular Cylinder, Triangles



