

10th Class Mathematics Examination Paper 
All questions are compulsory... 

Mock Test Class X Mathematics Time : 3 hours  Maximum marks: 80  General Instructions (i)  All questions are compulsory.  (ii)  Section A comprises of ten questions of 1 mark each. Section B comprises of five questions of 2 marks each, Section C comprises of tem questions of 3 mark each and Section D comprises of five questions of 6 marks each.  (iii)  All question is Section A are to be answered in one word, one sentence or as per the exact requirement of the question.  (iv)  There is no over all choice. Internal choice has been provided in one question of 2 marks each, three question of 3 marks each and two questions of 6 marks each. You have to attempt only one of the alternative in all such questions.  (v)  In questions on construction, drawings should be neat and exactly as per the given measurements.  Section A Q.1  A die is thrown once, what is the probability of getting the lowest whole number?  Q.2  In the given figure, What are the angles of depression from the points O_{1} and O_{2} of the object at A?  Q.3  Which measure of central tendency is given by the x  coordinates of the point of intersection of the more than 'O give' and less than ' O give'?  Q.4  Two tangents TP and TQ drawn from an external point T to a circle with centre O, as shown in the figure. If they are inclined to each other at an angle of 80o. What is the value of POQ?  Q.5  Without drawing the graphs state whether the following system of equations will represent intersection lines, coincident lines of parallel lines. Also state whether the system of equations is consistent / inconsistent : x + 2y = 8 2x + 3y = 12  Q.6  Write the condition to be satisfied so that a rational number p /q has a terminating decimal representation.  Q.7  Which term of the sequence 134, 129, 124....is the first negative term.  Q.8  A cylinder, a cone and a hemisphere are of equal bases and have the same height. What is the ratio of their Volumes.  Q.9  What is the nature of the roots of the equation 9y^{2}  12y + 4 = 0?  Q.10  State the converse of " If a line divides any two sides of a triangle in the same ratio" then the line is parallel to the third side.  Section B Q.11  Verify whether the points A (a, a), B (a, a) and C ( √3 a, √3 a) are the vertices of an equilateral triangle.  Q.12  Solve Or Solve 2x  = 1  Q.13  Justify the statement: " Tossing a coin is a fair way of deciding which team should bat first, at the beginning of a cricket match."  Q.14  If tanθ + = 2 find the value of tan^{2}θ +  Q.15  The perimeters of two similar triangles are 30 cm and 20 cm respectively. If one side of the first triangle is 12 cm. determine the corresponding side of the second triangle.  Section C Q.17  Find a quadratic polynomial, the sum and product of whose zeroes are  3 and 2 respectively. Does this polynomial alone satisfy the given condition? Explain.  Q.18  Divide and verify: 3x^{3} + x^{2} + 2x + 5 by 2x + 1 + x^{2}  Q.19  ABCD is a cyclic quadrilateral as given in the figure. Find the angles of quadrilateral Or If z = 3y = 2 (x + y) in a triangle xyz, find the three angles.  Q.20  If P, Q, R are interior angles of a triangle PQR show that: Sin = Cos Or If Sin 3A = Cos ( A  26^{o}), Where 3A is an acute angle. Find the value of A.  Q.21  Construct a right triangle ABC in which AB = 6 cm BC = 8 cm and B = 90o. Draw BD perpendicular from B to AC. Draw the circle through B, C and D. Construct the tangents from A to this circle.  Q.22  The incircle of ABC touches the sides BC, CA and AB at D, E and F respectively. If AB = AC, prove that BD = CD  Q.23  Prove that the points A (3, 0), B (1, 3 ) and C (4, 1) are the vertices of an isosceles right triangle.  Q.24  Mayank made a bird bath for his garden in the shape of a cylinder with a hemispherical depression at one end. The height of the cylinders 1.45 m and its radius is 30 cm. Find the lateral surface area and the total surface area of the bath.  Q.25  Sides AB, AC and median AD of Δ ABC are respectively proportional to sides PQ, PR and median PM of ΔPQR. Show that ΔABC ~ ΔPQR.  Q.26  State and prove Thales Theorem. Using the above theorem prove that a line drawn through the mid point of one side of a triangle parallel to another side bisects the third side.  Q.27  Solve the following system of linear equations graphically: 3x + y  12 = 0 x  3y + 6 = 0 Shade the region bounded by these lines and the x  axis. Also find the ratio of areas of triangles formed by the given lines with x axis and y  axis Or Form a pair of linear equations in two variables using the following information and solve it graphically. Five years ago, Sagar was twice as old as Venu. Ten years later Sagar's age will be ten years more than Venu's age. Find their present ages. What was the age of Sagar when Venu was born?  Q.28  The mean of the following frequency table is 53. Find the missing frequencies f_{1} and f_{2}: Age (in years)  0  20  20  40  40  60  60  80  80 100  Total  Number of people  15  f1  21  f2  17  100  Or The following tables shows the marks obtained by 100 students of class 10 in a school during Mid term examination. Find the mode of this distribution: Marks  Number of students  <10  07  <20  21  <30  34  <40  46  <50  66  <60  77  <70  92  <80  100   Q.29  From a solid cylinder whose height is 12 cm and diameter 10 cm, a conical cavity of same height and same diameter is carved out. Find the volume and total surface area of the remaining solid.  Q.30  The angle of elevation of a cloud from a point 60 metres above a lake is 30^{o} and the angle of depression of the reflection of the cloud in the lake is 60^{o}. Find the height of the cloud.  

Related Words: 
Probability, Lowest Whole Number, Intersection, Tangents, Coincident Lines, Hemisphere, Triangle, Cricket Match, Quadratic Polynomial, Shape of Cylinder, Lateral Surface Area, Linear Equations



