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10th Class Mathematics Mid Term Examination Paper

The question paper consists of 30 questions...

Mathematics [All]

Central Board of Secondary Education [10]

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Mid Term Examination

Class X Mathematics

Time : 3 hours

Maximum marks: 80

General Instructions


All questions are compulsory.


The question paper consists of 30 questions, divided into four section - A, B, C and D.


Section A contains 10 questions of 1 mark each, Section B is of 5 questions of 2 marks each. Section C is of 120 questions of 3 marks each and Section D is of 5 questions of 6 marks each.


Use of calculators is not permitted.

Section - A



Why (7 x 11 x 13 + 13 x 2) is a composite number.


Write a quadratic equation whose roots are -2 and 5.


The graph of two linear equations is a pair of parallel lines. Which type of system of equations is it?


The graph of polynomial x2 - 2x - 35 cuts the x - axis at (7,0) and (-5, 0). Find all the zeroes of the polynomial x2 - 2x - 35.


If Cosθ + Secθ = 2, find the value of Cos2θ + Sec2θ.


If P(E) = 0.03. What is P (E)?


Diagonals of a trapezium ABCD with AB || CD intersect each other at O. If AB = 2CD then find the ratios of areas of triangles AOB and COD


A wire is in the form of a circle of radius 7 cm. it is rebent into a square form. Find the length of the side of the square.


A letter is selected from the letters of the word MATHEMATICS. What is the probability that it is a vowel?


In the adjoining figure, DE || BC. Find CE. If AD = 1.5 cm, BD = 3 and AE = 2 cm.

Section - B


Find the area of the triangle formed by the points A (3, 5), B (4, 7) and C (7, -4).


Evaluate:- cot230o - 2cos260o - 3/4 sec245o - 4sec230o



If 10 times of the 10th term of an A. P. is equal to 15 times the 15th term. Find its 25th term.


Tickets numbered 2, 3, 4, 5 ------- 99, 100, 101 are placed in a box and mixed thoroughly. One ticket is drawn at random from the box. Find the probability that the number on the ticket is

(i)    an even number                                           (ii) a number less than 16

(iii)  a number which is a perfect square              (iv) a prime number less than 20


Two right triangle BAC and BDC, right angled at A and D respectively are drawn on the same base BC and on the same side of BC. If AC and BD intersect at P, prove that AP x PC = DP x PB.

Section - C


Using Euclid's division algorithm, find the HCF of 56, 84 and 312.


Prove that 5 - √2 is an irrational number.


Solve graphically the following system of linear equations: 2x - y = 2 and 4x - y = 8. Also, find the co-ordinates of the points where the lines meet the axis of x.


If two zeroes of the polynomials 3x4 - 5x3 - 11x2 + 15x + 6 are √3 and -√3, find the other zeroes of the polynomial.


Prove that


Find the sum of all three digit natural numbers which are divisible by 7.


If the sum of first n terms of an A. P. is given by Sn = Sn2 + 3n, find the 20th term of the A - P.


Find the point on the x - axis, which is equidistant from (2, -5) and (-2, 9).


In the given figure ΔABC and ΔDBC are on the same base BC. If AD and BC intersect at O. Prove that ar (Δ ABC) / ar(Δ DBC) = Ao / Do


In a right angled triangle ABC with C = 90o, a point D is taken on AB such that CD | AB. Prove that


An iron solid sphere of radius 3 cm is melted and recast into small spherical balls of radius 1 cm each. Find the number of small spherical balls made from the given sphere.


In what ratio does the point P(2, -5) divide the line segment joining A(-3, 5) and B (4, 9).


ABCD is a flower bed. If OA = 21 cm and OC = 14 cm. Find the area of the flower bed.

Section - D


From the top of a building 100 m high, the angles of depression of the top and bottom of a tower are observed to be 45o and 60o respectively. Find the height of the tower. Also find the distance between the foot of the building and bottom of the tower.


The angle of elevation of the top of a tower at a point on the ground is 30o. After walking a distance of 100m towards the foot of the tower along the horizontal line the angle of elevation of the top of the tower is 60o. Find the height of the tower.


Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Use the above theorem, in the following if ABC is an isosceles triangle right angled at C, then prove that AB2 = 2AC2 .


A cylindrical container is filled with ice cream whose diameter is 12 cm and height is 15 cm. The whole ice cream is distributed to 10 children in equal cones having hemispherical tops. It the height of conical portion is twice the diameter of its base, find the diameter of the ice - cream cone.


A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 100cm and the diameter of hemispherical ends is 28cm. Find the cost of polishing the surface of the solid at the rate of Rs. 5 per square centimeters.


A shopkeeper buys a number of books for Rs. 80. if he had bought 4 more books for the same amount each book would have cost Re 1 less. How many books did he buy?


If the coordinates of the mid points of the sides of a triangle are (3, 2), (5, 4) and (4, 3). Find the coordinates of the vertices of the triangle.

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Related Words:

System of Equations, Linear Equations, Graph of Polynomial, Diagonals of Trapezium, Areas of Triangles, Probability, Natural Numbers, Spherical, Hypotenuse, Hemispherical, Vertices of Triangle




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