Kendriya Vidyalaya Sangathan Class -X Subject- Mathematics Time - M.M - 80 General Instruction :-. All Questions are compulsory, however internal choices are given in some questions.. This question paper consists of four section and marks of each section against each section. 3 Use of calculators is not permitted SECTION - A (*6 = 6 marks) Q. Use Euclid s Division Algorithm to find the H.C.F of 455 and 40. Q. Find a quadratic polynomial whose sum and product of zeroes are 0 and respectively. Q 3. In the given figure, ABC is circumscribing a circle, then find the length of BC. A 3 cm N M 8 cm 4 cm B L C Q 4. Find the nature of the roots of quadratic equation x - 5x+=0 Q 5. Find the distance between points A(, 3) and B(4, ). Q 6. If then find the value of. SECTION - B (*6 = marks) Q 7 Using Euclid s division algorithm, find the HCF of 60 and 350. Q 8. For what value of is the system of equation and is inconsistent. Q 9. Find the 0 th term of the AP, 8, 8 Q 0. Find the mean of the given frequency distribution table: Class Interval 5-5 5-35 35-45 45-55 55-65 65-75 75 85 Frequency 6 7 4 4
Q. Find the ratio in which divides the join of and. Q. Three different coins are tossed together. Find the probability of getting (i) Exactly two heads (ii) at least two heads SECTION - C (3*0 = 30 marks) Q 3. Use Euclid division lemma to show that the square of any positive integer is either of the form 3m or 3m+ for some integer. Prove that is irrational. Q 4. The three vertices of a parallelogram ABCD are A(3, 4), B(, 3) and C( 6, ). Find the coordinates of vertex D. Find the area of triangle ABC (in sq. units). Whose vertices are A(,3), B(-,0) and C(4,0). Q 5. Find the zeroes of the quadratic polynomial x + 7x + 0, and verify the relationship between the zeroes and the coefficients Q 6. Solve the following system of equations :- Q 7. The chord of a circle of radius cm subtends an angle of 0 at centre. Find the corresponding minor segment of the circle. Q 8. Prove that. If A, B and C are interior angles of a triangle ABC, then show that ( ) Q 9. Q 0. Q. Prove that the parallelogram circumscribing a circle is a rhombus. Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ABC = 60. Then Construct a triangle whose sides are ABC. of the corresponding sides of the triangle A 0 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform m by 4 m. Find the height of the platform. Q. A box contains 3 blue, white and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will be (i) White (ii) Blue (iii) Not Blue If a card is drawn randomly from a deck of well shuffled cards, what is the probability that it will be (i) A black jack (ii) An Ace (iii) A queen
SECTION - D (4*8 = 3 marks) Q 3. Check whether the equation has real roots and if it has, find them by the method of completing the square. Also verify that roots obtained satisfy the given equation. An express train takes hour less than a passenger train to travel 3 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is km/h more than that of the passenger train, find the average speed of the two trains. Q 4. If the sum of first 7 terms of an AP is 49 and that of 7 terms is 89, find the sum of first n terms. Q 5. Q 6. A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 6 cm with radii of its lower and upper ends as 8 cm and 0cm, respectively. Find the cost of the milk which can completely fill the container, at the rate of Rs 0 per litre. Prove that Prove that (cosec A sin A)(sec A cos A) = Q 7. The angle of elevation of the top of a building from the foot of the tower is 30 and the angle of elevation of the top of the tower from the foot of the building is 60. If the tower is 50 m high, find the height of the building. Q 8. In given figure ABPC is a quadrant of a circle of radius 4 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region. Q 9. Show that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Prove that the ratio of area of two similar triangles is equal to ratio of squares of corresponding sides.
Q 30. The following table shows the data of the amount donated by 00 people in a blind school. Amount Donated (in Rs.) Number of persons 0 00 00 00 5 00 300 300 400 400 500 7 500 600 0 600 700 700 800 9 800 900 7 900-000 4 If the median of the above data is 55, find the value of and.
Marking Scheme H.C.F= 35 Correct formula X + = 0 3 BL = 4,LC = 5 BC = 9 4 Finding D=-3 NO real roots 5 Correct answer = 6 5/4 7 Using Euclid s algorithm Calculation Answer 8 Condition for inconsistency Calculation K = ± 6 9 a=,d= a 0 =0 0 Using correct formula calculation Correct mean Section formula Ratio 5:3 P(E)= 3/8 P(E)=4/8 = 3 Let the integers be 3a, 3a +, 3a + Squaring the integers and rearrangement Or Assumption Correct proof 4 Using mid point formula to find the mid point of diagonal
Calculation of coordinates x = -, y = Or Using formula for area of triangle Calculation area = 7.5 cm 5 Finding zeroes of polynomial x= -, -5 Verification of relationship 6 Substitution or elimination of variables Calculation and answer x =, y= 3 7 Area of Sector Area of triangle Area of segment = 50.4 cm 8 Multiplying sin on both the numerator and denominator Simplification Or ( B + C)/ = 90 0 A/ Sin ( B + C)/ = Sin (90 0 A/) = Cos A/ 9 Given, To prove, diagram Tangents from exterior points are equal Adding the equations 0 Correct Construction 3 Volume of well Volume of platform Calculation of height =.5 m /9 /3 6/9 3 Finding b - 4ac Solving by completing square Verifying Or Forming the correct quadratic equation
Calculation and answer 44km/hr and 33 km/hr 4 Forming equations in terms of a and d Calculating the value of a and d Finding sum of n terms = n 5 Finding volume= 0450 cm 3 cost of milk =Rs 09 6 Dividing by sin Using correct identity Getting required RHS Or Changing of coseca and sec Ato sina and cosa Using identities Simplifying RHS 7 Diagram Using proper trigonometric ratios and calculation Height of building = 50/3 m 8 Finding BC Correct calculation and area = 98 cm 3 9 Given, to prove,diagram Correct proof of Pythagoras theorem 3 Given, to prove, construction Expressing ratio of the altitudes in terms of ratio of sides Substitution of the ratio 30 Finding cumulative frequency Using formula for median Calculation of x Calculation of y
Class X (07-8) Mathematics Blue Print Unit Number Systems Algebra VSA mark SA- marks SA- 3 marks LA 4 marks Total () () 3() 6(3) 3() () 0(8) () 4()
Coordinate Geometry () () 3() 6(3) Geometry () 3() 4() 5(5) Trigonometry () 3() 4() (4) Mensuration 3() 0(3) 4() Statistics & Probability 3() 4() (4) 4() Total 80(30)