# PRE BOARD EXAMINATION CODE : E SESSION CLASS : X MAXIMUM MARKS: 80 SECTION A

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1 PRE BOARD EXAMINATION CODE : E SESSION CLASS : X MAXIMUM MARKS: 80 SUBJECT : MATHEMATICS TIME : HOURS General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 0 questions divided into four section A, B, C and D. (iii) Section A comprises 6 questions of 1 mark each, Section B comprises 6 questions of marks each, Section C comprises 10 questions of marks each and Section D comprises 8 questions of marks each. (iv) Use calculator is not permitted. SECTION A 1 If x= - 1 is a zero of the polynomial x +kx-,find the value of k. 1 For what value of k will the consecutive terms k+1, k+ and 5k-1 form an A.P? 1 In the given figure, AOB is a diameter of the circle with centre O and AC is a tangent to the circle at A. If BOC=10, then find ACO. 1 A B C A segment AB is divided at point P such that PB = then find the ratio AP: PB. 1 AB 7 5 What is the area of the square that can be inscribed in a circle of radius 1 cm? 1 6 Two cubes each of volume 8 cm are joined end to end,and then what is the surface area of resulting cuboid? 1 SECTION B 7 The length, breadth and height of a room are 8m50cm, 6m5cm and m75cm respectively. Find the length of the longest rod that can measure the dimensions of the room exactly. 8 Find the values of p for which the quadratic equation x +px+=0 has equal roots. 9 Find the 7 th term from the end of A.P. 7,10,1,, In an equilateral triangle ABC,AD is drawn perpendicular to BC meeting BC in D. Prove that AD =BD. 11 If Sin(A+B)=1and Sin(A-B)=1/,0 A+B 90,and A>B, then find Aand B. 1 A metallic solid sphere of radius. cm is melted and recast into the shape of a solid cylinder of radius 6 cm. Find the height of the cylinder.

2 SECTION C 1 Find the value of a and b so that 8x +1x -x +ax+b is exactly divisible by x +x-. 1 Solve the following pair of equations for x and y: a - b = 0, a b b+ a= a+b, x 0,y 0. x y x y 15 If the point C(-1,)divides internally the line segment joining the points A(,5)and B(x,y)in the ratio :,find the value of x +y. 16 The area of a triangle is 5sq.unit.Two of its vertices are(,1)and(,-).if the third vertex is ( 7,y), find the value of y. 17 In the given figure,op is equal to the diameter of a circle with center O and PA and PB are the tangents.prove that ABP is an equilateral triangle. A 18 P B Prove that sinθ sin θ = tanθ. cos θ cosθ 19 If xsin θ+ycos θ=sinθcosθand x sinθ =y cosθ,prove that x +y =1. 0 Find the area of shaded region in given figure,where radii of the two concentric circles with center O are 7cm and 1cm respectively and AOB=0 0. C D A B 1 A toy is in the form of a cone mounted on a hemisphere of common base of diameter 7cm. If the height of the toy is 15.5 cm, find the total surface area of the toy.(use π=/7). In a single throw of a pair of different dice, what is the probability of getting (i) a prime number on each dice? (ii) a total of 9 or 11. SECTION D Show that any positive odd integer is in the form of m+1 or m+, where m is some integer. The denominator of a fraction is two more than its numerator.if the sum of the fraction and its reciprocal is find the fraction If Sn denotes the sum of first n terms of an A.P., prove that S0=(S0-S10) 6 In the given figure, AB PQ CD,AB=x units, CD=y units and PQ= z units, prove that x y = 1 z A P C x z y B Q D

3 7 Construct an isosceles triangle with base 8cm and altitude cm.construct another triangle whose sides are /times the corresponding sides of the isosceles triangle. 8 The angle of elevation of the top of a tower at a distance of 10m from a point A on the ground is 5 0.Ifthe angle of elevation of the top of a flagstaff fixed at the top of the tower at A is 60 0, then find the height of the flagstaff. (Use =1.7) 9 A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is (i) a card of spade or an ace.(ii)a black king (iii) neither a jack nor a king. (iv) either a king or a queen. 0 The following table shows the marks obtained by 100 students of class X in a school during a particular academic session. Find the mode of this distribution. Marks No of students Less Less Less Less Less Less Less Less than 10 than 0 than 0 than 0 than 50 than 60 than 70 than **************

4 PRE BOARD EXAMINATION CODE : J 1 SESSION CLASS : X MAXIMUM MARKS: 80 SUBJECT : MATHEMATICS TIME : HOURS General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 0 questions divided into four section A, B, C and D. (iii) Section A comprises 6 questions of 1 mark each, Section B comprises 6 questions of marks each, Section C comprises 10 questions of marks each and Section D comprises 8 questions of marks each. (iv) Use calculator is not permitted. SECTION A 1 Evaluate: tan5 0 tan5 0 tan0 0 tan65 0 tan Given that HCF (5,0) =11 and LCM (5,0) =5 R, find the value of R. 1 A tangent of length 1cm is drawn to a circle of radius 5cm from a point P away from a centre. Find the distance of the point P from the centre. 1 Two dice are tossed simultaneously what is the probability that both show identical numbers 1 5 Find the area enclosed by two concentric circles of radius cm and cm. 1 6 Find the zeroes of the quadratic polynomial 6x 7x 1 SECTION-B 7 The 6 th term of an AP is -10 and the 10 th term is -6. Determine the 15 th term of the AP. 8 For the polynomial p(x) = (α+1)x + (α + )x + (α + ), the sum of zeros is -1. Find the value of α. 9 A cone and a cylinder of same radius.5 cm have same curved surface area. If the height of thecylinder is 1 cm, find the slant height of the cone. 10 A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC + DA. 11 If seca = cosec(a 0 0 ) where A is an acute angle. Find the value of A. 1 The king, queen and jack of clubs are removed from a deck of 5 playing cards and then well shuffled. One card is selected from the remaining cards. Find the probability of getting (i) a heart (ii) a club. SECTION-C 1 If (, y) is equidistant from the points (,5) and (6,), find y. 1 Solve:- ax b by a = a + b, ax by = ab (a 0, b 0) 15 A train travels a distance of 80 km at a uniform speed. If the speed had been 8 km/hr less, then it would have taken hours more to cover the same distance. Find the speed of the train. 16 Prove that (sina + coseca) + (cosa + seca) = 7 + tan A + cot A 17 Construct an isosceles triangle whose base is 6cm and altitude is cm, and then construct another triangle whose sides are times the corresponding sides of the first triangle.

5 18 Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. 19 A solid consisting of a right circular cone of height 10 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm. 0 In a circular table cover of radius cm, a design is formed leaving an equilateral triangle ABC in the middle. Find the area of the design. 1 The sum of n terms of a sequence is n + n.find the nth term and show that the sequence is an AP. A die is thrown twice. What is the probability that (i) 5 will not come up either time? (ii) 5 will come up at least once? SECTION-D Show that any positive odd integer is in the form of m+1 or m+, where m is some integer. The hypotenuse of aright angled triangle is 6cm more than twice the shortest side. If the third side is cm less than the hypotenuse, find the sides of the triangle Solve for x and y x+y x y x+y x y where x y, x -y. 6 From a point P, two tangents are drawn to a circle C (o, r). If OP=r, show that APB is equilateral. 7 In an equilateral triangle ABC, D is a point on side BC such that BD = 1 BC. Prove that 9AD = 7AB. 8 From the top of a 7m high building, the angle of elevation of the top of a cable tower is 60 0 and the angle of depression of the foot is 5 0. Determine the height of the tower. 9 An ice cream seller has two types of ice cream containers, one in the form of cylindrical shape and other in the shape of a frustum. Both have the same height of 7cm and the diameter of cylindrical container is 7cm. Upper and lower radii of frustum are.5cm and cm respectively (i) Calculate the volume of both the containers. (ii) If the cost of the containers is the same and the seller prefers to sell ice-cream in the cylindrical container,then which value is depicted by the seller? 0 The following table gives production yield per hectare of wheat of 100 farms of a village. Production yield (in kg/ha) No. of farms Change the distribution to a more than type distribution, and draw its ogive. Also find median

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7 CODE: P PRE BOARD EXAMINATION SESSION CLASS : X MAXIMUM MARKS: 80 SUBJECT : MATHEMATICS TIME : HOURS General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 0 questions divided into four section A, B, C and D. (iii) Section A comprises 6 questions of 1 mark each, Section B comprises 6 questions of marks each, Section C comprises 10 questions of marks each and Section D comprises 8 questions of marks each. (iv) Use calculator is not permitted. SECTION-A(each question carry 1 mark) 1. For what value of k will k+9, k-1 and k+7 are the consecutive terms of an AP?. Find the nature of the roots of the quadratic equation x x + = 0.. If the sun s angle of elevation is 0 and the height of the pole is 8 m, then find the length of the shadow.. Find the mean of first five Prime numbers. 5. The area of the circle is numerically equal to twice its circumference; find the diameter of the circle. 6. If the areas of two similar triangles are in the ratio 5:6, write the ratio of their corresponding sides. SECTION-B(each question carry marks) 7. Find the middle term of the AP 6, 1, Use Euclid s division algorithm to find the HCF of 867 and If α, β are zeroes ofx + 5x + 5,find the value of 1 α + 1 β. 10. A chord of a circle of radius 1 cm subtends a right angle at the centre. What is the area of the minor sector? [ π= 7 ] 11. PQR is a right angled triangle right angled at Q. PQ=5 cm, QR=1 cm. A circle with centre O is inscribed in PQR, touching its all sides. Find the radius of the circle. 1. ABC is an isosceles right triangle right-angled at C. Prove that AB = AC SECTION-C(each question carry marks) 1. Solve for x and y: x + y = 1 y = x 1. In an equilateral ABC, D is a point on BC such that BD= 1 BC.Prove that 9AD =7AB 15. If 7sin θ + cos θ = and θ is an acute angle, then prove that : secθ + cosecθ = Solve for x: x+1 x 1 x 1 x+1 = 5 6, x 1, x Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle

8 18. A toy is in the form of a cone of radius.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy. 19. Following frequency distribution shows the daily expenditure on milk of 0 households in a locality. Daily expenditure on milk( in l ) Number of house holds Find the mode for the above data. 0. One card is drawn from a well-shuffled deck of 5 cards. Find the probability of drawing: I. An Ace II. of spades III. 10 of a black suit. x 1. If P(x, y) is any point on the line joining the points A (a, 0) and B (0, b). Then show that + y = 1. a b. Find a relation between x and y such that the point (x, y) is equidistant from the points (, -6) and (-,) SECTION-D (each question carry marks). Prove that 5 is an irrational number.. Students of class X collected Rs They wanted to divide it equally among a certain number of students residing in slums area. When they started distributing the amount, 0 more students from near by slums also joined. Now each student got Rs 0 less. (a) Find the number of students living in the slum. (b)which value is depicted by the students? 5. Draw a triangle ABC with side BC= 7 cm, B=5 0, A= Then construct a triangle whose sides are times the corresponding sides of ABC. 6.How many terms of the AP: 9, 17, 5, must be taken to give a sum of 66? 7.Prove that (sina + coseca) +(cosa+seca) =7+tan A+cot A 8. Prove that: tanθ 1 cotθ + cotθ 1 tanθ = 1 + tanθ + cotθ 9. The radii of the circular ends of a bucket of height 15 cm are1cm and r cm (r<1cm).if the volume of bucket is 590cm,then find the value of r.(use π= 7 ) 0. The annual rainfall record of a city for 66 days is given in the following table: Rainfall (in cm): Number of days: Draw a less than type and a more than type ogive from the above data. Hence obtain the median rainfall from the graph. ****************

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