S MATHEMATICS (E) Subject Code VI Seat No. : Time : 2½ Hours

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1 2018 VI Seat No. : Time : 2½ Hours MTHEMTIS (E) Subject ode S Total No. of Questions : 8 (Printed Pages : 7) Maimum Marks : 80 INSTRUTIONS : i) nswer each main question on a fresh page. ii) ll questions are compulsor. iii) The question paper consists of eight questions, each of 10 marks. iv) There is no overall choice. However, internal choice has been provided in three questions of three marks each. v) In questions on constructions, the drawing should be clear and eactl as per the given measurements. The construction lines and arcs should also be maintained. vi) Graph paper will be supplied on request. vii) Use of calculator and mathematical tables is not permitted. 1. ) Select and write the most appropriate alternative from those given below : If α and β are the zeroes of a quadratic polnomial , then the 1 1 value of + = [1] α β a) 5 7 b) 7 5 c) 5 7 d) 7 5 ) Use Euclid s division algorithm to find the HF of 81 and 135. [2] ) ssuming that 7 is an irrational number, prove that is also an irrational number. D) If two zeroes of the polnomial are 3 and 3, then find the other two zeroes. [4] S P.T.O.

2 S *S021* 2. ) Select and write the most appropriate alternative from those given below : [1] bo contains some discs which are numbered from 5 to 15. If one discs is drawn at random from the bo, then the probabilit of getting a multiples of 3 or 4 is. 6 a) 11 5 b) 11 3 c) 10 7 d) 10 ) die and a coin are thrown once simultaneousl. Find the probabilit of getting : [2] i) prime number and a head ii) number greater than 4 and a tail. ) Find the roots of NY ONE of the following quadratic equations. i) = 0 ( Factorisation method) ii) = 0 ( using quadratic formula) D) group of students planned a picnic and estimated the ependiture to be ` 5,000. Five more students joined the group so the ependiture was increased b ` 1,000, but the average epenses per student was decreased b ` 10. Find the total number of students who went for the picnic. [4] 3. ) Select and write the most appropriate alternative from those given below : [1] car takes hours to travel from a cit to cit with a speed of km/hour, then the distance between the two cities can be written as km. a) + b) c). d) ) The numerator of a fraction is greater than the denominator b 2. If 1 is added to the numerator the value of the fraction becomes 2. Represent the above statements b two linear equations in and. [2]

3 ) Find the solution of NY ONE of the following linear equations : i) = = 13 ( Elimination method) ii) = = 25 ( ross-multiplication method) D) Find the solution of the following pair of linear equations graphicall. [4] = 7 and = 6 Rewrite and complete the following tables. = = 6 (Plot atleast 3 points for each line using a graph paper) 4. ) Select and write the most appropriate alternative from those given below : [1] The sum of first n terms of an.p. whose first term is 8 and the last term is 62, is 700. Therefore the.p. consists of terms. a) 15 b) 20 c) 25 d) 30 ) The following table shows the weight of 30 students of a class. Weight (kg) No. of students Find the median of the above data upto two decimal places. [2] ) man started saving mone from the first week of Januar He saved ` 25 in the first week, ` 40 in the second week, ` 55 in the third week and so on, till the last week of December Find the total saving of the man in the ear S P.T.O.

4 D) The distribution given below shows the dail wages of the emploees working in a factor : [4] Wages (Rs.) No. of emploer lass-mark Deviation f i d i.i. f i i d i = i a f i = 50 f i d i = Taking the class-mark denoted b a of the class interval ( ) as the assumed mean, rewrite and complete the table and also find the mean of the dail wages b the assumed mean method. 5. ) Select and write the most appropriate alternative from those given below : [1] P and P are tangent segments drawn from eternal point P to a circle with centre O at and respectivel. If O and P are in the ratio 3 : 2, then PO =. a) 72 b) 36 c) 108 d) 90 ) Given : circle with centre O is inscribed in Δ, where =. The sides, and touches the circle at points P, Q and R respectivel. Prove that : Q is a mid-point of. P O R S Q

5 ) Draw a circle with centre and radius 3.5 cm, then take a point P at a distance of 8.5 cm from the centre of the circle. Using a pair of compasses and ruler, construct two tangent segments PX and PY to the circle. Measure and state the length of tangent segments. D) Using a pair of compasses and ruler, construct Δ with sides = 6.5 cm, = 7.2 cm and = 60. Then construct Δ whose sides are 3 of the corresponding sides of Δ ) Select and write the most appropriate alternative from those given below : [1] If 3 Sin 4 os = 0, then the value of Tan =. a) 7 4 b) 4 7 c) 4 3 d) 3 4 ) ttempt NY ONE of the following : i) In Δ, if = 90 and Tan = Find : a) The length of b) The value of Sec c) The value of Sin. ii) Evaluate the following epression using known numerical values of trigonometrical ratios : 2sin cot cosec ) Prove the following identit. [2] 1 sin = sec tan 1+ sin D) i) If the points (6, 1), (8, 2), (9, 4) and D(, ) are the vertices of a parallelogram, taken in order, find the value of and. [2] ii) Find the area of the triangle whose vertices are ( 5, 7), (4, 5) and (4, 5). [2] S P.T.O.

6 7. ) Select and write the most appropriate alternative from those given below : [1] In Δ, points P and Q are on sides and respectivel such that PQ. If P : P = 1 : 2 and ar(pq) = 6 sq.units, then ar( PQ) = sq. units. a) 12 b) 18 c) 36 d) 48 ) With reference to the given figure and given condition, write onl the proof with reasons of the following theorem. In Δ, = 2 and Δ PQR is constructed such that PQ =, QR = and Q = 90. Prove that : Δ is right angled triangle. P Q R ) Given : In PQRS, PQ SR, diagonals PR and QS intersect at X, line through R parallel to PS intersect diagonal SQ on producing at Y. (S Q Y). 2 PX QX Prove that : = RX. XY Y P Q X S R S

7 D) The shadow of a tower, standing on a level ground is found to be 50 m longer when the sun s altitude is 30 than when it is 60 find the height of the tower (take 3 = 1.73). D m 8. ) Select and write the most appropriate alternative from those given below : i) If the area of a circle is numericall equal to twice the circumference then its radius is cm. [1] a) 16 b) 8 c) 4 d) 2 ii) The total surface area of a right circular clinder with radius of its base 3 cm and height 2 cm is sq.cm. [1] a) 15π b) 30π c) 18π d) 36π ) container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 21 cm, with radii of its lower and upper ends 6 cm and 10 cm respectivel. Find the volume of the container (Take π = 22 7 ) [2] ) In the given figure, DEF is a regular heagon of side 10 cm. Taking and DE as radii two sectors are drawn as shown in the figure. Taking π = 3.14 and 3 = 1.73, find the area of shaded region. F E D S D) metallic ball of radius 10.5 cm is melted and recast into 126 cones of equal size. If the height of the cones formed is 3 cm, then find the radius of the each cone formed (Take π = 22 ). 7

MATHEMATICS ( CANDIDATES WITH PRACTICALS/INTERNAL ASSESSMENT ) ( CANDIDATES WITHOUT PRACTICALS/INTERNAL ASSESSMENT )

Total No. of Printed Pages 6 X/5/M 0 5 MATHEMATICS ( CANDIDATES WITH PRACTICALS/INTERNAL ASSESSMENT ) Full Marks : 80 Pass Marks : 4 ( CANDIDATES WITHOUT PRACTICALS/INTERNAL ASSESSMENT ) Full Marks : 00