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,.. , .,.~ ...,.,.. "~ ., , . -=---~ DHI RUBHA I AM SA NI IN l ~rJ.. l l f) .., .:. t \; M ; 1fl t PRACTICE EXAMINATION 2022 - 2023 Date: December 6, 2022 Subject: Mathematics Std: X A Marks: 80 -------------------------------------- -----------------------------------Time allowed: Two and half hours Answers to this paper must be written on the paper provided separately. You will not be allowed to write during first 10 minutes. This time is to be spent in reading the question-paper. The time given at the head of this paper is the time allowed for writing the answers. Attempt all questions from section A and any four questions from Section B. All working, including rough work, must be clearly shown, and must be done on the same sheet as the rest of the answer. Omission of essential working will result in loss of marks. The intended marks for questions or parts of questions are given in brackets [ J Mathematical tables are provided. This paper consists of JO questions on JO printed sides. Section A Attempt all questions Question 1 Choose the correct answers to the questions from the given options. (Do not copy the question. Write the correct answer only.) (i) The co-ordinates of the point which divides the line segment joining (-3, 10) and (6, -8) in the ratio 2 : 7 are : (a) (1 ,6) (b) (1,-6) (c) ( -1, -6) (d) (-1,6) A point P (-2,3) is reflected in the line x = 2, the coordinates of the point of reflection p' are: (a) (2,3) (b) (4,3) (c) (6,3) (d) (8,3) (iii) A cumulative frequency curve is also known as: (a) Parabola (b) Hyperbola (c) Histogram - 1- (d) Ogive ~. ' ,..,, ' :, . 'I\ ' ,,, (iv) A D ':'------ IC In the given figure, LABC = LBDC = 90 each. Choose the correct similarity from the given choices: (a) MBC ~ liCBD (b) MBC ~ tiDCB (c} MBC ~ tiBCD (d) MBC ~ tiBDC (v) The volume of the cone is 330 cm 3. The volume of the cylinder having same radius and height as that of the given cone is: (a) 330 cm (vi) 3 (b} 110 cm 3 (c) 990 cm 3 (d) 660 cm 3 If O is the center of the circle and LAOC = 120 , then LABC will be : (a) 60 (b) 120 (c) 240 (d) 300 0 (vii) Evaluate: ---2_ + --2._ 1+ tan 2 A (a) 0 (viii) 1+ cot 2 A (b} 1 (c) -1 If the radius of a right circular cone is halved and the height is doubled the percentage of increase/decrease in its volume is: (a) Increased by 50% (b) Increased by 100% (c) Decreased by 25% (ix) (d) Decreased by 50% If the line 2y =3x +2 and y =ax+ 5 are perpendicular to each other, then a is: 3 (a} - 2 I-- (d} 2 (b} -2 3 (c)3 - 2- (d) -3 2 ..,,....,a~ , . ,), ~ "......, 11.. . ~l DHl~UBHAI AMBANI INJtktJAII OPi ~l \( HOO l (x) AB and CD be th e d.Iameters of circle . . centre O. If LCAB = 30 , with then 'x' is: C (a) 30 (xi) Which of the folloiwing is not a form of probability? (a)~ (b) -i 3 (xii) (d) 0.27 (c) 25% 7 Find the value of p, if average= 42, "[Jx = 16p + 40 and IJ = 20 (d) 70 (c) 50 (b) 40 (a) 30 (xiii) (d)90 (c) 60 (b) 45 Mr. Pankaj took Health Insurance Policy for his family and paid 900 as SGST. If the rate of GST is 18%, find the Annual Premium paid by him for his policy. (a)~ 8000 (xiv) 9000 (c) 10,000 (d) 12,000 If x: y = 3: 4, then (7x + 3y): (7x-3y) is: (a) 5 : 2 e (b) (b) 4: 3 (c)11:3 (d)37 : 19 Given A.P. 21, 18, 15, .... . . Which term of the above A.P. is (-81)? (a) 30 th term (b) 31 st term (c) 34 th term - 3- (d) 35 th term - OHIRUBHAI AMBANI ~11t1w111 r1n M.:. l \l li llOl Question 2 (i) l,\J A registered computer ~ lie, ineer t~vides computer maintenance to a 2(4] customer four times in a year. He offers different discounts for each service depending upon the mode of payment and the type of service. Service First Second Third Fourth Service Service service Service Service costs { 8200 { 13600 { 8000 { 12500 Discount 30% 20% 15% 10% If the GST 1s 18%, Calculate the amount of bill for the computer engineer. (ii) An exhibition tent is in the form of~ der surmounted by a cone. Ji_ [4] The height of the tent above the -tem-is 85 m and the height of the cylindrical part is 50 m. If the diameter of the base is 168 m, find the quantity of canvas required to make the tent. Allow 20% extra for folds and stiching.Give your answer to the nearest m2. (iii) - .2... In the given figure, ABCDE is a pentagon inscribed in a circle such that [4] AC is the diameter and side BC is parallel to AE, LBAC = 50 . Find giving reasons: (a) LACB @LsEc_J (b) LEDC (d) LEBC B Question 3 (i) tan A tanA secA-1 secA+l Prove that: - - + - - = 2 cosec A -4( c~ .J_ [4] ,:, .. .... ,...,, , . / DttlR UBHAI AM 6ANt IN l ~hllA " lflN .:. 1 \l >H:Ol If the mean of the following distribution is 14.7, find the values of p & q. / (iii) Class Interval Frequency 0-6 10 6 -12 p 12-18 4 18-24 7 24-30 q 30-36 4 36-42 1 Total 40 [4] Use a graph paper for this question. Use 2cm = 1 unit on both the axes. [5] (a) Plot P(6,3) and Q (3,0). 0 is the origin. (b} Reflect Pin x-axis to get p' and write the co-ordinates of P'. (c) Give the geometrical name of POP'Q . ..::Ep (d) Name a point from the figure which is invariant on reflection on xaxis. (e) Find the area of the figure obtained. Section B (Attempt any four questions from this section) j__ Question 4 (i) Solve the following quadratic equation by the formula method and write the roots correct to 2 decimal places. (x +1) (x + 4) + 1 = 0 (ii) Prove that: 1-tanA -===- [3] S5"x 3- + I-cotA = cos A + sinA -5- [3] ....... , \~ \\._ -'.,~~! ~ -p OtltRUBliAI AM8 ANI ,t-1 1! 1,r,,. 1m":. 1 \ l ~ un , i4J ' (iii) If two-digit numbers are made with . . 1, 3, 6, and 7, what Is the probability that the number is: (a} less than 60 (b) a prime number (c) a number divisible by 3 (d) a multiple of 2 or 3 Question 5 (i) 2 (2m + 1) x (ii) (iii) _j_ Find the value/s of m if the equation - (3] (2m +5) x +( 2m +1) = 0 has equal and real roots .J2a+1+ ..J2a-1 . . f rt If x = rim 2a+1- 2a-! , using properties o propo I0n, prove that x2 - 4ax + 1 = 0. (3] A solid metallic cylinder of base radius 3cm and height 5cm is melted ..::?.::.. (4] and recast into identical cones, each of height 0.02m and diameter 1 cm. Find the number of cones formed. (ale. Question 6 (i) The fourth term of an AP is 11 and the 81h term exceeds twice the fourth term by 5. Find: (a) the first term (b) common difference (c} the sum of the first 50 terms. -6- (3] ft_ ,. (~ .,,. \ \~ / DH IRUBHAI AM6 ANI IJ,,j l l lHU IIO N.:. L \ l l-l l)O t (ii) [3] In the given figure ABCD is a trapezium such that AB is parallel to CD. The diagonals AC and BO intersect each other at 0 . Prove that: (a) I:,, OCD - I:,, OAB (b) If OA = (2p +1), OB= (Sp- 3), OC = ( 6p- 5) and OD= (3p -1), find the value/s of p. (iii) A (1, 4), B (3, 2) and C (7, 5) are the vertices of 1:,, ABC. Find: [4] (a) the co-ordinates of the centroid G of 1:,, ABC. (b) the equation of a line through G and parallel to AB. Question 7 (i) Solve the following inequation and represent the solution set on a -L [3] number line. _]_ Draw a line segment AB = 6cm. Construct a circle with AB as diameter. Mark a point Pat 7cm from the mid-point of AB. Construct two tangents from P to the circle with AB as diameter. Measure and write down the length of the tangents. (iii) 7500 w'ere divided equally among a certain number of children. Had there been 20 less children, each would have received~ 100 more. Find the original number of children. -7- [3] 8 Question (i) if From a point on the ground the angle of elevation of the bottom and top of a water tank kept at the top of 20 m high tower are 45 and 60 respectively. Find the height of the water tank to the nearest meter. [3] (ii) The inner circumference of the rim of a circular metal tub is 44 cm. Find: (a) The inner radius of the tub (b) The volume of the material of the tub if its outer radius is 8 cm. Use 7[ = -227 Give your answer correct to three significant figure. (iii) The line 4x - 3y + 12 = 0 meets the x-axis at A. Write down the co- [3] ordinates of A. Find the equation of the line passing through A and perpendicular to 4x - 3y + 12 =0 Question 9 (i) / A manufacturer sells a mobile set for 35,000 to a wholesaler who 2... -,:rr- sells it to a retailer at a profit of 15%. The retailer sells it to a customer at 10% profit. If the rate of GST is 18%, calculate: (a) The price paid by the retailer for the mobile. (b) GST paid by the retailer to the government. (c)The price paid by the customer for the mobile. (ii) Find the sum of all two-digit numbers which are divisible by 3. - 8- l. [3] DHIRUBHAI A.MBANI 1Pf l! k fl4110N.l.l \ ( HO(ll [4] A T In the adjoining diagram, TB is a tangent to the circle at B with Centre 0 . SegTO meets the circle at C and A. Dis another point on the circle. LBTC = 22 . Calculate: a) L BOC b) LOAB c) LABT d)LBDC Question 10 (i) In the given figure, PO is a transverse common tangent to two circles with centres A and Band of radius 5 cm and 3 cm respectively. If PO intersects AB at C such that OP= 16 cm, calculate AB in surd form only. A -9- [4] I ,f (ii) Use a graph paper for this question. The results of an examination are tabulated below. The results of an examination are tabulated below. Marks (less than) No. of candidates 10 8 20 20 30 40 40 75 50 125 60 160 70 188 80 192 90 197 100 200 Draw an ogive and use it to determine: (a) the median (b) the lower quartile (c) the number of candidates who failed if the pass mark is 35 (d) the number of candidates who obtained grade A, If the lowest mark for the grade A is 75. - IO - [G]
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