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OOL S ARY AVI DYA MANDIR GROUP OF SCH PRELIM REVIEW- JAN UAR Y 2023 MATHEMATICS Mar ks:8 0 Time: 2 hr Std: X Date: 06/01/2023 --------------------------------------------------------------------------------------------------------- er prov ided separately. the pap Answers to this pap er mus t be written on first 15 minutes. You will not be allo wed to write during the stion pap er. This time is to be spe nt in reading the que the time allotted for writing the answers. The time given at the hea d of the pap er is ----------------------------------------- - tion B - ---------------------------------tion Sec A and any fou r questions from Atte mpt all the questions from Sec e rly sho wn whe nev er nee ded on the sam All ess enti al working sho uld be clea ks. working will resu lt in the loss of mar sheet. The omi ssio n of the ess enti al pap er. Do the rough working at the bottom of the [ J. s of questions are given in the brac kets The inte nde d marks for questions or part This pap er comprises 10 printed pag es. ----------------------------------------------------------------------------------------------------------------Section -A (40 marks) (Attempt all the questions from this Section) Que stio n 1 s from the given options: Choose the correct answers to the question (i) [15] 2 + bx + c = O is equal to If the discriminant of quadratic equation ax zero, then two equal roots are: (a) -b 2a (b) ~ 2a (c) (d) a -a 2b ...2 Contd ... Std X Mathematics Prelim Review January 2023 (ii) ( ii'1) A shopkeeper buys goods worth ~ 1000 and sells at a profit of 10%. If rate of GST is 5%, then the bill amount is : (a) ~1050 (b)~1155 (c) ~1080 (d) ~1000 The solution set representing the following number line, is: ( ll I -3 -2 I -1 I 0 I 1 ~ I 2 ) 3 (a) {x: x E R, -3 < x < 3} (b) {x: XE R, -3 < X ~ 3} (c) {x: x E z, -3 < x < 3} (d){x: x EZ, -3 s x < 3} (iv) Manisha opens a Recurring Deposit Account with the Bank of Assam and deposits ~ 600 per month for 20 months. Calculate the interest accrued , if the bank pays interest at the rate of 10% per annum. (a) ~1050 (b) ~1000 (c) {1200 (d) ,1 soo (v) In the given figure, we have LACB = 90 , CD 1.. AB, then LlACB~ LlADC by: A (a) SSS similarity rule (b) SAS similarity rule (c) AA similarity rule (d) None of these D ...3 -3Contd ... Std X Mathematics Prelim Review January 2023 (vi) The curved surface area of a cylinder of height 14 cm is 88 sq. cm. The diameter of the cylinder is: (a) 0.5 cm (b) 1.0 cm (c) 1.5cm (d) 2.0 cm (vii) If g(x) is: = x + 1 is a factor of h(x) = 5x3 + px2 - 8x - 12, then the value of p (a) -8 (b) 5 (c) 9 (d) 12 (viii) If the nth term of an A.P. is 7 - 4n, then find its 6 th term is: (a) 17 (b)- 17 (c) 18 (d) - 18 (ix) Drawing of an ogive table is useful in determining the: (a) (b) (c) (d) (x) mode mean median all the three above In the given figure, P (2,4) is the mid point of the line segment AB. v The coordinates of A and 8 are : (a) A (8, 0), B(0, 4) (b) A(0 ,4), 8(8, 0) (c) A(4, 0), B(0, 8) (d) A(0, 8), 8(4 , 0) "' B ~ ~ ( 2, 4) ' .. .4 -- - - r -4- Contd ... Std X Mathematics Prelim Review January 2023 (xi) Two matrices A and B are multiplied to get AB if: (a) Both have same order (b) Both are rectangular (c) Number of columns in matrix A is equal to the numb er of rows in matrix B (d) Number of ffiWS in matrix Bis equal to the number of columns . t . A CO hH'f10 :, Q O uJ ~ 1n ma nx (xii) The point (5, -6) on reflection in a line is mapped to (-5, -6). Name the mirror line and write its equation. (a) X-axis, y = O (b) Y - axis, x = O (c) X-ax is, x :-: 0 (d) Y - axis, y = 0 (xiii) The probability of not winning a game is 0.35. What is the probability of winning? (a) 0.15 (b) 0.25 (c) 0.65 (d) 1.50 (xiv) In the figure given, if AB is a chord of the circle and AC is its diameter such that LACB = 50 . If AT is the tangent to the circle at the point A, then LCA B is equal to : (a) 65 (b) 50 (c) 40 (d) 60 (: B 0 A T ... 5 -5Contd ... Std X Mathe matics Prelim Revie w Janua ry 2023 If x, 9, 5 and 3 are in proportion, then x equals to: (a) 15 (b) 45 (c) 27 (d) 18 Question 2 0) sion : Using the properties of proportion, find the value of x in the expres (4) ,./a+x +.Ja="x = 5 a+ x-../a=x (ii) (iii) points Find the equation of the line perpendicular to the line joining the A(2, 4) and 8(6, 8) and passing through the point (5,7). (4) l The given figure represents a hemisphere surmounted by a conica slant block of wood. The diameter of their base is 12 cm each and the height of the cone is 10 cm. Calculate : (a) the perpendicular height of the cone, {Take TT = 3.14) (b) the volume of the solid (4) Question 3 (i) it Ritwik deposits :t1600 per month for 18 months in a recurring depos account. If he gets ~31080 at the time of maturity. Find: (a) The total interest earned by Ritwik (b) The rate of interest per annum (4) .. .6 r -6Contd ... Std X Mathematics Prelim Review Janu ary 2023 (ii) (iii) Prove that: 2 cos A cosA- s inA +~ =s in A+ cos A. 1- cotA Use graph pape r for this question. The point R (6, 3) was reflected in the origin to get the image R'. 4 ( ) (5) (a) Write down the coordinates of R'. (b) If M is the foot of the perpendicular from R to the line y = 0, find the coordinates of M. (c) If N is the foot of the perpendicular from R' to the line y = 0, find the coordinates of N. (d) Name the figure RMR'N. Section - B (40 marks) (Attempt any four questions from this Section) Ques tion 4 (i) If A=[ ! !] and A 2 = I, where I is the identity matrix. (3) Find the value of x and y. (ii) Solve the inequation and represent the solution set on the number line: (3) 2y- 3 Sy+ 1 S 4y + 7, XE 2 (iii) By using step-deviation method, compute the arithmetic mean for the follow ing data: - - Mark s obtained - - 0-1 0 10-2 0 20-3 0 30-4 0 40-5 0 50-6 0 (4) -- No. of workers - 14 22 37 58 67 75 ... 7 -7Contd ... Std X Mathematics Prelim Review January 2023 Question 5 (3) (i) Without solving the following quadratic equation, find the value of 'p' if the roots of the equation px2 - (2p - 2)x + p = 0 has real and equal roots. (ii) (3) In an intra-state transaction the marked price of an article is ~6000. A wholeseller sells it to a dealer at 20% discount. The dealer further sells the article to a customer at a discount of 10% on the marked price. If the rate of GST at each stage is 18%, find the amount of tax(under GST) paid by the dealer to the government. (iii) PA and PB are two tangents of a circle. AC is parallel to PB. Find the angles of .'.\ABC. (4) C. Question 6 (i) (3) If a, band care in continued proportion, prove that c b a 1 1 1 -+ -=-+ +-+ a 2b2 ,2a2 c3 b2,2 a 3 b3 (ii) The daily profits in rupees of 100 shops in a departmental store are (3) distributed as follows : Profit per shop (in 0-100 100-200 200-300 300-400 400-500 500-600 ~) No. of Shops 12 18 27 20 17 6 Draw a histogram of the data given above on the graph paper and estimate the mode. . .. 8 I .-;:-,.. -8- ,. . Contd ... Std X Mathematics Prelim Review January 2023 (iii) 1111 ... If 2x3 + ax 2 + bx - 6 has a factor (2x + 1) and leaves the remainder 12 when divided by (x + 2). Calculate the values of a and b. Question 7 (i) Find the sum of n terms of the A.P. 8, 5, 2, -1 , ... to 11 terms. (3) (ii) P(-4, 6), Q(-1 , 6) and R(-1 , 2) are the vertices of a triangle. (a) Find the coordinates of the centroid G of the triangle. (b) Find the equation of the line through G passing through P. (3 , (iii) Construct a circle of radius 3 .5 cm with centre O. Construct 2 tangents PT and PR from a point P outside the circle such that LTOR = 120 . (4) Question 8 (i) A hollow copper pipe of inner diameter 14 cm and outer diameter 16 cm is melted into another solid cylinder is of same height as that of pipe. Find the diameter of the solid cylinder. (3) (ii) In the given figure, AB and CD are two chords of a circle intersecting each other at a point P, such that AP= CP. Prove that AB= CD. (3) (iii) A man standing on a window of the first floor of a building observes that the angle of depression of a dustbin which is 1Om from the foot of the building is 45 . He climbs to the window of the second floor, directly above the first floor and observes the angle of depression of the dustbin to be 60 . Calculate the difference in height between the first floor and the second floor. (4) - - - - - - --- - - - -- .. .9 ---- - -- -9- Contd ... Std X Mathe matics Prelim Review Januar y 2023 Question 9 (i) A ar travels x km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol. (a) Write down the numbe r of litres of petrol, use by car A and car C (4) B in coverin g a distanc e of 200km . (b) If car A uses 2 litres of petrol more than car B in coverin g the 200km , write down an equatio n in x and solve it to determ ine the numbe r of litres of petrol used by car B for the journe y. (ii) (6) Use graph paper for this questio n. Marks obtaine d by 200 studen ts in an examin ation are given below: No. of Studen ts Marks 5 0 10 11 10 20 10 20 30 20 30 40 28 40 50 37 50 - 60 40 60 70 29 70 80 14 80 90 6 90 - 100 I one Draw an ogive for the given distribu tion taking J cm = 10 marks on axis and 2 cm = 20 studen ts on the other axis. Determ ine: (a) The median marks (b) The numbe r of studen ts who failed if the minimu m marks require d is 40. (c) If scoring 85 and above is grade one , find the numbe r of studen ts who secure d grade one in the examin ation. Question 10 (i) (3) Prove that: cotA + tanll = cot A tan B cotB + tanA .. 10 - ------- I -10- Contd ... Std X Mathematics Prelim Review January 2023 (ii) (iii) Two dice are thrown at the same time. Find the probablity that the sum of two numbers appearing on the dice. (a) 10 (b) Atleast 12 (3) In the adjoining figure; QR II ST and s divides PQ in the ratio 1 : 2. Find: (4) (a)PT TR ) (b(T PR (c) ST if QR= 4.5 cm _ _ _ _ _ _ _ _THE END_ _ _ _ _ _ _ __
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