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SEMESTER I PRELIMINARY EXAMINATION 2021 2022 Date: February 23, 2022 Subject: Mathematics Std: XA Maximnm Marks: 40 Time alloed: One and a hulf hours Answers to this Paper must be written on the paper provided separulely. You will not be allowed to write during the 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. Section B. lempt all questions from Section A and any three questions from The intended marks for questions or parts of questions are given in brackets []. This paper consists of6 questions on 9 printed sides. Section A Attempt all questions Question 1 Choose the correct answers to the questions from the given options. (Do not copy the (i) question, The Write the correct image ofa point answer only.) under reflection in x-axis is A' coordinates of the point A are (a)(-5,-3) (b) (5, 3) (c)(5, 3) (d) (-3, 5) - 1 (- 5,3). The 10] DHIRUBHAI AMBANI wTEONATIONAL SCHOOL INTLNNA (i) In the figure, O is the centre of the circle. The value of'x 'is (a) 125 (b) 90 (c):55 (d) 35 455 (ii) The curved surface area of a cylinder is 4400cm2 and the circumference of its base is 110 cm. Then its height is: (a) 30 cm (b) 40 cm (c) 50 cm (d) 60 cm (iv) The point P(-3, 7) is reflected in the point M (5, -1) to point P". Then the coordinates of P' are: (a) (13, 9) (b) (-13, -9) (c) (-9,-13) (d) (13,9) (v) cosece cot 6cos 6 is equal to: (a) 1 (b) cos (c) sin (d) tan 0 2 DHIRUBNAI AMBANI INTERMATIONAI SCHO (vi) Seg AB is the diameter of a circle with centre O. P is a point on the circle other than point A' and point 'B'. Then- is a right angle. (a) PAB (6) AOB c) AOP (d) <APBB (vii) The lines 2x+3y -7 = 0 and 4y -px - 12 = 0 are perpendicular to each other. Then the value of 'p' is: (a)-1 (b) 2 (c) 12 (d) 6 (vi) The modal class for the following distribution is: Length lin cm)_ 2.0-2.5 | No of nails 5 2.5 3 3-3.5 11 9 3.5-4 (a) 2.5-3 (6) 2.0-2.5 (c) 3.5-4 (d) 3-3.5 ) An unbiased die is tossed. The probability of geting a multiple of 2 or 3 is (a) (b) (c) (d) .3 DHIRUBHAI AMDANI IMTERNATiONAL SCH0OL (x) The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. The ratio of their volumes is: (a) 20 9 (b) 10 9 (c) 20 27 (d) 10 27 Section B (Attempt any three questions from this section) Question 2 ) Write down the coordinates of the point P that divides the line segment (2 joining A(-4,1) and B(17,10) in the ratio 1:2. In what ratio does the y-axis divide the line AB? () A box contains cards bearing numbers 6 random from the box, find the (a) (b) (i) probability that it bears a one digit even prime number. an odd number less than 30 In the given figure, O is the centre of the circle. Chord CD is parallel to the diameter AB. If L BCD = 25 , find (i) LACD (ii) 2CAB (ii) 2CED A iv) to 70. If one card is drawn at B As observed from the top of depression of two ships on a 80 m tall light house, the same side of line with its base are between the two ships correct 30 and 40 a respectively. the angles light house of in horizontal Find the distance to the nearest metre. (2 DHIRUBHAI AMBANI INTEANATIONAL SCHOoL Question 3 PAB is a secant of a circle and PT is a tangent of the same circle at T, ) meeting externally at P. If AB = 7cm and PT [21 12 cm, Find the length of PA (i) A solid cylinder has a total surface area of 462cm. Its curved [21 surface area is one third of its total surface area. Find it Volume () Prove that: (cos (iv) The following distribution represents the height of 160 students of a - cosec 8)+(sin - sec e)2 (1- = sec Ocosec 8) 131 school. Construct Height (in cm) No. of students 140 145 12 145 150 20 150 155 30 155- 160 38 160- 165 24 165 170 16 170-175 12 175-180 8 less than cumulative a frequency curve for the above data, using 2cm = 5cm of height on one axis and 2cm = 20 students on the other axis. Using the graph estimate the median height. Questionh4 ) From the following frequency distribution table calculate mean Variate 15 Frequency 8 21 4 12 10 18 25 5 |7 12 4 12 DHIRUBHAI AMBANI IHTUANATIONAL SCH00t (i) 121 4y3X+5 A 4y 3x B From the figure, find (The co-ordinates of point A. The equation of line AB perpendicular to 4y = 3x +8 and passing through A. 31 28 cm 1as e From a solid wooden conical cavities of 6 cm Taking are cylinder of height 28 cm and diameter 6cm, hollowed out. The diameters of the andheight 10.5 cm. TT= find the volume of the remaining .6 solid. two cones are also DHIRUBHAI AMBANI INTERNATIONAL SCHOOL (V) Use graph paper for this question. Take 1 cm = 1unit on both x and y- [31 axis Plot the following points on your graph sheets. A(-4 0), B(-3.2), C(0,4), D4,1) and E(7,3). Reflect the points B, C, D and E on the x-axis and name them as BC,D' and E' respectively. Jion the points A,B,C,D,EE,D'C,B' and A in order. Name the closed figure formed. Question 5 () In the figure, a circle touches the side BC of A ABC at P and AB and (2] AC produced at Q and R respectively. If AQ = 15 cm, find the perimeter of A ABC B P Q (1) (i) Prove that. R = 1+coS A (cot A - cosec A) A (5, -2), B(6, 3), C(8,5) are the vertices ofthe AABC. Find the equation of i)the median ofthe triangle through A. i) the alttude of the triangle through B. 1 [2] 131 DHIROBHAAM INTNNAToNAL SEDO (iv) A mathematics aptitude test of 50 students Marks No. of students 50 - 60 4 60-70 8 70-80 14 80-90 19 90 100 5 was recorded as followS. Draw a histogram for the above data using a graph paper and determine the mode. Question 6 ) In the figure, PTU is the tangent at the point T to the circle QRST and PQR is a straight line. PQT = 100 , 4UTS = 55 and PQ =QT. find, giving your reasons in full, the size of i) TRQ, i) 2 STR NOT TO SCALE 55 100 Q R - 8 [21 DHIRUBHAI AMBANI NNATIONAL SCHOoL (i) Find the co-ordinate'of the pointyof trisection of the line points (-3,0) (ii) and (6,6) The mean marks obtained 'b' are missing frequencies. Marks 0 (iv) by 50 students in a joining the test is 23, where 'a' and [2 131 Find 'a' and 'b' No. of students 10 4 10-20 a 20-30 20 30-40 b 40 50 4 The angle of elevation of a jet plane from a point A on the ground is 60 . After a flight of 15 seconds, the angle of elevation changes to 30 If the jet plane is flying at a constant height of 1500/3 meters, find the speed of the jet plane. 9 [31
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