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ARYA VIDYA MANDIR GROUP OF SCHOOLS Std. X Date: 19.03.2021 PRELIMINARY REVIEW MARCH 2021 MATHEMATICS Marks: 80 Time: 2 hrs Answers to this paper must be written on the paper provided separately. You will not be allowed to write during the first 15 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 I and any four from Section II. 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 the loss of marks. The intended marks for questions or parts of questions are given in brackets [ ]. This paper consists of 6 printed pages. Please ensure the following: It is suggested to attempt the Preliminary Review using only a Laptop or a Desktop (with a webcam). In case a mobile or tab is being used, please have an alternate device with a camera so that you are visible to the invigilator at all times. Camera must be kept ON during the entire paper. You are not allowed to use ear-phones or head-phones during the reviews. Preliminary Review paper comprises two sections i.e. Section-A and Section-B. Please begin writing Section-B from a fresh page. Each section will have to be uploaded separately in the space provided in the form with the necessary renaming of the file as mentioned in the form. If students encounter any problem accessing or submitting the review, he/she must inform the invigilator. Question 1 SECTION I (40 marks) (Attempt all questions from this section) a) In what ratio does the point (a, 6) divide the join of (-4, 3) and (2, 8)? Also, find the value of a. b) [3] Find the value of x and y if: c) The points (6, 2), (3, 1) and ( 2, 4) are the vertices of a right angled triangle. Check whether it remains a right angled triangle after reflection in the y-axis. [3] [4] ..2 ..2.. Contd Std X Math Prelim Review March 2021 Question 2 a) Solve x 3 (2 + x) > 2 (3x 1), x I. Also represent its solution on the number line. b) c) [3] Mr. Dhruv deposits Rs 600 per month in a recurring deposit account for 5 years at the rate of 12.5% per annum. Find the amount he will receive at the time of maturity. [3] Sixteen cards are labelled as a, b, c m, n, o, p. They are put in a box and shuffled. A boy is asked to draw a card from the box. What is the probability that the card drawn is : (i) a vowel (ii) a consonant (iii) none of the letters of the word median (iv) the letter y [4] Question 3 a) Prove that: (sin + cos )(tan + cot ) = sec + cosec [3] b) The median of the observations 11, 12, 14, (x 2), (x + 4), (x + 9), 32, 38, 47 arranged in ascending order is 24. Find the value of x and hence find the mean. [3] c) [4] In the figure given, O is the centre of the circle. DAE = 700. Find giving suitable reasons, the measure of: (i) BCD (ii) BOD (iii) OBD ..3 ..3.. Contd Std X Math Prelim Review March 2021 Question 4 a) b) c) If (2x+1) is a factor of the polynomial 3x + 2kx 3, find the value of k. [3] National Trading Company, Meerut (UP) made the supply of the following goods/services to Samarth Traders, Noida (UP). Find the total amount of bill if the rate of GST = 12% [3] (i) If the common difference of an A.P. is 3 and the 18th term is 5, then [4] find its first term. (ii) If the first term of an A.P. is 18 and its 10th term is zero, then find its common difference. Question 5 a) b) c) Section II (40 marks) (Attempt any four questions from this section) [3] If a,b and c are in continued proportion, prove that: a : c = (a+b)2 : (c+b)2 A die is thrown once. Find the probability of getting: (i) an odd number (ii) even number between 3 and 8 (iii) an even number or a multiple of 3 [3] In what ratio does the point (1, a) divided the join of (-1, 4) and (4, -1)? Also, find the value of a. [4] Question 6 a) [3] Mr. Chaturvedi has a recurring deposit account in Grindlay s Bank for 3 years at 9.5% p.a. If he gets Rs.16,509 at the time of maturity, find the monthly instalment. ..4 ..4.. Contd Std X Math Prelim Review March 2021 b) c) (i) Calculate the mean marks of the following distribution. (ii) State the modal class. [3] A and B are two points on the x-axis and y-axis respectively. P (2, -3) is the midpoint of AB. Find the (i) Coordinates of A and B. (ii) Slope of line AB. (iii) Equation of line AB. [4] Question 7 a) b) [4] A boy 1.6 m tall is 20 m away from a tower and observes that the angle of elevation of the top of the tower is 60 . Find the height of the tower. The weight of 50 workers is given below: Weight in Kg No. Workers [6] 50-60 60-70 70-80 80-90 90-100 4 7 11 14 6 100110 110-120 5 3 Draw an ogive of the given distribution using a graph sheet. Take 2 cm = 10 kg on one axis and 2 cm = 5 workers along the other axis. Use a graph to estimate the following: (i) the upper quartile (ii) Lower quartile (iii) if weighing 95 kg and above is considered overweight find the number of workers who are overweight. ..5 ..5.. Contd Std X Math Prelim review March 2021 Question 8 a) If A = b) Prove that: c) In the figure given below, DE || BC and AD : DB = 1 : 2, find the ratio of the areas of ADE and trapezium DBCE. [3] and B = ,C= , compute A(B + C) + = cosecA cotA [3] [4] Question 9 a) b) c) [3] If x R and 1 < 3 2x 7, find solution set and represent it on a number line. The sum of the square of two positive integers is 208. If the square of larger number is 18 times the smaller number, find the numbers. [3] The ratio between the curved surface and the total surface of a cylinder is [4] 1 : 2. Find the volume of the cylinder, given that its total surface area is 616 cm2. ..6 ..6.. Contd Std X Math Prelim review March 2021 Question 10 a) Given that AC is the diameter. Find ADM and BAD. [3] b) Find the equation of the line passing through the point (2,3) and having the x-intercept of 4 units. [3] Use factor theorem to factorize the polynomial x3 + 2x2 - 5x - 6 completely. [4] c) Question 11 a) b) c) In the given figure, ABCD is a trapezium in which AB || DC. If 2AB = 3DC, find the ratio of the areas of AOB and COD. [3] The upper part of a tree, broken over by the wind, makes an angle of 45 o with the ground and the distance from the root to the point where the top of [3] the tree touches the ground is 15 m. What was the height of the tree before it was broken? If x= 8 + find the value of + + + ------ THE END ------ [4]
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