Maths Past Paper March 2019 PDF
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Uploaded by KindlyOrientalism
2019
CBSE
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This is a past paper from a March 2019 maths exam. It includes a variety of questions covering different maths topics. The paper is suitable for secondary school students.
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BOARD QUESTION PAPER: MARCH 2019 MATHS (PART - I) Time: 2 Hours Max. Marks: 40 Note: i. All questions are compulsory. ii. Use of calculator is not allowed. iii. Figures to the right...
BOARD QUESTION PAPER: MARCH 2019 MATHS (PART - I) Time: 2 Hours Max. Marks: 40 Note: i. All questions are compulsory. ii. Use of calculator is not allowed. iii. Figures to the right of questions indicate full marks. 1. (A) Solve the following questions (Any four): i. Find the median of: 66, 98, 54, 92, 87, 63, 72. ii. Multiply and write the answer in the simplest form: 5 7 2 7 iii. If 3x + 5y = 9 and 5x + 3y = 7, then find the value of x + y. iv. Write the ratio of second quantity to first quantity in the reduced form: 5 dozen pens, 120 pens. v. Write the following polynomial in coefficient form: 2x3 + x2 – 3x + 4. vi. For computation of income tax which is the assessment year of financial year 01–04–2016 to 31–03–2017? (B) Solve the following questions (Any two): i. Find the value of the polynomial 2x3 + 2x, when x = –1. ii. If A = {11, 21, 31, 41}, B = {12, 22, 31, 32}, then find: a. A B b. A B iii. Sangeeta’s monthly income is ` 25,000. She spent 90% of her income and donated 3% for socially useful causes. How much money did she save? 2. (A) Choose the correct alternative: i. In the A.P. 2, –2, –6, –10,...... common difference (d) is: (A) –4 (B) 2 (C) –2 (D) 4 2 ii. For the quadratic equation x + 10x – 7 = 0, the values of a, b, c are: (A) a = –1, b = 10, c = 7 (B) a = 1, b = –10, c = –7 (C) a = 1, b = 10, c = –7 (D) a = 1, b = 10, c = 7 iii. The tax levied by Central Government for trading within a state is: (A) IGST (B) CGST (C) SGST (D) UTGST iv. If a die is rolled, what is the probability that number appearing on upper face is less than 2? 1 1 1 (A) (B) (C) 1 (D) 3 2 6 (B) Solve the following questions (Any two): i. First term and common difference of an A.P. are 12 and 4 respectively. If tn = 96, find n. 4 5 ii. If = 22, then find the value of m. m 3 iii. Solve the following quadratic equation: x2 + 8x + 15 = 0. 3. (A) Complete the following activites (Any two): i. Smita has invested ` 12,000 to purchase shares of FV rs 10 at a premium of ` 2. Find the number of shares she purchased. Complete the given activity to get the answer. Activity: FV = ` 10, Premium = ` 2 MV = FV + + 2 = 12 Totalinvestment Number of shares = MV = shares 12 ii. The following table shows the daily supply of electricity to different places in a town. To show the information by a pie diagram, measures of central angles of sectors are to be decided. Complete the following activity to find the measures: Supply of electricity Places Measure of central angle (Thousand units) 4 Roads 4 360 48 30 Factories 12 360 144 6 Shops 6 360 30 Houses 8 360 Total 30 iii. Two coins are tossed simultaneously. Complete the following activity of writing the sample space (S) and expected outocomes of the events: a. Event A : to get at least one head. b. Event B : to get no head. Activity: If two coins are tossed simultaneously S={ , HT, TH, } a. Event A : at least getting one head. A = {HH, , TH}. b. Event B : to get no head. B={ }. (B) Solve the following questions (Any two): i. Find the 19th term of the A.P. 7, 13, 19, 25, ……. ii. Obtain a quadratic equation whose roots are –3 and –7. iii. Two numbers differ by 3. The sum of the greater number and twice the smaller number is 15. Find the smaller number. 4. Solve the following questions (Any three): i. Amit saves certain amount every month in a specific way. In the first month he saves ` 200, in the second month ` 250, in the third month ` 300 and so on. How much will be his total savings in 17 months? ii. A two digit number is to be formed using the digits 0, 1, 2, 3. Repetition of the digits is allowed. Find the probability that a number so formed is a prime number. iii. Smt. Malhotra purchased solar panels for the taxable value of ` 85,000. She sold them for ` 90,000. The rate of GST is 5%. Find the ITC of Smt. Malhotra. What is the amount of GST payable by her? iv. Solve the following simultaneous equations graphically: x + y = 0; 2x –y = 9. 5. Solve the following questions (Any one): i. The following frequency distribution table shows marks obtained by 180 students in Mathematics examination: Marks Number of Students 0 – 10 25 10 – 20 x 20 – 30 30 30 – 40 2x 40 – 50 65 Find the value of x. Also draw a histogram representing the above information. 1 ii. Two taps together can fill a tank completely in 3 minutes. The smaller tap takes 3 minutes 13 more than the bigger tap to fill the tank. How much time does each tap take to fill the tank completely? 6. Solve the following questions (Any one): i. The co-ordinates of the point of intersection of lines ax + by = 9 and bx + ay = 5 is (3, –1). Find the values of a and b. ii. The following frequency distribution table shows the distances travelled by some rickshaws in a day. Observe the table and answer the following questions: Class Frequency Cumulative Continous (Daily distance (Number of Frequency Classes travelled in km) rickshaws) less than type 60 – 64 59.5 – 64.5 10 10 65 – 69 64.5 – 69.5 34 10 + 34 = 44 70 – 74 69.5 – 74.5 58 44 + 58 = 102 75 – 79 74.5 – 79.5 82 102 + 82 = 184 80 – 84 79.5 – 84.5 10 184 + 10 = 194 85 – 89 84.5 – 89.5 6 194 + 6 = 200 a. Which is the modal class? Why? b. Which is the median class and why? c. Write the cumulative frequency (C.F.) of the class preceding the median class. d. What is the class interval (h) to calculate median? BOARD QUESTION PAPER: July 2019 Maths Part - I Time: 2 Hours Max. Marks: 40 Note: i. All questions are compulsory. ii. Use of calculator is not allowed. iii. Figures to the right of questions indicate full marks. 1. (A) Solve the following questions (Any four): i. If | 7 | | –4 | = a, then find the value of a. ii. If x + y = 5 and x y = 1, then find the value of x. iii. Find the median of the scores 7, 10, 5, 8, 9. iv. Write the degree of Polynomial 5x2 + 2x + 3x4 + 4. v. If A = {1, 2, 3, 4, 5} and B = {1, 3, 7}, then A B = ? vi. Find out the ratio of 1 mm to 1 cm. (B) Solve the following questions (Any two): i. Find the factors of the Polynomial 3x2 2x 1. ii. ABCD is a parallelogram. The ratio of measures of A and B is 5 : 4. Find the measure of B. iii. Alka spends 90% of the money that she gets every month and saves `120. How much money does she get monthly? 2. (A) Choose the correct alternative: 5 3 i. Find the value of 7 4 (A) –1 (B) –41 (C) 41 (D) 1 ii. Out of the following equations which one is not a quadratic equation? (A) x2 + 4x = 11 + x2 (B) x2 = 4x 2 (C) 5x = 90 (D) 2x x2 = x2 + 5 1 iii. If n(A) = 2, p(A) = , then n(S) = ? 5 (A) 10 (B) 2 (C) 5 (D) 20 iv. For a given A.P., a = 3.5, d = 0, then tn = _______ (A) 0 (B) 3.5 (C) 103.5 (D) 104.5 (B) Solve the following questions (Any two): i. Find the value of k, if x = 3 is a root of the equation kx2 10x + 3 = 0 ii. Market value of a share is ` 200. If the brokerage rate is 0.3%, then find the purchase value of the share. iii. The following table shows the number of students and the time they utilized daily for their studies. Find the mean time, spent by students for their studies: Time (hrs.) No. of Students 0–2 8 2–4 14 4–6 18 6–8 10 8 – 10 10 3. (A) Complete the following activities (Any two): i. There are 9 tickets in a box, each bearing one of the numbers from 1 to 9. One ticket is drawn at random from the box. Event A: Ticket shows an even number. Complete the following activity from the given information: Activity: S= n(S) = A= n(A) = ii. Complete the following activity to form a quadratic equation. Activity: I am a quadratic equation My standard form in My roots are 3 and 4. Sum of my roots = and product of my roots = My equation is iii. Complete the following activity to find the number of natural numbers between 1 and 171, which are divisible by 5: Activity From 1 to 171, natural numbers divisible by 5 are 5, 10, 15, _______, 170 In this A.P. a= ,d= , tn = 170 tn = a + (n 1)d 170 = 5 + (n 1) n= (B) Solve the following questions (Any two): i. Solve the following simultaneous equations: 4x + 3y = 11; 3x + 4y = 10 ii. Find the 23rd term of the following A.P.: 9, 4, 1, 6, 11, … iii. Find the mode from the following information: L = 10, h = 2, f0 = 58, f1 = 70, f2 = 42. 4. Solve the following questions (Any three): i. Solve the following simultaneous equations graphically: x + y = 2; x y = 4. ii. Sachin invested some amounts in National Saving Certificates in a specific way. In the first year he invested ` 4,000 in the second year ` 6,000 in the third year ` 8,000 and so on for 12 years. Find the total amount he invested in 12 years. iii. A readymade garment shopkeeper gives 5% discount on a dress of ` 2,000 and charges 5% GST on the remaining amount. What is the purchase price of the dress for the customer? iv. A bag contains 3 red, 3 white, 3 green and 3 black balls. One ball is picked up from the bag at random. What is the probability that the ball drawn is: a. white b. not white. 5. Solve the following questions (Any one): i. Out of 555 km, Vishal travelled certain distance by bus and remaining distance by car. Bus travels with an average speed of 60 km/hr and the average speed of car is 75 km/hr. He takes total 8 hours to complete the journey. Find the distance that Vishal travelled by bus. ii. The time required for some students to complete a science experiment and the number of students is shown in the following grouped frequency distribution table. Draw the frequency polygon with the help of histogram using given information: Time required Number of for experiment Students (minutes) 20 – 22 6 22 – 24 14 24 – 26 20 26 – 28 16 28 – 30 12 30 – 32 10 6. Solve the following questions (Any one): i. Construct a word problem on quadratic equation, such that one of its answers is 20 (years, rupees, centimetre etc.). Also solve it. ii. A student made a cube shaped die from a card sheet. Instead of writing numbers 1, 2, 3, 4, 5, 6 on its faces, he wrote letters a, b, c, d, e, f; one on each face, randomly. If he rolls the die twice, find the probability that he gets a vowel on the upper face both times. BOARD QUESTION PAPER: MARCH 2020 Mathematics Part - I Time: 2 Hours Max. Marks: 40 Notes: i. All questions are compulsory. ii. Use of calculator is not allowed. iii. The numbers to the right of the questions indicate full marks. iv. In case of MCQ’s Q. No. 1(A) only the first attempt will be evaluated and will be given credit. v. For every MCQ, the correct alternative (A), (B), (C) or (D) of answers with subquestion number is to be written as an answer. Q.1. A. For every subquestion 4 alternative answers are given. Choose the correct answer and write the alphabet of it: i. In the format of GSTIN there are _______ alpha-numerals. (A) 15 (B) 10 (C) 16 (D) 9 ii. From the following equations, which one is the quadratic equation? 5 (A) – 3 = x2 (B) x(x + 5) = 4 x 1 (C) n – 1 = 2n (D) (x + 2) = x x2 iii. For simultaneous equations in variables x and y, if Dx = 49, Dy = – 63, D = 7, then what is the value of x? (A) 7 (B) –7 1 1 (C) (D) 7 7 1 iv. If n(A) = 2, P(A) = , then n(S) = ? 5 2 5 (A) (B) 5 2 1 (C) 10 (D) 3 Q.1. B. Solve the following subquestions: i. Find second and third term of an A.P. whose first term is – 2 and common difference is – 2. ii. ‘Pawan Medicals’ supplies medicines. On some medicines the rate of GST is 12%, then what is the rate of CGST and SGST? iii. Find the values of a and b from the quadratic equation 2x2 – 5x + 7 = 0. iv. If 15x + 17y = 21 and 17x + 15y = 11, then find the value of x + y. Q.2. A. Complete and write any two activities from the following: i. Complete the following table to draw the graph of 2x – 6y = 3: x –5 y 0 (x, y) ii. First term and common difference of an A.P. are 6 and 3 respectively. Find S27. Solution: First term = a = 6, common difference = d = 3, S27 = ? n Sn = [ + (n – 1)d] – formula 2 27 S27 = [12 + (27 – 1) ] 2 27 = 2 = 27 45 S27 = iii. A card is drawn from a well shuffled pack of 52 playing cards. Find the probability of the event, the card drawn is a red card. Solution: Suppose ‘S’ is sample space. n(S) = 52 Event A: Card drawn is a red card. Total red cards = hearts + 13 diamonds n(A) = p(A) = – formula n(S) 26 p(A) = 52 p(A) = Q.2. B. Solve any four subquestions from the following: i. Find the value of the determinant: 7 5 3 3 3 1 2 2 ii. Solve the quadratic equation by factorisation method: x2 15x + 54 = 0 iii. Decide whether the following sequence is an A.P. if so, find the 20th term of the progression: 12, 5, 2, 9, 16, 23, 30, ………….... iv. A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is an odd number? v. If L = 10, f1 = 70, f 0 = 58, f 2 = 42, h = 2, then find the mode by using formula. Q.3. A. Complete and write any one activity from the following: i. Age group Measure of central No. of Persons (in years) angle 20 25 80 360 200 60 360 25 30 60 200 35 63 30 35 35 200 25 360 35 40 25 200 Total 200 ii. Shri Shantilal has purchased 150 shares of FV ` 100, for MV of ` 120, Company has paid dividend at 7%, then to find the rate of return on his investment, complete the following activity: Solution: FV = ` 100; Number of shares = 150 Market value = ` 120 1. Sum investment = MV No. of Shares = Sum investment = ` 18,000 2. Dividend per share = FV Rate of dividend = 100 =`7 Total dividend received = 150 7 = Dividend income 3. Rate of return = 100 Sum invested 1050 = 100 18000 = Q.3. B. Attempt any two subquestions from the following: i. A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets: 1. a red balloon. 2. a blue balloon. ii. The denominator of a fraction is 4 more than twice its numerator. Denominator becomes 12 times the numerator, if both the numerator and the denominator are reduced by 6, find the fraction. iii. A milk centre sold milk to 50 customers. The table below gives the number of customers and the milk they purchased. Find the mean of the milk sold by direct method: Milk Sold (litre) No. of Customers 1–2 17 2–3 13 3–4 10 4–5 7 5–6 3 iv. In an A.P. sum of three consecutive terms is 27 and their products is 504. Find the terms. (Assume that three consecutive terms in an A.P. are a – d, a, a + d.) Q.4. Attempt any two subquestions from the following: i. Represent the following data by histogram: Price of Sugar Number of Weeks (per kg in `) 18–20 4 20–22 8 22–24 22 24–26 12 26–28 6 28–30 8 ii. One person borrows ` 4,000 and agrees to repay with a total interest of ` 500 in 10 instalments. Each instalment being less than the preceding instalment by ` 10. What should be the first and the last instalments? iii. The sum of the areas of two squares is 400 sq.m. If the difference between their perimeters is 16 m, find the sides of two squares. Q.5. Attempt any one subquestion from the following: i. Convert the following equations into simultaneous equations and solve: x 1 1 1 4, y x y xy ii. A dealer sells a toy for ` 24 and gains as much percent as the cost price of the toy. Find the cost price of the toy. BOARD QUESTION PAPER: JULY 2020 Maths - I Time: 2 Hours Max. Marks: 40 Notes: i. All questions are compulsory. ii. Use of calculator is not allowed. iii. The numbers to the right of the questions indicate full marks. iv. In case of MCQ’s (Q. No. 1(A)) only the first attempt will be evaluated and will be given credit. v. For every MCQ, the correct alternative (A), (B), (C) or (D) with sub-question number is to be written as an answer. Q.1. (A) Four alternative answers are given for every sub-question. Choose the correct alternative and write its alphabet with sub-question number: i. To draw graph of 4x + 5y = 19, what will be the value of y when x = 1: (A) 4 (B) 3 (C) 2 (D) –3 ii. What is the sum of the first 10 natural numbers? (A) 55 (B) 20 (C) 65 (D) 11 iii. From the following equations, which one is the quadratic equation? 5 1 (A) 3 x2 (B) x(x + 5) = 2 (C) n – 1 = 2n (D) ( x 2) x x x2 iv. In the format of GSTIN there are _______ alpha-numerals. (A) 9 (B) 10 (C) 16 (D) 15 Q.1. (B) Solve the following subquestions: i. For simultaneous equations in variable x and y, if Dx = 25, Dy = 40, D = 5, then what is the value of x? ii. Find the first term and common difference for the following A.P: 127, 135, 143, 151, ……… iii. A die is rolled then write sample space ‘S’ and number of sample point n(S). iv. If fidi 108 and fi 100, then find d = ? Q.2. (A) Complete the following activities and rewrite it (any two): i. Activity: 3 2 =3 4 4 5 = –8 = 7 ii. One of the roots of quadratic equation 5m2 + 2m + k = 0 is . 5 Complete the following activity to find the value of k. Activity: 7 is a root of quadratic equation 5 5m2 + 2m + k = 0 Put m = in the equation 2 7 5 2 +k=0 5 14 + + k = 0 5 k= iii. Complete the activity to prepare a table showing the co-ordinates which are necessary to draw a frequency polygon: Class 18 – 19 19 – 20 20 – 21 Class Mark 18.5 19.5 21.5 Frequency 4 15 19 Co-ordinates of point (19.5, 13) (20.5, 15) (21.5, 19) Q.2. (B) Solve the following sub-questions (any four): i. Sum of two numbers is 7 and their difference is 5. Find the numbers. ii. Solve the quadratic equation by factorisation method: x2 + x – 20 = 0 iii. Find the 19th term of the following A.P.: 7, 13, 19, 25, ……... iv. For the following experiments, write sample space ‘S’ and number of sample points n(S): Two digit numbers are formed using digits 2, 3 and 5 without repeating a digit. v. The following table shows causes of noise pollution. Find the measure of central angles for each, to draw a pie diagram: Construction Traffic Aircraft take offs Industry 10% 50% 15% 25% Q.3. (A) Complete the following activity and rewrite it (any one): i. In an A.P. the first term is –5 and last term is 45. If sum of ‘n’ terms in the A.P. is 120, then complete the activity to find n. Activity: t1 = –5, tn = , Sn = n Sn = [t1 + ] 2 n = [–5 + 45] 2 240 = n n= ii. A card is drawn from a well shuffled pack of 52 playing cards. Complete the activity to find the probability of the event that the card drawn is a red card. Activity: ‘S’ is the sample space. n(S) = 52 Event A: Card drawn is a red card. Total number of red cards = hearts + diamonds n(A) = p(A) = n(S) p(A) = 52 p(A) = Q.3. (B) Solve the following subquestions (any two): i. Solve the following simultaneous equations graphically: x + y = 5; x – y = 1. ii. Solve quadratic equation using formula method: 5m2 + 13m + 8 = 0. iii. A retailer sold 2 tins of lustre paint and taxable value of each tin is ` 2,800. If the rate of GST is 28%, then find the amount of CGST and SGST charged in the tax invoice. iv. Time allotted for the preparation of an examination by some students is shown in the table. Draw a histogram to show this information: Time (minutes) No. of Students 60-80 14 80-100 20 100-120 24 120-140 22 Q.4. Solve the following subquestions (any two): i. If one root of the quadratic equation ax2 + bx + c = 0 is half of the other root, show that, 9ac b2 =. 2 ii. Bhujangrao invested ` 2,50,590 in shares of F.V. ` 10 when M.V. is ` 250. Rate of brokerage is 0.2% and GST is 18%, then find: a. the number of shares purchased, b. the amount of brokerage paid, and c. GST paid for the trading. iii. The following table shows frequency distribution of number of trees planted by students in the school: No. of Trees Planted No. of Students 0-10 30 10-20 70 20-30 100 30-40 70 40-50 40 Find the mode of trees planted. Q.5. Solve the following subquestions (any one): i. Six faces of a die are as shown below: A B C D E O If the die is rolled once, find the probability of event ‘M’ that ‘English vowel appears on upper face’. ii. Construct any one linear equation in two variables. Obtain another equation by interchanging only coefficients of variables. Find the value of the variables. BOARD QUESTION PAPER: MARCH 2022 Mathematics - I Time: 2 Hours Max. Marks: 40 Notes: i. All questions are compulsory. ii. Use of calculator is not allowed. iii. The numbers to the right of the questions indicate full marks. iv. In case of MCQ’s [Q. No. 1(A)] only the first attempt will be evaluated and will be given credit. v. For every MCQ, the correct alternative (A), (B), (C) or (D) with subquestion number is to be written as an answer. Q.1. (A) Four alternative answers are given for every subquestion. Choose the correct alternative and write its alphabet with subquestion number. i. Which one is the quadratic equation? 5 (A) – 3 = x2 (B) x(x + 5) = 2 3 1 (C) n 1 = 2n (D) (x + 2) = x x2 ii. First four terms of an A.P. are _______, whose first term is –2 and common difference is –2. (A) –2, 0, 2, 4 (B) –2, 4, –8, 16 (C) –2, –4, –6, –8 (D) –2, –4, –8, –16 iii. For simultaneous equations in variables x and y, Dx = 49, Dy = –63, D = 7, then what is the value of y? (A) 9 (B) 7 (C) –7 (D) –9 iv. Which number cannot represent a probability? 2 (A) 1.5 (B) 3 (C) 15% (D) 0.7 (B) Solve the following subquestions: i. To draw a graph of 4x + 5y = 19, find y when x = 1. ii. Determine whether 2 is a root of quadratic equation 2m2 – 5m = 0. iii. Write second and third term of an A.P. whose first term is 6 and common difference is –3. iv. Two coins are tossed simultaneously. Write the sample space ‘S’. Q.2. (A) Complete the following activities and rewrite it (any two): i. Complete the activity to find the value of the determinant. Activity: 2 3 9 = 2 3 –9 2 3 3 = –18 = ii. Complete the following activity to find the 19th term of an A.P., 7, 13, 19, 25, ………. : Activity: Given A.P. : 7, 13, 19, 25, ……… Here first term a = 7; t19 = ? tn = a + ( ) d ……. (formula) t19 = 7 + (19 – 1) t19 = 7 + t19 = iii. If one die is rolled, then to find the probability of an event to get prime number on upper face, complete the following activity. Activity: One die is rolled. ‘S’ is sample space. S={ } n(S) = 6 Event A: Prime number on the upper face. A={ } n(A) = 3 P(A) = …….. (formula) n(S) P(A) = (B) Solve the following subquestions (any four): i. To solve the following simultaneous equations by Cramer’s rule, find the value of Dx and Dy. 3x + 5y = 26 x + 5y = 22 ii. A box contains 5 red, 8 blue and 3 green pens. Rutuja wants to pick a pen at random. What is the probability that the pen is blue? iii. Find the sum of first ‘n’ even natural numbers. iv. Solve the following quadratic equations by factorisation method: x2 + x – 20 = 0 v. Find the values of (x + y) and (x – y) of the following simultaneous equations: 49x – 57y = 172 57x – 49y = 252 Q.3. (A) Complete the following activity and rewrite it (any one): i. One of the roots of equation kx2 – 10x + 3 = 0 is 3. Complete the following activity to find the value of k. Activity: One of the roots of equation kx2 – 10x + 3 = 0 is 3 Putting x = in the above equation k( )2 – 10 +3=0 – 30 + 3 = 0 9k = k= ii. A card is drawn at random from a pack of well shuffled 52 playing cards. Complete the following activity to find the probability that the card drawn is – Event A: The card drawn is an ace. Event B: The card drawn is a spade. Activity: ‘S’ is the sample space. n(S) = 52 Event A: The card drawn is an ace. n(A) = P(A) = ……..(formula) P(A) = 52 P(A) = 13 Event B: The card drawn is a spade. n(B) = n B P(B) = n S P(B) = 4 (B) Solve the following subquestions (any two): i. Solve the simultaneous equations by using graphical method: x + 3y = 7 2x + y = –1 ii. There is an auditorium with 27 rows of seats. There are 20 seats in the first row, 22 seats in the second row, 24 seats in the third row and so on. Find how many total seats are there in the auditorium? iii. Sum of the present ages of Manish and Savita is 31 years. Manish’s age 3 years ago was 4 times the age of Savita at that time. Find their present ages. iv. Solve the following quadratic equation using formula: x2 + 10x + 2 = 0 Q.4. Solve the following subquestions (any two): i. If 460 is divided by a natural number, then quotient is 2 more than nine times the divisor and remainder is 5. Find the quotient and divisor. ii. If the 9th term of an A.P. is zero, then prove that the 29th term is double the 19th term. iii. The perimeter of an isosceles triangle is 24 cm. The length of its congruent sides is 13 cm less than twice the length of its base. Find the lengths of all sides of the triangle. Q.5. Solve the following subquestions (any one): i. A bag contains 8 red and some Blue balls. One ball is drawn at random from the bag. If ratio of probability of getting red ball and blue ball is 2 : 5, then find the number of blue balls. ii. Measures of angles of a triangle are in A.P. the measure of smallest angle is five times of common difference. Find the measures of all angles of a triangle. (Assume the measures of angles as a, a + d, a + 2d) BOARD QUESTION PAPER: MARCH 2023 Mathematics Part - I Time: 2 Hours Max. Marks: 40 Note: i. All questions are compulsory. ii. Use of a calculator is not allowed. iii. The numbers to the right of the questions indicate full marks. iv. In case of MCQs [Q. No. 1(A)] only the first attempt will be evaluated and will be given credit. v. For every MCQ, four alternatives (A), (B), (C), (D) of answers are given. Alternative of correct answer is to be written in front of the subquestion number. Q.1. (A) Choose the correct answer and write the alphabet of it in front of the subquestion number: i. To draw the graph of 4x + 5y = 19, find y when x = 1: (A) 4 (B) 3 (C) 2 (D) –3 ii. Out of the following equations which one is not a quadratic equation? (A) x2 + 4x = 11 + x2 (B) x2 = 4x 2 (C) 5x = 90 (D) 2x – x2 = x2 + 5 iii. For the given A.P. a = 3.5, d = 0, then tn = _______ (A) 0 (B) 3.5 (C) 103.5 (D) 104.5 1 iv. If n(A) = 2, P(A) = , then n(S) = ? 5 5 2 1 (A) 10 (B) (C) (D) 2 5 3 (B) Solve the following subquestions: i. Find the value of the following determinant: 4 3 2 7 ii. Find the common difference of the following A.P.: 2, 4, 6, 8, … iii. On certain article if rate of CGST is 9%, then what is the rate of SGST? iv. If one coin is tossed, write the sample space ‘S’. Q.2. (A) Complete any two given activities and rewrite it: i. Complete the following activity; find the value of x: 5x + 3y = 9 …(I) 2x – 3y = 12 …(II) Add equations (I) and (II) 5x + 3y = 9 + 2x – 3y = 12 7x = x= x= ii. Complete the following activity to determine the nature of the roots of the quadratic equation x2 + 2x – 9 = 0: Solution: Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0 a = 1, b = 2, c = b2 – 4ac = (2)2 – 4 =4+ = 40 b2 – 4ac > 0 The roots of the equation are real and unequal. iii. Complete the following table using given information: Sr. No. FV Share is at MV 1. ₹ 100 Par 2. Premium ₹ 500 ₹ 575 3. ₹ 10 ₹5 4. ₹ 200 Discount ₹ 50 (B) Solve the following subquestions (any four): i. Solve the following simultaneous equations: x + y = 4; 2x – y = 2 ii. Write the following equation in the form ax2 + bx + c = 0, then write the values of a, b, c: 2y = 10 – y2. iii. Write an A.P. whose first term is a = 10 and common difference d = 5. iv. Courier service agent charged total ₹ 590 to courier a parcel from Nashik to Nagpur. In the tax invoice taxable value is ₹ 500 on which CGST is ₹ 45 and SGST is ₹ 45. Find the rate of GST charged for this service. v. Observe the following table and find Mean: Assumed mean A = 300 Class mark di = xi A Frequency Frequency Deviation Class xi di = xi 300 fi fi di 200 – 240 220 80 5 – 400 240 – 280 260 –40 10 – 400 280 – 320 300 A 0 15 0 320 – 360 340 40 12 480 360 – 400 380 80 8 640 Total fi = 50 fidi = 320 Q.3. (A) Complete any one activity and rewrite it: i. Form a ‘Road Safety Committee’ of two, from 2 boys (B1, B2) and 2 girls (G1, G2). Complete the following activity to write the sample space: a. Committee of 2 boys = b. Committee of 2 girls = c. Committee of one boy and one girl = B1G1 , B1G 2 , , d. Sample space (S) = B1B2 , B1G1 , , , B2 G 2 , G1G 2 ii. Fill in the boxes with the help of given information: Tax invoice of services provided (Sample) Food Junction, Khed-Shivapur, Pune Invoice No. 58 Mob. No. 7588580000, [email protected] GSTIN : 27AAAAA5555B1ZA Invoice Date : 25 Feb., 2020 Food Rate Taxable SAC Qty CGST SGST items (in `) amount 9963 Coffee 1 20 20.00 2.5 % ` 0.50 2.5 % Masala 9963 1 10 10.00 ` 0.25 2.5 % Tea Masala 9963 2 60 2.5% 2.5% ` 3.00 Dosa Total 150.00 ` 3.75 Grand Total = ` 157.50 (B) Solve the following subquestions (any two): i. Solve the following simultaneous equations using Cramer’s rule: 4m + 6n = 54; 3m + 2n = 28 ii. Solve the following quadratic equation by formula method: x2 + 10x + 2 = 0 iii. A two digit number if formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability of the following events? Event A: The number formed is an odd number. Event B: The number formed is a multiple of 5. iv. The frequency distribution table shows the number of mango trees in a grove and their yield of mangoes. Find the median of data: No. of Mangoes No. of Trees 50 100 33 100 150 30 150 200 90 200 250 80 250 300 17 Q.4. Solve the following subquestions (any two): i. If the first term of an A.P. is p, second term is q and last term is r, then show that sum of all terms is (q + r 2p) p r. 2(q p) ii. Show the following data by a frequency polygon: Electricity bill (₹) Families 200 – 400 240 400 – 600 300 600 – 800 450 800 – 1000 350 1000 – 1200 160 iii. The sum of the squares of five consecutive natural numbers is 1455. Find the numbers. Q.5. Solve the following subquestions (any one): i. Draw the graph of the equation x + 2y = 4. Find the area of the triangle formed by the line intersecting to X-axis and Y-axis. ii. A survey was conducted for 180 people in a city. 70 ate Pizza, 60 ate burgers and 50 ate chips. Draw a pie diagram for the given information. Board Question Paper: July 2023 BOARD QUESTION PAPER: JULY 2023 Mathematics Part - I Time: 2 Hours Max. Marks: 40 Note: i. All questions are compulsory. ii. Use of a calculator is not allowed. iii. The numbers to the right of the questions indicate full marks. iv. In case of MCQs [Q. No. 1(A)] only the first attempt will be evaluated and will be given credit. v. For every MCQ, four alternatives (A), (B), (C), (D) of answers are given. Alternative of correct answer is to be written in front of the subquestion number. Q.1. (A) Choose the correct answer and write the alphabet of it in front of the subquestion number: i. Sum of first five multiples of 3 is _______ (A) 45 (B) 55 (C) 15 (D) 75 3 2 ii. Find the value of determinant : 4 5 (A) 2 (B) 7 (C) 7 (D) 23 iii. Which of the following quadratic equations has roots 3 and 5? (A) x2 15x + 8 = 0 (B) x2 8x + 15 = 0 (C) x2 + 3x + 5 = 0 (D) x2 + 8x 15 = 0 iv. Two coins are tossed simultaneously. Write the number of sample points n(S): (A) 2 (B) 8 (C) 4 (D) 6 (B) Solve the following subquestions: i. If 15x + 17y = 21 and 17x + 15y = 11, then find the value of x + y. ii. Given sequence is an A.P. Find the next two terms of this A.P.: 5, 12, 19, 26, ……... iii. On certain article if rate of CGST is 9%, then what is the rate of SGST and what is the rate of GST? iv. If n(S) = 2 and n(A) = 1, then find P(A). Q.2. (A) Complete the following activity and rewrite (any two): i. Complete the following table to draw the graph of the equation x + y = 3: x 3 y 5 3 (x, y) (3, 0) (0, 3) ii. Complete the following activity to find the value of discriminant of the equation x2 + 10x – 7 = 0. Solution: Comparing x2 + 10x – 7 = 0 with ax2 + bx + c = 0 a = 1, b = 10, c = b2 – 4ac = – 4 1 (7) = 100 + = 1 Mathematics Part - I iii. Complete the following table using given information: Sr. No. FV Share is at MV 1. ₹ 10 Premium of ₹ 7 2. ₹ 25 ₹ 16 3. ₹ 300 ₹ 315 4. at par ₹5 (B) Solve the following subquestions (any four): i. Solve the following simultaneous equations: x + y = 6; x – y = 4 ii. Solve the following quadratic equation by factorisation method: x2 + 15x + 54 = 0 iii. The first term a = 8 and common difference d = 5 are given. Write an A.P. iv. Mr. Rohit is a retailer. He paid GST of ₹ 6,500 at the time of purchase. He collected GST of ₹8,000 at the time of sale. (a) Find his input tax and output tax. (b) What is his input tax credit? (c) Find his payable GST. (d) Hence find the payable CGST and payable SGST. v. Find the mean from the given values: xifi = 1265; N = 50 Q.3. (A) Complete the following activity and rewrite (any one): i. Smita has invested ₹ 12,000 and purchased shares of FV ₹ 10 at a premium of ₹ 2. Find the number of shares she purchased. Complete the given activity to get the answer. Solution: FV = ₹ 10, Premium = ₹ 2 MV = FV + = 10 + = Totalinvestment 12,000 Number of shares = = MV = shares Ans. Smita has purchased shares. ii. If one die is rolled once, then find the probability of each of the following events: (a) Number on the upper face is prime. (b) Number on the upper face is even. Solution: ‘S’is the sample space S = {1, 2, 3, 4, 5, 6} n(S) = (a) Event A : Prime number on the upper face A = {2, 3, 5} n(A) = n(A) P(A) = n(S) 3 P(A) = = 22 Board Question Paper: July 2023 (b) Event B : Even number on the upper face B = {2, 4, 6} n(B) = n(B) P(B) = n(S) 1 P(B) = = 2 (B) Solve the following subquestions (any two): i. Two numbers differ by 3. The sum of the twice the smaller number and thrice the greater number is 19. Find the numbers. ii. Solve the given quadratic equation by using formula method: 5x2 + 13x + 8 = 0 iii. A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets: (a) a red balloon (b) a blue balloon (c) a green balloon. iv. The following table shows the number of students of class X and the time they utilized daily for their studies. Find the mean time spent by 50 students for their studies by direct method: Time (hrs.) No. of students 02 7 24 18 46 12 68 10 8 10 3 Q.4. Solve the following subquestions (any two): i. The sum of two roots of a quadratic equation is 5 and sum of their cubes is 35, find the equation. ii. If p times the pth term of an A.P. is equal to q times qth term, then show that (p + q)th term of that A.P. is zero (p q). iii. Draw a pie diagram to represent the world population given in the following table : Country Japan England India China Percentage of World Population 20 10 40 30 Q.5. Solve the following subquestions (any one): i. Represent the following data using histogram: Daily Income (₹) No. of Workers 130 135 4 135 140 7 140 145 14 145 150 16 3 Mathematics Part - I ii. Observe the following flow chart and solve it: 3x y = 7; x + 4y = 11 Find the value of D, Dx and Dy Find the value of Find the value of Find the value of Dx D Dy Find the value of Find the value of x y Write the values of x and y 44 Board Question Paper: March 2024 BOARD QUESTION PAPER: MARCH 2024 Mathematics Part - I Time: 2 Hours Max. Marks: 40 Note: i. All questions are compulsory. ii. Use of a calculator is not allowed. iii. The numbers to the right of the questions indicate full marks. iv. In case of MCQs [Q. No. 1(A)] only the first attempt will be evaluated and will be given credit. ns Q.1. (A) Choose the correct alternative from given: i. If 3 is one of the root of the quadratic equation kx2 – 7x + 12 = 0, then k = _______ (A) 1 (B) –1 (C) 3 (D) –3 io ii. To draw the graph of x + 2y = 4, find x when y = 1: (A) 1 (B) 2 (C) –2 (D) 6 at iii. For an A.P., t7 = 4, d = –4, then a = _______ (A) 6 (B) 7 lic (C) 20 (D) 28 iv. In the format of GSTIN, there are _______ alpha-numerals. (A) 9 (B) 10 (C) 15 (D) 16 (B) Solve the following subquestions: i. If 17x + 15y = 11 and 15x + 17y = 21, then find the value of x – y. ub ii. Find first term of the sequence tn = 3n – 2. iii. If the face value of a share is ₹ 100 and market value is ₹ 150. If rate of brokerage is 2%, find brokerage paid on one share. P iv. Two digit numbers are formed using digits 2, 3 and 5 without repeating a digit. Write the sample space. et Q.2. (A) Complete the following activities and rewrite it (any two): i. If (0, 2) is the solution of 2x + 3y = k, then to find the value of k, complete the following activity: Activity: rg (0, 2) is the solution of the equation 2x + 3y = k. Put x = and y = in the given equation; 2 +32=k Ta 0+6=k k= ii. If 2 and 5 are the roots of the quadratic equation, then complete the following activity to form quadratic equation: Activity: Let = 2 and = 5 are the roots of the quadratic equation. Then quadratic equation is: x2 – ( + )x + = 0 x2 – (2 + )x+ 5=0 x2 – x+ =0 1 Mathematics Part - I iii. Two coins are tossed simultaneously. Complete the following activity to write the sample space and the given events A and B in the set form: Event A: To get at least one head. Event B: To get no head. Activity: Two coins are tossed simultaneously. Sample space is S= , HT, TH, Event A: To get at least one head. A= , HT, TH Event B: To get no head. ns B= (B) Solve the following subquestions (any four): i. ABCD is a rectangle. Write two simultaneous equations using information given below in io the diagram, in the form of ax + by = c: 2x + y + 8 A B at 2y lic x+4 D C 4x – y ii. Solve the following quadratic equation using factorisation method: x2 + x – 20 = 0 ub iii. Find the 19th term of the following A.P.: 7, 13, 19, 25, ……. iv. A card is drawn from well shuffled pack of 52 playing cards. Find the probability that the P card drawn is a face card. v. The following table shows classification of number of workers and number of hours they work in software company. Prepare less than upper limit type cumulative frequency et distribution table: Number of hours daily Number of workers 8 – 10 150 rg 10 – 12 500 12 – 14 300 14 – 16 50 Ta Q.3. (A) Complete the following activity and rewrite it (any one): i. The following frequency distribution table shows the classification of the number of vehicles and the volume of petrol filled in them. To find the mode of the volume of petrol filled, complete the following activity: Class Frequency (Petrol filled in Liters) (Number of Vehicles) 0.5 – 3.5 33 3.5 – 6.5 40 6.5 – 9.5 27 9.5 – 12.5 18 12.5 – 15.5 12 22 Board Question Paper: March 2024 Activity: From the given table, Modal class = f1 f 0 Mode = + h 2f1 f 0 40 33 Mode = 3.5 + 2 40 33 27 Mode = 3.5 + 7 3 80 60 ns Mode = The mode of the volume of petrol filled is. io ii. The total value (with GST) of remote controlled toy car is ₹ 2360. Rate of GST is 18% on toys. Complete the following activity to find the taxable value for the toy car: Activity: at Total value for toy car with GST = ₹ 2360 Rate of GST = 18% Let taxable value for toy car be ₹ x lic 18 GST = x 100 taxable value Total value for toy car = + ….. Formula for toy car ub 2360 = + x 100 x P 2360 = 100 2360 100 = 118x 2360 100 et x= Taxable value for toy car is ₹ rg (B) Solve the following subquestions (any two): i. Solve the following quadratic equation by formula method: 3m2 – m – 10 = 0 Ta ii. Solve the following simultaneous equations using Cramer’s rule: 3x – 4y = 10, 4x + 3y = 5 iii. 50 shares of face value ₹ 10 were purchased for market value of ₹ 25. Company declared 30% dividend on the shares, then find: a. Sum invested b. Dividend received c. Rate of return. iv. One coin and a die are thrown simultaneously. Find the probability of the following events: Event A: To get a head and a prime number. Event B: To get a tail and an odd number. 3 Mathematics Part - I Q.4. Solve the following subquestions (any two): i. A tank can be filled up by two taps in 6 hours. The smaller tap alone takes 5 hours more than the bigger tap alone. Find the time required by each tap to fill the tank separately. ii. The following table shows the classification of percentage of marks of students and the number of students. Draw frequency polygon from the table without drawing histogram: Result Number of (Percentage) Students 20 – 40 25 40 – 60 65 60 – 80 80 80 – 100 15 ns iii. In a ‘Mahila Bachat Gat’ Kavita invested from the first day of month ₹ 20 on first day, ₹ 40 on second day and ₹ 60 on third day. If she saves like this, then what would be her total saving in the month of February 2020? Q.5. Solve the following subquestions (any one): io i. In the given figure, the pie diagram represents the amount spent on different sports by a school administration in a year. If the money spent on football is ₹ 9,000, answer the following questions: at a. What is the total amount spent on sports? b. What is the amount spent on cricket? lic Cricket Kabaddi 160 55 Football 45 Hockey ub 100 ii. Draw the graph of the equation x + y = 4 and answer the following questions: P a. Which type of triangle is formed by the line with X and Y-axes based on its sides. b. Find the area of that triangle. et rg Ta 44
