Maharashtra Board Class 10 SSC Algebra Question Paper 2021-22

Mukund Pathak March 19, 2023

 

Maharashtra Board Class 10 SSC Algebra Question Paper



STD: X                                                  EXAMINATION                                          DATE: 2022

TIME: 2 Hours               SUBJECT: MATHEMATICS 1 (ALGEBRA)                    MARKS: 40

 

Note:     (i) All questions are compulsory.

(ii)   Use of calculator is not allowed.

(iii)  The numbers to the right 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 sub-question number is to be written as an answer.

…………………………………………………………………………………………………………………………

 Q. 1. (A)  For every sub-question 4 alternative answers are given. Choose the correct answer and write the letter of the alphabet of it:                                        [4]
 

𝟑

(i) Find the value of |

𝟏

−𝟏

|

𝟒

 

     (A) -13         (B) 11 

(C) 13 

(D) -11

(ii)    A die is rolled. What is the probability of getting an even number on the upper face?

(A)  𝟏            (B) 𝟏                 (C) 𝟏                 (D) 𝟑

            𝟐                               𝟑                                      𝟒                                      𝟒

(iii)  For an A. P., the first term is 4 and the last term (tn) is 31. The sum of all the terms is  420. What is the value of n?

(A)  12          (B) 24  (C) 10  (D) 20

(iv)  What is the value of k for the quadratic equation 3x2 – kx + k = 0 has equal roots?

(A)  6            (B) – 6              (C) 12  (D) – 12

(B) Solve the following sub-questions:                                                            [4]

(i)      One coin and one die are thrown simultaneously. What is the number of sample points?

(ii)    For drawing the graph of 2x + y = - 4, if y = -2, what is the value of x?

(iii)  For quadratic equation 10x2 + 10x + 1 = 0, what is the value of the discriminant?

(iv)  If for an A. P., t2 = 4 and d = -2, then what is the value of a?

 Q. 2. (A) Complete and write any two activities from the following:         [4]

(i) Complete the following activity to solve the simultaneous equations 2x + y = 19 and        

2x – 3y = - 3 by Cramer’s rule.



(B) Solve any four of the following sub-questions:                     [8]

(i) Solve the following quadratic equation:  x2 – 8x + 15 = 0

(ii) The first term of an A. P. is – 5 and the 6th term is 45. Find S6 

(iii)  If x = 5 and y = 3 is the solution of 3x + ky = 3, Find the value of k.

(iv)  26 cards each bearing one English letter are kept in a box. One card is drawn at random. What is the probability that the card drawn is a vowel card?

(v)  Find the value of the discriminant for the quadratic equation x2 – 6x – 5 = 0.

 

Q. 3. (A) Complete and write any one activity from the following:   [3]

(i) A person got a job with salary Rs. 1,80,000 per year. He was given Rs. 10,000 increment per year. Complete the following activity to find the number of years (n), when his salary will be Rs. 2,50,000.


(ii) Two-digit numbers are formed from the digits 2, 0, 5, 7 without repetition. Complete the following activity to find the probability that the numbers so formed are divisible (a) by 3, (b) by 5.


(B) Attempt any two sub-questions from the following:           [6]

i) 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.

ii)  In an A. P., the sum of three consecutive terms is 27 and their product is 504. Find the terms. (Assume that three consecutive terms in an A. P. are a – d, a, a + d.)

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?

(1) a red balloon                                 (2) a blue balloon.

 

iv) Solve the following quadratic equation using formula method.

            25x2 + 30x + 9 = 0

 Q. 4. Attempt any two sub-questions from the following:                    [8]

(i)    Solve the simultaneous equations graphically.

            2x + y = 8;        2y = 1 + x

(ii)  Two dice are rolled simultaneously. Find the probability

(a)  of event A that the sum of the digits on the upper faces is a prime number. 

(b)  of event B that the sum of the digits on the upper faces is a multiple of 5.

(iii) Anvar saves some amount in every month starting from January 2020. In first month, he saves Rs. 200, Rs. 250, Rs. 300 and so on. In which month will his saving savings be Rs. 1000? Also, what will be his total savings in December 2022?

 Q. 5. Attempt any one sub-question from the following:                                      [3]

            𝟐            −𝒚                     𝟑          𝟐

(i)    If |𝟏            𝒙 | = 16 and |𝒚            𝒙| = 3, form two simultaneous equations from the given determinants and solve.

(ii)  Find two consecutive odd positive integers, sum of whose squares is 290.

***** 

 


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