Monday, April 5, 2021

Math I, Test - 2

  

उद्या दि. 07/04/21 रोजी होणारा पेपर - गणित भाग - II & Mathematics Part - II, वेळ - 12 : 00 ते 2 :15

 जिल्हा परिषद माध्यमिक विद्यालय, विडूळ ता . उमरखेड जि. यवतमाळ


 Online Exam

Class - 10th, Sub - Mathematics- I , Marks - 40, Time - 2 Hours


Date - 06 / 04 / 2021 , Timing - 12 : 00 ते 2 : 15

-----------------------------------------------------------------



Q. 1 (A) For every subquestion 4 alternative answers are given. Choose the correct answer and write the alphabet of it:         04


i. The solution of the equation x-y=10 and x+y=70 is --------.


A) (40,30)          B) (30,40)    
      
C) (10,60)          D) (50,20)



ii.   If one of the roots of quadratic equation x² – kx + 27 = 0 is 3 then find the value of ‘k’.


A) 10          B) 12           C) -12           D) 16


iii.  A set of numbers where the numbers are arranged in a definite order, like the natural numbers, is called a .........

(A) index        (B) numbers    
     
(C) line            (D) sequence



iv.  In how many ways a card can be drawn from a well shuffled pack of playing
cards,

A) 4           B) 1              C) 26        D) 52



Q.1. B. Solve the following subquestions:     04


i. If x+2y=5 and 2x+y=7 then find the value of x+y


ii. If b2 – 4ac> 0 and b
2 – 4ac< 0 then write the nature of roots of the quadratic equation for each given case.


iii.  tn = 2n-5 in a sequence, find its first two terms.


iv. write the event in the set form for the following random experiment.

 ‘ If one die is thrown, the number obtained on the upper face is even.’



Q.2. A. Complete and write any two activities from the following: 04



i) To find the values of x and y for the equations x- 2 y =5 and 2 x+ 3 y =10 complete the activity.









ii) Complete the following activity to solve the given quadratic equation 


by factorization method.


Activity: 

x² + 8 x – 20 = 0 


x² + (....) – 2x – 20 = 0


x (x+10) – (....) (x+10) = 0


 (x + 10) (.......) = 0


x = …… or x = 2






iii) Two coins are tossed simultaneously. Write the sample space (S) and expected

 sample points in the given events by completing the activity.


i) Event A : to get at least one head.

ii) Event B : to get no head.


Activity : Let ‘S’ is the sample space , when two coins are tossed

simultaneously.


 ∴ { = S ,HT, TH,  }


Event A : to get at least one head.


 ∴ A { = HH, , TH }


Event B : to get no head.


 ∴ B { =  }





Q.2. B. Solve any four subquestions from the following:    08



i. State with reason whether the point (3, −2) will lie on the graph of

the equation 5 𝑚 − 3 𝑛 = −21.



ii. Find the value of discriminant for the quadratic equation : 

x² + 8x – 48= 0 



iii. In an A.P. a=4 and d=0, then find first five terms.



iv. There are 30 cards in a box, each bearing one of the numbers from 1 to 30. One card is drawn at random from the box. Find the probability of eventt that the card drawn shows a number which is a multiple of 5.


v. For the equation a + 2b = 7 find a when b = 4




प्र. 3 A.  खालीलपैकी कोणतीही एक कृती सोडवा.      03



i. Complete the following activity to solve the given word problem.

Sum of squares of two consecutive even natural numbers is 244 then findt those numbers.

Activity: let the first even natural number be X,

 Therefore its consecutive even natural number will be = (.....)


 By the given condition,


X2 + (x+ 2)2 = 244


X2+X2+4x+4 – (....) = 0


 2x2 + 4x – 240 = 0


 X2 + 2x – 120 = 0


 X2+ (……..) – (……..) – 120 = 0


X (x+12) – (…..) (x+12) = 0


 (x + 12) (x – 10) = 0


 X = (……) / X = 10


But natural number cannot be negative x = -12 is not possible.


 Therefore first even natural number is x = 10.


Second even consecutive natural number = x+ 2= 10+ 2= 12.







ii. A box contains 5 strawberry chocolates, 6 coffee chocolates and 2

peppermint chocolates. If one of the chocolates is picked from the box at

randomly, Find the probability of the following events by completing the

activity. (i) Event A : it is a coffee chocolate.

 (ii) Event B : it is a peppermint chocolate.




 



प्र. 3. B . पुढील कोणतेही दोन उपप्रश्न सोडवा‌.      06



i.  Ajay is younger than Vijay by 3 years. The sum of their ages is 25 years, what is the age of Ajay.



ii. Solve :


√3 x² + √𝟐 x – 2√𝟑 =0



iii. If One coin and one die are thrown simultaneously, find the probability of the following events.


i) Event A : To get a tail and an even number.

 ii) Event B: To get head and an odd number.



iv.  Merry got a job with salary Rs.15000 per month. If her salary

increases by Rs.100 per month, how much would be her salary after 20 months?




Q.4. Attempt any two subquestions from the following:          08


i. Sum of the roots of the quadratic equation is 5 and sum of their cubes is 35 then find the quadratic equation.




ii. Solve the following equations by graphical method :


𝑥 + 𝑦 = 5;  3 𝑥 - 𝑦 = 11



iii. What is the probability that an ordinary year has 53 Sundays ?




Q.5. Attempt any one subquestion from the following:  03



i. From the railway station I took a rickshaw to go home. It is decided

that I have to pay Rs. X for the first kilometre and for each kilometre Rs.Y for the next. For 10 kilometres the fare is Rs. 40 and for 16 kilometres fare is Rs. 58. Find the fare for the first kilometres.



ii. A bag contains 8 red balls and some blue balls. If one ball is drawn randomly the probability of drawing a red ball to a blue ball are in the ratio 5 : 2, determine the probability of drawing a blue ball from the bag.


------------------------------------------------------