Board Paper of Class 10 2019 Maths - Solutions

(a) i. Find the median of: 66, 98, 54, 92, 87, 63, 72.
ii. Multiply and write the answer in the simplest form: $5\sqrt{7}\times 2\sqrt{7}$ 
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: $2x^3+x^2-3x+4$.
vi. For computation of income tax which is the assessment year of financial year 01–04–2016 to 31–03–2017?

(b) i. Find the value of the polynomial $2x^3+2x$, when $x=-1$.
ii. If A = {11, 21, 31, 41}, B = {12, 22, 31, 32}, then find: a. $\mathrm{A}\cup \mathrm{B}$ b. $\mathrm{A}\cap \mathrm{B}$
iii. Sangeeta’s monthly income is Rs 25,000. She spent 90% of her income and donated 3% for socially useful causes. How much money did she save? VIEW SOLUTION

(a) i. In the A.P. 2, –2, –6, –10, ...... common difference (d) is:
(A) –4 (B) 2 (C) –2 (D) 4
ii. For the quadratic equation $x^2+10x-7=0$, 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? (A) 1/ 3 (B) 1 /2 (C) 1 (D) 1/ 6

(b)  i. First term and common difference of an A.P. are 12 and 4 respectively. If tn = 96, find n.
ii. If $\left[\begin{array}{cc}4& 5\\ m& 3\end{array}\right]=22$, then find the value of m.
iii. Solve the following quadratic equation: $x^2+8x+15=0$. VIEW SOLUTION

(a) i. Smita has invested Rs 12,000 to purchase shares of FV  Rs 10 at a premium of Rs 2. Find the number of shares she purchased. Complete the given activity to get the answer. Activity: FV =  Rs 10, Premium =  Rs 2 
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: 

Places	Supply of electricity (Thousand units)	Measure of central angle
Roads	4	$\frac{4}{30}\times 360°=48°$
Factories	12	$\left(\frac{}{}\right)\times 360°=144°$
Shops	6	$\frac{6}{30}\times 360°=\left(\right)$
Houses	8	$\left(\frac{}{}\right)\times 360°=\left(\right)$
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

(b) 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 VIEW SOLUTION

(a) Amit saves certain amount every month in a specific way. In the first month he saves Rs 200, in the second month Rs 250, in the third month Rs 300 and so on. How much will be his total savings in 17 months?
 

(b) 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.

(c) mt. Malhotra purchased solar panels for the taxable value of Rs 85,000. She sold them for Rs 90,000. The rate of GST is 5%. Find the ITC of Smt. Malhotra. What is the amount of GST payable by her?

(d) Solve the following simultaneous equations graphically: x + y = 0; 2x –y = 9.  VIEW SOLUTION

(a) 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

Determine x.

(b) Two taps together can fill a tank completely in $3\frac{1}{13}$ minutes. The smaller tap takes 3 minutes more than the bigger tap to fill the tank. How much time does each tap take to fill the tank completely?  VIEW SOLUTION

(a) The co-ordinates of the point of intersection of lines $ax+by=9$ and $bx+ay=5$ is $\left(3, -1\right)$. Find the values of a and b. 
 

(b) The following frequency distribution table shows the distances travelled by some rickshaws in a day. Observe the table and answer the following questions

Class(Daily distance travelled in km)	Continuous classes	Frequency(Number of rickshaws)	Cumulative frequency(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? VIEW SOLUTION