Board Paper of Class 10 2020 Math - Solutions

(a) (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?
(A) $\frac{5}{x}-3=x^2$ (B) $x\left(x+5\right)=4$ (C) $n-1=2n$ (D) $\frac{1}{x^2}\left(x+2\right)=x$
(iii)
For simultaneous equations in variables x and y, if $D_x=49, D_y=-63, D=7,$ then what is the value of x? (A) 7 (B) –7 (C) $\frac{1}{7}$ (D) $\frac{-1}{7}$
(iv)
If $n\left(A\right)=2, P\left(A\right)=\frac{1}{5}$ , then n(S) = ? (A) $\frac{2}{5}$ (B) $\frac{5}{2}$ (C) 10 (D) $\frac{1}{3}$
 

(b) 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$2x^2-5x+7=0$. 
iv. If 15x + 17y = 21 and 17x + 15y = 11, then find the value of x + y.  VIEW SOLUTION

(a) (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 $S_{27}$.
(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.  

(b) (i) Find the value of the determinant:  
$\left[\begin{array}{cc}\frac{7}{3}& \frac{5}{3}\\ \frac{3}{2}& \frac{1}{2}\end{array}\right]$
(ii)
Solve the quadratic equation by factorization method: 
$x^2-15x+54=0$
(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 $L=10$, $f_1=70$, $f_0=58$, $f_2=42$, $h=2$, then find the mode by using formula.   VIEW SOLUTION

(a) (i)

Age group(in years)	Number of Persons	Measure of central angle
20-25	80	$\frac{\left(\right)}{200}\times 360=\left(\right)$
25-30	60	$\frac{60}{200}\times 360=\left(\right)$
30-35	35	$\frac{35}{200}\times \left(\right)=63$
35-40	25	$\frac{25}{200}\times 360=\left(\right)$
Total	200

(ii)
Shri Shantilal has purchased 150 shares of FV Rs 100, for MV of Rs 120, Company has paid dividend at 7%, then to find the rate of return on his investment, complete the following activity:

(b)

(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. VIEW SOLUTION

(a) Represent the following data by histogram: 

Price of Sugar (per kg in Rs)	Number of weeks
18-20	4
20-22	8
22-24	22
24-26	12
26-28	6
28-30	8

(b) One person borrows Rs 4,000 and agrees to repay with a total interest of Rs 500 in 10 instalments. Each instalment being less than the preceding instalment by Rs 10. What should be the first and the last instalments?

(c) 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.  VIEW SOLUTION

(a) Convert the following equations into simultaneous equations and solve: 
$\sqrt{\frac{x}{y}}=4, \frac{1}{x}+\frac{1}{y}=\frac{1}{xy}$

(b) A dealer sells a toy for Rs 24 and gains as much percent as the cost price of the toy. Find the cost price of the toy.  VIEW SOLUTION