Maharashtra Board Class 10 MATHEMATICS-ALGEBRA-71-N-913 Question Paper 2023 with Solution PDF pdf is available for download here.
The question paper was divided into two sections - Section A for objective questions and Section B for subjective questions.
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To draw the graph of \(4x + 5y = 19\), find \(y\) when \(x = 1\):
Out of the following equations, which one is not a quadratic equation?
For the given A.P. \(a = 3.5, \, d = 0\), find \(t_n = \, ?\)
If \(n(A) = 2\), \(P(A) = \frac{1}{5}\), then find \(n(S) = ?\)
Find the value of the following determinant:
\[ \begin{vmatrix} 4 & 3
2 & 7 \end{vmatrix} \]
Find the common difference of the following A.P.: \[ 2, \, 4, \, 6, \, 8, \ldots \]
On a certain article, if the rate of CGST is 9%, then what is the rate of SGST?
If one coin is tossed, write the sample space ‘S’.
i.Complete the following activity and find the value of \(x\):
\[ \begin{aligned} 5x + 3y &= 9 \quad ...(I)
2x - 3y &= 12 \quad ...(II) \end{aligned} \]
Complete the following activity to determine the nature of the roots of the quadratic equation \(x^2 + 2x - 9 = 0\):
Complete the following table using the given information:
\[ \begin{array}{|c|c|c|c|} \hline \textbf{Sr. No.} & \textbf{FV (₹)} & \textbf{Share is at} & \textbf{MV (₹)}
\hline 1 & 100 & Par & \boxed{100}
\hline 2 & \boxed{75} & Premium ₹500 & 575
\hline 3 & 10 & \boxed{Discount ₹5} & 5
\hline 4 & 200 & Discount ₹50 & \boxed{150}
\hline \end{array} \]
Solve the following simultaneous equations: \[ x + y = 4 \quad and \quad 2x - y = 2 \]
Write the following equation in the form \(ax^2 + bx + c = 0\), then write the values of \(a, b, c\):
\[ 2y = 10 - y^2 \]
Write an A.P. whose first term is \(a = 10\) and common difference \(d = 5\).
A courier service agent charged ₹590 to courier a parcel from Nashik to Nagpur. In the tax invoice, the taxable value is ₹500 on which CGST = ₹45 and SGST = ₹45. Find the rate of GST charged for this service.
Observe the following table and find the Mean:
\[ Assumed Mean (A) = 300 \]
\[ \begin{array}{|c|c|c|c|} \hline Class Interval & Class Mark (x_i) & Frequency (f_i) & f_i d_i
\hline 200 - 240 & 220 & 5 & -400
240 - 280 & 260 & 10 & -400
280 - 320 & 300 & 15 & 0
320 - 360 & 340 & 12 & 480
360 - 400 & 380 & 8 & 640
\hline \textbf{Total} & & \Sigma f_i = 50 & \Sigma f_i d_i = 320
\hline \end{array} \]
Form a ‘Road Safety Committee’ of two, from 2 boys (B\textsubscript{1}, B\textsubscript{2}) and 2 girls (G\textsubscript{1}, G\textsubscript{2}). Complete the activity to write the sample space:
Fill in the boxes with the help of given information:
Tax invoice of services provided (Sample)
Food Junction, Khed-Shivapur, Pune
Invoice Date: 25 Feb., 2020
\[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline \textbf{SAC} & \textbf{Food Items} & \textbf{Qty} & \textbf{Rate (₹)} & \textbf{Taxable Amount (₹)} & \textbf{CGST} & \textbf{SGST} & \textbf{Amount (₹)}
\hline 9963 & Coffee & 1 & 20 & 20.00 & 2.5% = 0.50 & 2.5% = 0.50 & 21.00
\hline 9963 & Masala Tea & 1 & 10 & 10.00 & 2.5% = 0.25 & 2.5% = 0.25 & 10.50
\hline 9963 & Masala Dosa & 2 & 60 & 120.00 & 2.5% = 3.00 & 2.5% = 3.00 & 126.00
\hline \textbf{Total} & & & & 150.00 & & &
\hline \textbf{Grand Total} & & & & & & & \textbf{₹157.50}
\hline \end{array} \]
Solve the following simultaneous equations using Cramer’s Rule: \[ 4m + 6n = 54 \quad and \quad 3m + 2n = 28 \]
Solve the following quadratic equation by formula method: \[ x^2 + 10x + 2 = 0 \]
A two-digit number is formed with digits 2, 3, 5, 7, 9 without repetition. Find 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.
The frequency distribution table shows the number of mango trees in a grove and their yield of mangoes. Find the median of the data:
\[ \begin{array}{|c|c|} \hline No. of Mangoes & No. of Trees (f)
\hline 50 - 100 & 33
100 - 150 & 30
150 - 200 & 90
200 - 250 & 80
250 - 300 & 17
\hline \end{array} \]
If the first term of an A.P. is \(p\), second term is \(q\), and last term is \(r\), then show that the sum of all terms is \[ S = (q + r - 2p) \times \frac{(p + r)}{2(q - p)} \]
Show the following data by a frequency polygon:
\[ \begin{array}{|c|c|} \hline Electricity Bill (₹) & Families (f)
\hline 200 - 400 & 240
400 - 600 & 300
600 - 800 & 450
800 - 1000 & 350
1000 - 1200 & 160
\hline \end{array} \]
The sum of the squares of five consecutive natural numbers is 1455. Find the numbers.
Draw the graph of the equation \(x + 2y = 4\). Find the area of the triangle formed by the line intersecting the X-axis and Y-axis.
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.
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