All questions
- Q.2 (A)(i) Complete the following table to draw the graph of x + 2y = 4.Activity :x–2____y____1(x, y)________ Answer: x = –2 gives y = 3; y = 1 gives x = 2; points (–2, 3) and (2, 1). x + 2y = 4. When x = –2: –2 + 2y = 4, so 2y = 6, y = 3 → (–2, 3).... 1
- Q.2 (A)(ii) Complete the following activity to form a quadratic equation.Activity :I am a quadratic equation. → My standard form is ____ . → My roots are 5 and 12. → Sum of my roots ____ . → Product of my roots ____ . → My quadratic equation is ____… Answer: x² - 17x + 60 = 0 Standard form: ax² + bx + c = 0 , a ≠ 0 . Sum of roots = 5 + 12 = 17 . Product of roots = 5 × 12 = 60 . Equation:... 1
- Q.2 (A)(iii) Pushpmala has invested ₹ 24,000 and purchased share of FV ₹ 20 at a premium of ₹ 4. Complete the following activity to find the number of shares she purchased.Activity :FV = ₹ 20Premium = ₹ 4MV = FV + ____ = 20 + ____ = ₹ 24Number of sha… Answer: 1000 shares MV = FV + premium = 20 + 4 = ₹ 24. Number of shares = Total investment ÷ MV = 24,000 ÷ 24 = 1000. 1
- Q.2 (B)(i) Solve the following simultaneous equations : x + y = 3; 3x – 2y = 4 Answer: x = 2, y = 1 Multiply x + y = 3 by 2: 2x + 2y = 6. Add to 3x – 2y = 4: 5x = 10, so x = 2. Then y = 3 – 2 = 1. Check: 3(2) – 2(1) = 4... 1
- Q.2 (B)(ii) Solve the following quadratic equation by factorisation method : \(m^2 + 14m + 13 = 0\) Answer: m = –1 or m = –13 m² + 13m + m + 13 = 0 m(m + 13) + 1(m + 13) = 0 (m + 13)(m + 1) = 0 So m + 13 = 0 or m + 1 = 0 , giving m = –13 or... 1
- Q.2 (B)(iii) Find the 19th term of the following A.P. : 7, 13, 19, 25, ... Answer: t₁₉ = 115 a = 7, d = 13 – 7 = 6. t_n = a + (n - 1)d , so t₁₉ = 7 + 18 × 6 = 7 + 108 = 115 . 1
- Q.2 (B)(iv) A share is sold for the market value of ₹ 2,000. Brokerage is paid at the rate of 0.5%. What is the amount received after the sale ? Answer: ₹ 1,990 Brokerage = 0.5% of 2000 = 0.5/100 × 2000 = ₹ 10. On a sale, brokerage is deducted: amount received = 2000 – 10 = ₹ 1,990. 1
- Q.2 (B)(v) The following table shows the number of students and the time they utilized daily for their studies. Find the mean time spent by the students for their studies.Class Time (In hours)Class Marks (xi)No. of Students (fi)fixi0–218082–4314424–6… Answer: Mean time = 5 hours Σ f_i = 8 + 14 + 18 + 10 + 10 = 60 Σ f_i x_i = 8 + 42 + 90 + 70 + 90 = 300 x = Σ f_i x_i/Σ f_i = 300/60 = 5 hour... 1
- Q.3 (A)(i) Shri Maniklal has purchased 300 shares of F.V. ₹ 100, for M.V. ₹ 120. Company has paid dividend at 7%. Complete the following activity to find the rate of return on his investment.Activity :F.V. = ₹ 100, Number of shares = 300, Market valu… Answer: Rate of return = 55/6 % ≈ 5.83% (a) Sum invested = 120 × 300 = ₹ 36,000. (b) Dividend per share = 100 × 7/100 = ₹ 7; total dividend... 1
- Q.3 (A)(ii) A two digit number is to be formed from the digits 2, 3, 5 without repetition of the digits. Complete the following activity to find the probability that the number so formed is an odd number.Activity :Let S be the sample space.S = {23, 2… Answer: P(A) = 2/3 S = 23, 25, 32, 35, 52, 53, n(S) = 6. Odd numbers end in 3 or 5: A = 23, 25, 35, 53, n(A) = 4. P(A) = n(A)/n(S) = 4/6 = 2... 1
- Q.3 (B)(i) Solve the following simultaneous equations by Cramer’s rule : 4x + 3y = 18; 3x – 2y = 5 Answer: x = 3, y = 2 D = beginvmatrix 4 & 3 \\ 3 & -2 endvmatrix = -8 - 9 = -17 D_x = beginvmatrix 18 & 3 \\ 5 & -2 endvmatrix = -36 - 15 =... 1
- Q.3 (B)(ii) Solve the following quadratic equation by using formula method : \(x^2 - 2x - 3 = 0\) Answer: x = 3 or x = –1 a = 1, b = –2, c = –3. b² - 4ac = 4 + 12 = 16 . x = -b ± √(b² - 4ac)/2a = 2 ± 4/2 x = 6/2 = 3 or x = -2/2 = -1 . 1
- Q.3 (B)(iii) A committee of two members is to be formed from three boys and two girls. Find the probability of the following events :Event A : At least one girl must be a member of the committee.Event B : Committee must be of one boy and one girl. Answer: P(A) = 7/10, P(B) = 3/5 Let the boys be B₁, B₂, B₃ and the girls G₁, G₂. S = B₁B₂, B₁B₃, B₂B₃, B₁G₁, B₁G₂, B₂G₁, B₂G₂, B₃G₁, B₃G₂, G... 1
- Q.3 (B)(iv) In a general store the prices of different articles and its demand is shown in the following frequency distribution table. Find the Median of the prices.Price in RupeesNo. of ArticlesLess than 2014020—4010040—608060—806080—10020 Answer: Median price = ₹ 32 Treat \"less than 20\" as 0–20. Cumulative frequencies: 140, 240, 320, 380, 400. N = 400, N/2 = 200. The cumulat... 1
- Q.4 (i) Find the value of ‘m’ if the quadratic equation \((m - 12)x^2 + 2(m - 12)x + 2 = 0\) has real and equal roots. Answer: m = 14 a = m – 12, b = 2(m – 12), c = 2. For real and equal roots, b² - 4ac = 0 : 4(m-12)² - 8(m-12) = 0 4(m-12) [(m-12) - 2] = 0 4(... 1
- Q.4 (ii) A farmer borrows ₹ 1,000 and agrees to repay with a total interest of ₹ 140, in 12 instalments. Each instalment being less than the preceding instalment by ₹ 10. What should be the amount of his first and last instalment ? Answer: First instalment ₹ 150, last instalment ₹ 40 Total amount repaid = 1000 + 140 = ₹ 1140. The instalments form an A.P. with n = 12, d... 1
- Q.4 (iii) The following table shows the marks of 180 students in Mathematics.MarksNo. of Students0—102510—20x20—303030—402x40—5065Find the value of ‘x’ and draw histogram. Answer: x = 20 25 + x + 30 + 2x + 65 = 180, so 3x + 120 = 180, 3x = 60, x = 20. Frequencies: 0–10: 25, 10–20: 20, 20–30: 30, 30–40: 40, 40–5... 1
- Q.5 (i) Draw the graphs representing the equation 2x = y + 2 and 4x + 3y = 24 on the same graph paper. Find the area of the triangle formed by these lines and the X-axis. Answer: Area = 10 square units 2x = y + 2, i.e. y = 2x – 2: points (1, 0), (0, –2), (3, 4). 4x + 3y = 24: points (6, 0), (0, 8), (3, 4). Plo... 1
- Q.5 (ii) The following pie-diagram shows percentage of persons according to blood group in a blood group checking camp. Answer the following questions :[Pie diagram: O – 45%, B – 30%, A – 20%, AB – 5%](a) Find the measure of central angle for each bl… Answer: (a) O = 162°, B = 108°, A = 72°, AB = 18°; (b) 2000 persons (a) Central angle = percentage/100 × 360^° : O: 45/100 × 360 = 162^° ; B... 1
- Q.1 (A)(i) \(\begin{vmatrix} 1 & 2 \\ 3 & 4 \end{vmatrix}\). Write the degree of the given determinant. Answer: B. 2 Answer: (B) 2 The determinant has 2 rows and 2 columns, so it is a determinant of order (degree) 2. 1
- Q.1 (A)(ii) From the following equations which one is the quadratic equation ? Answer: B. x(x + 5) = 2 Answer: (B) x(x+5)=2 x(x+5)=2 ⇒ x²+5x-2=0 , a polynomial equation of degree 2. (A) gives x³+3x-5=0 (degree 3), (C) i... 1
- Q.1 (A)(iii) Find the common difference of the following A.P. : 4, 4, 4, ... Answer: D. 0 Answer: (D) 0 d = t₂ - t₁ = 4 - 4 = 0 . Every term is the same, so the common difference is 0. 1
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- The general solution of \(\frac{dy}{dx}+\frac yx=x^2\) is Answer: B. xy=x⁴/4+C I.F. =e^(∫ dx/x)=x ; d/dx(xy)=x³⇒ xy=x⁴/4+C . 1