Solve English ma karna ha

Here are the solutions to your questions in English: 9. The system of linear equations 4x - 12y = k and x = 3y + 4 is inconsistent. Which of the following is true for the value of k? Step 1: Write the given equations in the standard form ax + by = c. The first equation is 4x - 12y = k. The second equation is x = 3y + 4, which can be rewritten as x - 3y = 4. Step 2: Apply the condition for an inconsistent system. For a system of two linear equations a_1x + b_1y = c_1 and a_2x + b_2y = c_2 to be inconsistent, the condition is (a_1)/(a_2) = (b_1)/(b_2) ≠ (c_1)/(c_2). From our equations, we have a_1 = 4, b_1 = -12, c_1 = k and a_2 = 1, b_2 = -3, c_2 = 4. Let's calculate the ratios: (a_1)/(a_2) = (4)/(1) = 4 (b_1)/(b_2) = (-12)/(-3) = 4 (c_1)/(c_2) = (k)/(4) Step 3: Use the inconsistency condition to find the value of k. (a_1)/(a_2) = (b_1)/(b_2) ≠ (c_1)/(c_2) 4 = 4 ≠ (k)/(4) This implies that 4 ≠ (k)/(4). Multiply both sides by 4: 4 × 4 ≠ k 16 ≠ k Therefore, the value of k must not be equal to 16. The final answer is C. 10. The diameter of a circle which passes through (2, -3) and whose center is (1, 1) is: Step 1: Find the radius of the circle. The center of the circle is (1, 1) and it passes through the point (2, -3). The radius r is the distance between the center and any point on the circle. We use the distance formula: d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2). r = sqrt((2 - 1)^2 + (-3 - 1)^2) Step 2: Calculate the radius. r = sqrt((1)^2 + (-4)^2) r = sqrt(1 + 16) r = sqrt(17) Step 3: Find the diameter of the circle. The diameter D is twice the radius: D = 2r. D = 2sqrt(17) The final answer is A. 11. Two dice are thrown simultaneously. The probability of getting both odd numbers is: Step 1: Determine the total number of possible outcomes. When two dice are thrown, each die has 6 possible outcomes. So, the total number of possible outcomes is 6 × 6 = 36. Step 2: Determine the number of favorable outcomes. For both dice to show odd numbers, each die must land on an odd number. The odd numbers on a single die are \1, 3, 5\, which are 3 possibilities. So, the number of favorable outcomes (both odd) is 3 × 3 = 9. These outcomes are: (1,1), (1,3), (1,5), (3,1), (3,3), (3,5), (5,1), (5,3), (5,5). Step 3: Calculate the probability. The probability of an event is given by the formula P(event) = Number of favorable outcomesTotal number of outcomes. P(both odd numbers) = (9)/(36) P(both odd numbers) = (1)/(4) The final answer is B. 12. Raju is wearing a conical birthday cap of diameter 16 cm and height 24 cm. The slant height of the cap is: Step 1: Find the radius of the cone. The diameter of the base of the cone is D = 16 cm. The radius r = (D)/(2) = (16)/(2) = 8 cm. The height of the cone is h = 24 cm. Step 2: Use the formula for the slant height. For a cone, the slant height l, radius r, and height h are related by the Pythagorean theorem: l^2 = r^2 + h^2. Step 3: Calculate the slant height. l^2 = (8)^2 + (24)^2 l^2 = 64 + 576 l^2 = 640 l = sqrt(640) Step 4: Simplify the slant height. l = sqrt(64 × 10) l = sqrt(64) × sqrt(10) l = 8sqrt(10) cm The final answer is A. 13. The quadratic equation 4x^2 + 8n = 0 has real and distinct roots. Which of the following is true for the value of n? Step 1: Identify the coefficients of the quadratic equation. The given quadratic equation is 4x^2 + 8n = 0. Comparing it with the standard form ax^2 + bx + c = 0, we have: a = 4 b = 0 (since there is no x term) c = 8n Step 2: Apply the condition for real and distinct roots. A quadratic equation has real and distinct roots if its discriminant D = b^2 - 4ac is greater than 0. Step 3: Calculate the discriminant and solve the inequality for n. Substitute the values of a, b, c into the discriminant formula: D = (0)^2 - 4(4)(8n) D = 0 - 128n D = -128n For real and distinct roots, D > 0: -128n > 0 To solve for n, divide both sides by -128. Remember to reverse the inequality sign when dividing by a negative number: n < (0)/(-128) n < 0 Therefore, the value of n must be less than 0. The final answer is D. 3 done, 2 left today. You're making progress.