I P.U.C Mathematics Model Paper 2024-25

• This is a Model Question Paper for I P.U.C Mathematics (35) for the year 2024-25
• The maximum marks for the paper are 80 and the duration is 3 hours
• The paper has five parts: A, B, C, D, and E, and all parts are to be answered

Part A: Multiple Choice Questions

• Part A consists of multiple-choice questions, each carrying 1 mark and totaling 15 marks for the section
• If U is a universal set and A is a subset of U, then U' ∩ A = Ø
• If (x - 1, y + 2) = (1, 5), then the coordinates (x, y) are (2, 3)
• Domain of sinx : (-∞, ∞)
• Domain of cotx: (-∞, ∞) - {nπ: n ∈ Z}
• Range of cosx: [-1, 1]
• The conjugate of a complex number -5 + 3i is -5 - 3i
• The solution to the inequality -8 ≤ 5x - 3 < 7 is -1 ≤ x < 2
• If 1/6! + 1/7! = x/8!, then x = 64
• 10C1+ 10C2 + 10C3 + ... + 10C10 = 1023
• With a₁ = 1 = a₂ and an = an-1 + an-2, the 4th term (a₄) of the sequence is 3
• The equation of the line parallel to the x-axis and passing through the point (-2, 3) is y = 3
• The length of the latus rectum of the parabola y² = -9x is 9
• The eccentricity of the hyperbola x²/9 - y²/16 = 1 is 5/3
• The perpendicular distance from the point P(6, 7, 8) to the zx-plane is 7
• The shortest distance of the point (a, b, c) from the x-axis is √(b² + c²)
• Statements 1 and 2 are both true, and statement 2 is a correct explanation for statement 1
• The Mean deviation about median for first 5 natural numbers is 3/2
• When two coins are tossed once, the number of simple events in the sample space is 4

Part A: Fill in the Blanks

• If A = {2, 4, 6, 8} and B = {6, 8, 10}, then n(A - B) = 2
• Given 5x - 3 < 3x + 1, where x is a natural number, the number of values for x is 1
• If 15C3r = 15C3+r, then r = 2
• For the line (k-5)x − (4-k²)y + k² - 7k + 6 = 0 to be parallel to the y-axis, the values of k are k=5, k=-2
• The derivative of f(x) = 4x at x = 0 is 4

Part B: Answer Any Six Questions

• If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, and C = {15, 17}, then A ∩ (B ∪ C) = {7, 9, 11}
• In a circle of diameter 40 cm where the length of a chord is 20 cm, the length of the minor arc of the chord can be determined using geometry and trigonometry
• (sin 3x + sin x) sin x + (cos 3x - cos x) cos x = 0 can be proven using trigonometric identities
• If x + iy = (a + ib) / (a - ib), then x² + y² = 1

Part C: Answer Any Six Questions

• Given U = {1, 2, 3, 4, 5, 6}, A = {2, 3}, and B = {3, 4, 5}, verify (A ∪ B)' = A' ∩ B'
• Determine the domain and range of the relation R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}
• Show that tan 3x tan 2x tan x = tan 3x - tan 2x - tan x using trigonometric identities
• If (x + iy)³ = u + iv, then show that u/x + v/y = 4(x² - y²)
• Find all pairs of consecutive odd positive integers, both smaller than 10, whose sum is more than 11
• Evaluate (√3 + √2)⁶ - (√3 - √2)⁶
• If the angle between two lines is π/4 and the slope of one line is 1/2, find the slope of the other line
• Find the equation of the set of points P such that its distances from A(3, 4, -5) and B(-2, 1, 4) are equal
• Find the derivative of tan x with respect to x from the first principle

Part E: Answer the Following Question

• Given sin x = 1/4 and x is in quadrant II, find sin(x/2), cos(x/2), and tan(x/2)
• Define ellipse and derive the equation of the ellipse in standard form as x²/a² + y²/b² = 1
• Find the derivative of f(x) = (x⁵ - cos x) / sin x with respect to x
• Find the sum of the series up to n terms: 5 + 55 + 555 + ...

Part F: For Visually Challenged Students Only

• The equations for the x and y axes are, the equation x = 0 represents the y-axis, and the equation y = 0 represents the x-axis