Act like a bit slow learner teach me this worksheet clearly, visually and practically that i can't fail even if I try---SRI AADYA
Class. JUNIORS
Duration: 2Hrs
BRIDGE COURSE TEST
MATHEMATICS
Date:28.05.2025
Max Marks: 60
Answer all the questions. Each question carries TWO marks
15x2=30M
1. Find the values of 'm' the quadratic equation x² - 15 - m(2x - 8) = 0 has equal roots
2. If x² + 2px - 2p + 8 > 0 for all real values of x, then the set of all possible values of 'p' are ____.
3. Let Sₙ denote the sum of the first n terms of an A.P. If S₄=16 and S₆=-48, then S₁₀ is ____.
4. The sum of the first three terms of a G.P. is 21/2 and their product is 27. Find the common ratio ____.
5. If cos θ = -3/5 ; π < θ < 3π/2, then tan θ/2 ?
6. If α is a root of the equation 25 cos² θ + 5 cos θ - 12 = 0 for π/2 < α < π, then sin 2α ?
7. Simplify cos 100°. cos 40° + sin 100°. sin 40° =
8. Find the value of k, for which the points (7,-2),(5,1),(3,k) are collinear.
9. Find the value of 'x' if the slope of the line passing through (2,5) and (x,3) is 2.
10. lim_(x→3) (x² - 8x + 15)/(x² - 9)
11. If y = (a - x)/(a + x) ; x ≠ -a. find dy/dx
12. If f(x) = 1 + x + x² + x³ + ........ + x¹⁰⁰, then f'(1) is ____.
13. ∫ (1 + 2/x - 3/x²) dx
14. Evaluate ∫₀ᵃ (a²x - x³) dx
15. Find sin² (π/10) + sin² (9π/10)
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Let's solve the first three questions from your bridge course test. Question 1 asks for values of m where a quadratic has equal roots. We expand the equation, set the discriminant to zero, and solve to get m equals 3 or 5. Question 2 requires a quadratic to be always positive, which means the discriminant must be negative, giving us negative 4 less than p less than 2. Question 3 uses the arithmetic progression sum formula with the given conditions to find that S ten equals negative 320.
Now let's tackle questions 4 through 6. Question 4 involves a geometric progression where we use the product to find the middle term a equals 3, then solve for the common ratio to get r equals 2 or one half. Question 5 uses the half-angle formula with cosine negative three fifths in the third quadrant, giving us tangent theta over 2 equals negative 2. Question 6 solves a quadratic in cosine theta, then uses the given range to find sine 2 alpha equals negative 24 over 25.