Please, fill out the information below to continue. NAME E,MAIL PHONE NUMBER 1. Express in partial fractions.2/(x-4) + 3/(x-6)1/(x+3) + 4/(x-4)4/(x+3) + 2/(x+1)5/(x-3) + 3/(x+4)2. Sinθ Cotθ is equal toCosecθTanθSinθSecθCosθ3. Find the tension T in the figure below if the system is in equilibrium. 200N/√3100N/√3100N300N/√34. Resolve into partial fractions2/(x-3) + 2/(2-x)1/(x+2) - 3/(2-x)7/(x+3) - 4/(x+2)1/(x+2) - 2/(4-x)5. A 4N force acting an angle to the horizontal has a horizontal component of 1N. The vertical component of the force is1N0.13N4N3.87N6. If tan θ + sec θ = 2/√3 and θ is a positive acute angle, find the value of sin θ.sin θ = -1/7sin θ = 1/8sin θ = 1/7sin θ = -1/87. In the figure, the point on segment JK that is four times as far from K as it is from J is: (2,0)(0, 2)(-1/3, 7/3)(-1, 3)8. The speed s of a particle after t seconds is given by v = 7 + 25t -4t² . Find the acceleration of the particle after 2 seconds.25 m/s²41 m/s²9 m/s²28 m/s²9. ∫sin 5x dx1/5sinx + C-1/5 sin 5x + C-1/5 cos5x + C1/5cos5x + C10. If the radius of the base of a cone is decreasing at 2 cm/s, find the rate of increase in volume when the radius of the base is 5 cm.25π cm³/s50π cm³/s10π cm³/s20.5π cm³/s11. A car starts from rest and moves with a uniform acceleration of 30m/s² for 20s. Calculate the distance covered at the end of the motion6km12km24km18km12. Given that sin(θ+α) = sinθcosα + cosθsinα, find the value of sin 75°4 (√6+√2)2 (√6+√2)1/4 (√6+√2)1/2 (√6+√2)13. A coin is tossed 3 times. What is the probability of getting 2 heads and a tail in any order?1/21/41/83/814. Given that y3=log10 100000000, find y1510215. Simplify the expression0-111/216. The gradient of a curve is given by dy/dx = 3x² - 8x + 3. If the curve passes through the origin, find the equation of the curve.y = x³ - 4x² + 3xy = x³ + 3xy = x³ - 4x² - 3xy = x³17. Evaluate the determinant 20-2118. Find the values of x for whichis equal to zero2 or 64 or 1/2-3 or 54 or -3/219. The gradient of a curve is given byx² - 4x + 3If the curve passes through the point (3, 1). Find the minimum point on the curve(3, 1)(1, 7)(2, 9)(0, 6)20. The seventh term of the G.P 16/9, -8/3, 4, ... is-9/216-32/381/421. Solve the equation 3x + 10 = x²-5 or 25 or -25 or 2-5 or -222. Find the value of sin (-150)°-0.20.2-0.50.523. Subtract the polynomials: (-x2 + 5 x) - (6 x2 + x - 2)-7x²+4x+25x²+6x-2-5x²+6x+25x²+6x24. If tanx = 12/5, find the value of sinx, 0° ≤ x ≤ 90°17/1822/452/312/1325. Cards are drawn from a pack of 52 playing cards one at a time. Calculate the probability of drawing without replacement at least one red card1/10231/10277/10217/10226. Find the value of cosec 90°1-12027. Given that find the value of x that satisfiesx + y -2z = 1, x+z = -1 and 2x -2y + z = 11-10228. Expand (1-x)³, using binomial theorem. Hence find the value of (0.999)³ correct to five decimal places.1 - 3x + 3x² - x³, 0.101 - 3x + 3x² - x³, 0.997001 - 3x + 3x² - x³, 11 - 3x + 3x² - x³, 0.99729. GATE Academy registers 300 candidates for an examination. 180 of the candidates offer Economics and 70 offer Geography. 80 candidates offer neither Economics nor Geography.The number of candidates offering both Economics and Geography is3040605030. The points of intersection of the graphs of y = x² + 2 and y = 2x + 5 when drawn on the same set of axes are(1, 0) and (-3, 0)(-1, 11) and (3, 3)(3, 0) and (-1, 0)(-1, 3) and (3, 11)31. Three boys play a game of luck in which their respective chances of winning are 1/2, 1/3 and 1/4. What is the probability that one and only one of the boys wins the game?16/1912/2111/241/232. If , find x±2±3±54533. Find the angles between 0° and 360° whose cosine is 0.6543.4°358°242°49.5°34. Find the value of θ (0° ≤ θ ≤ 90°), when sin2 θ - 3 sin θ + 2 = 090°70°60°80°35. In which quadrant does the point (-3,4) lie?2nd quadrant1st quadrant3rd quadrant4th quadrant36. If sin (x + y) = 1 and cos (x - y) = 3√232, find x and y.x = 21° and y = 48°x = 45° and y = 45°x= 60° and y =30°x = 30° and y = 90°37. Differentiate the function w.r.t x: y = 4(x² - 3)x²-38x6x8x²38. A G.P has 6 and 24 as its 2nd and 4th terms respectively. The sum of the first four terms is4066604539. Differentiate wrt x:x³(x - 1)(x²+2)x3x+21+x²x³ + 3x²(x-1)40. An object dropped from rest has position s = 7t² metres below its starting point. At what time does the object have velocity of 35 m/s.3 s14 s2.5 s2 s41. Given that dy/dx = 6x² + 5x, find the function which passes through the point (2, 30).y = 2x³ + 5/2 x² + 4y = 6x² + 5xy = x³ + 2x² + 4y = 2x³ + 5/2 x² - 442. A bag contains 6 red balls, 12 white balls and 9 green balls. A ball is selected at random. What is the probability that it is not a green ball?4/95/92/31/343. Evaluate:21/241/444. In the diagram above, a car, with its engine off, rolls down a slope with uniform speed. Which one of the following is correct about the frictional force between the car and the road?in the direction ORin the direction OSin the direction OQzeroin the direction OP45. Find the value ofsin 225°-√21/√2√2-1/√246. Solve for y: 25y + 3(5y) = 4-4 or 0101 or 447. A body of mass 5kg initially at rest is acted upon by two mutually perpendicular forces 12N and 5N as shown in the figure. If the particle moves in the direction OA, calculate the magnitude of the acceleration. 3.40m/s²2.60m/s²0.40m/s²0.26m/s²1.40m/s²48. Differentiate the functions wrt x:(x-2)(3x+5)4x+43x²6x-13x+249. A die is thrown and a coin is tossed. Find the probability that the die shows an even number and the coin shows a head11/24/61/41/650. Solve the equation 8 sin x = 3 for 0° ≤x≤ 360°100°98°17°22°51. Without using tables, evaluate sin(- 1320°)-1/20.866-0.8661/252. The value of T in the figure below is40N20N10N11.8N53. Find ∫cos2x cos 3x dx1/10 sin 5x + C1/10 sin 5x + 1/2 sinx + C-1/10 sin 5x + 1/2 sinx + C1/10 sin 5x + 1/2 cosx + C54. A boat is towed with a net force of 16000N acting at an angle of 60º to the water surface. If the boat moves with an acceleration of 20m/s², calculate its mass.400kg533.3kg133.3kg692.8kg55. Evaluate:log √40 + log √2 - log√821√100.556. At what rate in cm² per cm is the area of the circle changing w.r.t its radius when the radius is 5cm?3πcm²/cm20πcm²/cm5πcm²/cm10πcm²/cm57. Simplify: (32y + 1 × 9y × 42y) ÷ (18y × 2y × 62y)122y33y58. If log 4 = 0.6021, evaluate:log 40 - 3log 400-7.7958-7.2042-6.2042-6.795859. Use the binomial theorem to expand (1 + 5x)². Hence or otherwise, find the value of (1.05)² correct to two decimal places.1 + 10x + 25x²; 1.101 + 5x; 1.10211 + 5x + 20x²; 1.101 + 25x²; 1.160. PQRS is a quadrilateral in which, PS is parallel to QR. PQ = 16cm, SR = 15 cm and angle QPS = 60° and angle PSQ = 44°.Calculate <QRS24°57°67°64°61 out of 60Time is Up!