Q.9001·Miscellaneous·2016·EasyLet Q be the image of the point P(–2, 1, –5) in the plane 3x – 2y + 2z + 1 = 0. Consider the following : 1.The direction ratios of the line segment PQ are <3, –2, 2>. 2.The sum of the squares of direction cosines of the line segment PQ is unity. Which of the above statements is/are correct ?View question
Q.9002·Miscellaneous·2016·EasyA line L passes through the point P(5, –6, 7) and is parallel to the planes x + y + z = 1 and 2x – y – 2z = 3. What are the direction ratios of the line of intersection of the given planes ?View question
Q.9003·Miscellaneous·2016·EasyA line L passes through the point P(5, –6, 7) and is parallel to the planes x + y + z = 1 and 2x – y – 2z = 3. What is the equation of the line L ?View question
Q.9004·Miscellaneous·2016·EasyIn a right-angled triangle ABC, if the hypotenuse AB = p, then what is AB . AC + BC . BA + CA . CB equal to ?View question
Q.9005·Miscellaneous·2016·Easyf(x) = { 3x² + 12x – 1, –1 ≤ x ≤ 2 37 – x, 2 < x ≤ 3 } Which of the following statements is/are correct ? 1. f(x) is increasing in the interval [–1, 2]. 2. f(x) is decreasing in the interval (2, 3]. Select the correct answer using the code given below :View question
Q.9006·Miscellaneous·2016·Easyf(x) = { 3x² + 12x – 1, –1 ≤ x ≤ 2 37 – x, 2 < x ≤ 3 } Which of the following statements are correct ? 1. f(x) is continuous at x = 2. 2. f(x) attains greatest value at x = 2. 3. f(x) is differentiable at x = 2. Select the correct answer using the code given below :View question
Q.9007·Miscellaneous·2016·EasyLet f(x) = |x| – [x – 1]². What is f(x) equal to when x > 1 ?View question
Q.9008·Miscellaneous·2016·EasyLet f(x) = |x| – [x – 1]². What is f(x) equal to when 0 < x < 1 ?View question
Q.9009·Miscellaneous·2016·EasyLet f(x) = [x], where [·] is the greatest integer function and g(x) = sin x be two real valued functions over R. Which one of the following statements is correct ?View question
Q.9010·Miscellaneous·2016·EasyLet f(x) = [x], where [·] is the greatest integer function and g(x) = sin x be two real valued functions over R. Which of the following statements are correct ? 1. (fog)(x) = f(g(x)). 2.(gof)(x) = g(f(x)). 3.(fog)(x) = g(f(x)) only when x = 0. 4.(fog)(x) can take only three values. Select the correct answer using the code given below :View question
Q.9011·Miscellaneous·2016·EasyLet f(x) = { (e^x – 1)/x, x > 0 0, x = 0 } be a real valued function. Which one of the following statements is correct ?View question
Q.9012·Miscellaneous·2016·EasyLet f(x) = { (e^x – 1)/x, x > 0 0, x = 0 } be a real valued function. Which of the following statements is/are correct ? 1. f(x) is right continuous at x = 0. 2. f(x) is discontinuous at x = 1. Select the correct answer using the code given below :View question
Q.9013·Miscellaneous·2016·EasyConsider the parabola y = x² + 7x + 2 and the straight line y = 3x – 3. What are the coordinates of the point on the parabola which is closest to the straight line ?View question
Q.9014·Miscellaneous·2016·EasyConsider the parabola y = x² + 7x + 2 and the straight line y = 3x – 3. What is the shortest distance from the above point on the parabola to the line ?View question
Q.9015·Miscellaneous·2016·EasyA random sample of 20 people is classified in the following table according to their ages: Age: 15–25 | Frequency: 2 Age: 25–35 | Frequency: 4 Age: 35–45 | Frequency: 6 Age: 45–55 | Frequency: 5 Age: 55–65 | Frequency: 3 What is the mean age of this group of people?View question
Q.9016·Miscellaneous·2016·EasyThree independent events A1, A2 and A3 occur with probabilities P(Ai) = 1/(i+1), i = 1,2,3. What is the probability that at least one of the three events occurs?View question
Q.9017·Miscellaneous·2016·EasyA machine has three parts, A, B and C, whose chances of being defective are 0.02, 0.10 and 0.05 respectively. The machine stops working if any one of the parts becomes defective. What is the probability that the machine will not stop working?View question
Q.9018·Miscellaneous·2016·EasyA medicine is known to be 75% effective to cure a patient. If the medicine is given to 5 patients, what is the probability that at least one patient is cured by this medicine?View question