Q.9019·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.9020·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.9021·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.9022·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.9023·Miscellaneous·2016·EasyLet f(x) = { –2, –3 ≤ x ≤ 0 –x – 2, 0 < x ≤ 3 } and g(x) = f(|x|) + |f(x)| Which of the following statements is/are correct ? g(x) is differentiable at x = 0. g(x) is differentiable at x = 2. Select the correct answer using the code given below :View question
Q.9024·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.9025·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.9026·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.9027·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.9028·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.9029·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.9030·Miscellaneous·2016·EasyLet f(x) = { –2, –3 ≤ x ≤ 0 –x – 2, 0 < x ≤ 3 } and g(x) = f(|x|) + |f(x)| What is the value of the differential coefficient of g(x) at x = –2 ?View question
Q.9031·Miscellaneous·2016·EasyLet f(x) = { –2, –3 ≤ x ≤ 0 –x – 2, 0 < x ≤ 3 } and g(x) = f(|x|) + |f(x)| Which of the following statements are correct ? 1.g(x) is continuous at x = 0. 2.g(x) is continuous at x = 2. 3.g(x) is continuous at x = –2. Select the correct answer using the code given below :View question
Q.9032·Miscellaneous·2016·EasyWhat are the degree and order respectively of the differential equation satisfying e^(y'') - x^2 (y')^2 - y^2 = c e^x , (where c > 0, |x| < 1, |y| < 1)?View question
Q.9033·Miscellaneous·2016·EasyWhat is the curve which passes through the point (1,1) and whose slope is 2y/3x ?View question
Q.9034·Miscellaneous·2016·EasyIf x dy = y dx + y^2 dy, y > 0 and y(1) = 1, then what is y(-3) equal to?View question
Q.9035·Miscellaneous·2016·EasyWhich one of the following differential equations represents the family of straight lines which are at unit distance from the origin?View question
Q.9036·Miscellaneous·2016·EasyA special dice with numbers 1, -1, 2, -2, 0 and 3 is thrown thrice. What is the probability that the sum of the numbers occurring on the upper face is zero?View question