Q.9037·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.9038·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.9039·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.9040·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.9041·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.9042·Miscellaneous·2016·EasyIn a study of two groups, the following results were obtained: Group A: Sample size = 20, Sample mean = 22, Sample standard deviation = 10 Group B: Sample size = 25, Sample mean = 12, Sample standard deviation = 12 Which of the following statements is correct?View question
Q.9043·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.9044·Miscellaneous·2016·EasyFor 10 observations on price (x) and supply (y), the following data was obtained: Σx = 130, Σy = 220, Σx^2 = 2288, Σy^2 = 5506 and Σxy = 3467. What is the line of regression of y on x?View question
Q.9045·Miscellaneous·2016·EasyLet f(x) = |x| – [x – 1]². What is f(x) equal to when x > 1 ?View question
Q.9046·Miscellaneous·2016·EasyLet f(x) = |x| – [x – 1]². What is f(x) equal to when 0 < x < 1 ?View question
Q.9047·Miscellaneous·2016·EasyThe scores of 15 students in an examination were recorded as: 10, 5, 8, 16, 18, 20, 8, 10, 16, 20, 18, 11, 16, 14 and 12. After calculating the mean, median and mode, an error is found. One of the values "20" is wrongly written as "16" instead of "20". Which of the following measures of central tendency will change?View question
Q.9048·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.9049·Miscellaneous·2016·EasyConsider the following statements: 1.The mean and median are equal in symmetric distribution. 2.The range is the difference between the maximum value and the minimum value in the data. 3.The sum of the areas of the rectangles in the histogram is equal to the total area bounded by the frequency polygon and the horizontal axis. Which of the above statements are correct?View question
Q.9051·Miscellaneous·2016·EasyA particle executes linear simple harmonic motion with amplitude of 2 cm. When the particle is at 1 cm from the mean position, the magnitudes of the velocity and the acceleration are equal. Then its time period (in seconds) isView question
Q.9053·Miscellaneous·2016·EasyIf the image of an object, formed by a concave mirror is virtual, erect and magnified, then the object is placedView question
Q.9054·Miscellaneous·2016·EasyWhen three resistors, each having resistance r, are connected in parallel, their resultant resistance is x. If these three resistances are connected in series, the total resistance will beView question