Q.9199·Miscellaneous·2016·EasyA plane P passes through the line of intersection of the planes 2x − y + 3z = 2, x + y − z = 1 and the point (1, 0, 1). What is the equation of the plane P?View question
Q.9200·Miscellaneous·2016·EasyConsider the following statements : 1. If ABC is an equilateral triangle, then 3 tan (A + B) tan C = 1. 2. If ABC is a triangle in which A = 78°, B = 66°, then tan (B + C)/2 < tan A. 3. If ABC is any triangle, then tan (A + B)/2 = cot (C/2). Which of the above statements is/are correct?View question
Q.9201·Miscellaneous·2016·Easy(a, 2b) is the mid-point of the line segment joining the points (10, -6) and (k, 4). If a - 2b = 7, then what is the value of k?View question
Q.9202·Miscellaneous·2016·EasyConsider the following in respect of the matrix A = (-1 1; 1 1) 1. A² = -A 2. A³ = 4A Which of the above is/are correct?View question
Q.9203·Miscellaneous·2016·EasyA point is chosen at random inside a rectangle measuring 6 inches by 5 inches. What is the probability that the randomly selected point is at least one inch from the edge of the rectangle?View question
Q.9204·Miscellaneous·2016·EasyWhich of the following determinants have value zero? 1. | 4 1 1 | | 7 9 7 | | 2 9 5 | 2. | 1 a b+c | | 1 b c+a | | 1 c a+b | 3. | 0 c b | | -c 0 a | | -b -a 0 | Select the correct answer using the code given below.View question
Q.9205·Miscellaneous·2016·EasyA plane P passes through the line of intersection of the planes 2x − y + 3z = 2, x + y − z = 1 and the point (1, 0, 1). What are the direction ratios of the line of intersection of the given planes?View question
Q.9206·Miscellaneous·2016·EasyConsider a circle passing through the origin and the points (a, b) and (−b, −a). What is the sum of the squares of the intercepts cut off by the circle on the axes?View question
Q.9207·Miscellaneous·2016·EasyConsider a circle passing through the origin and the points (a, b) and (−b, −a). On which line does the centre of the circle lie?View question
Q.9208·Miscellaneous·2016·EasyLet f : R → R be a function such that f(x) = x³ + x²f′(1) + xf″(2) + f‴(3) for x ∈ R. Consider the following : 1. f′(2) = f(1) − f(0) 2. f″(2) − 2f′(1) = 12 Which of the above is/are correct?View question
Q.9209·Miscellaneous·2016·EasyThe system of linear equations kx + y + z = 1, x + ky + z = 1 and x + y + kz = 1 has a unique solution under which one of the following conditions?View question
Q.9210·Miscellaneous·2016·EasyFor the data 3, 5, 1, 6, 5, 9, 5, 2, 8, 6 the mean, median and mode are x, y and z respectively. Which one of the following is correct?View question
Q.9211·Miscellaneous·2016·EasyConsider the following statements in respect of a histogram: 1. The total area of the rectangles in a histogram is equal to the total area bounded by the corresponding frequency polygon and the x-axis. 2. When class intervals are unequal in a frequency distribution, the area of the rectangle is proportional to the frequency. Which of the above statements is/are correct?View question
Q.9212·Miscellaneous·2016·EasyWhat is the number of different messages that can be represented by three 0's and two 1's?View question
Q.9213·Miscellaneous·2016·EasyA fair coin is tossed 100 times. What is the probability of getting tails an odd number of times?View question
Q.9214·Miscellaneous·2016·EasyWhat is the number of ways in which 3 holiday travel tickets are to be given to 10 employees of an organization, if each employee is eligible for any one or more of the tickets?View question
Q.9215·Miscellaneous·2016·EasyWhat is the area of the parallelogram having diagonals 3i + j - 2k and i - 3j + 4k?View question
Q.9216·Miscellaneous·2016·EasyWhat is the number of four-digit decimal numbers (<1) in which no digit is repeated?View question