Q.10513·Miscellaneous·2015·EasyThe area of a triangle, whose vertices are (3, 4), (5, 2) and the point of intersection of the lines x = a and y = 5, is 3 square units. What is the value of a?View question
Q.10514·Miscellaneous·2015·EasyThe length of perpendicular from the origin to a line is 5 units and the line makes an angle 120° with the positive direction of x-axis. The equation of the line isView question
Q.10515·Miscellaneous·2015·EasyThe equation of the line joining the origin to the point of intersection of the lines x/a + y/b = 1 and x/b + y/a = 1 isView question
Q.10516·Miscellaneous·2015·EasyThe projections of a directed line segment on the coordinate axes are 12, 4, 3 respectively. What is the length of the line segment?View question
Q.10517·Miscellaneous·2015·EasyThe projections of a directed line segment on the coordinate axes are 12, 4, 3 respectively. What are the direction cosines of the line segment?View question
Q.10518·Miscellaneous·2015·EasyWhat are the direction ratios of the line segment PQ? From the point P(3, -1, 11), a perpendicular is drawn on the line L given by the equation x/2 = (y-2)/3 = (z-3)/4. Let Q be the foot of the perpendicular.View question
Q.10519·Miscellaneous·2015·EasyWhat is the length of the line segment PQ? From the point P(3, -1, 11), a perpendicular is drawn on the line L given by the equation x/2 = (y-2)/3 = (z-3)/4. Let Q be the foot of the perpendicular.View question
Q.10520·Miscellaneous·2015·EasyWhat are the intercepts made by the plane ABC on the axes? A triangular plane ABC with centroid (1, 2, 3) cuts the coordinate axes at A, B, C respectively.View question
Q.10521·Miscellaneous·2015·EasyWhat is the equation of the plane ABC? A triangular plane ABC with centroid (1, 2, 3) cuts the coordinate axes at A, B, C respectively.View question
Q.10522·Miscellaneous·2015·EasyWhat is the length of one of the diagonals of the cuboid? A point P(1, 2, 3) is one vertex of a cuboid formed by the coordinate planes and the planes passing through P and parallel to the coordinate planes.View question
Q.10523·Miscellaneous·2015·EasyWhat is the equation of the plane passing through P(1, 2, 3) and parallel to xy-plane? A point P(1, 2, 3) is one vertex of a cuboid formed by the coordinate planes and the planes passing through P and parallel to the coordinate planes.View question
Q.10524·Miscellaneous·2015·EasyConsider the following statements: 1.y = (e^x + e^(-x))/2 is an increasing function on (0, ∞). 2.y = (e^x − e^(-x))/2 is an increasing function on (−∞, ∞). Which of the above statements is/are correct?View question
Q.10525·Miscellaneous·2015·EasyFor each non-zero real number x, let f(x) = x/|x|. The range of f isView question
Q.10526·Miscellaneous·2015·EasyConsider the following statements: 1.f(x) = [x], where [.] is the greatest integer function, is discontinuous at x = n, where n ∈ Z. 2.f(x) = cot x is discontinuous at x = nπ, where n ∈ Z. Which of the above statements is/are correct?View question
Q.10527·Miscellaneous·2015·EasyGiven a function f(x) = -1 if x ≤ 0 f(x) = ax + b if 0 < x < 1 f(x) = 1 if x ≥ 1 where a, b are constants. The function is continuous everywhere. What is the value of a?View question
Q.10528·Miscellaneous·2015·EasyWhich one among the following happens when a swing rises to a certain height from its rest position?View question
Q.10529·Miscellaneous·2015·Easyf(x) = -1 if x ≤ 0 f(x) = ax + b if 0 < x < 1 f(x) = 1 if x ≥ 1 where a, b are constants. The function is continuous everywhere. What is the value of b?View question
Q.10530·Miscellaneous·2015·EasyConsider the following functions: 1.f(x) = x³, x ∈ R 2.f(x) = sin x, 0 < x < 2π 3.f(x) = e^x, x ∈ R Which of the above functions have inverse defined on their ranges?View question