Q.3007·Miscellaneous·2022·EasyWhat is the equation of the locus of the mid-point of the line segment obtained by cutting the line x + y = p, (where p is a real number) by the coordinate axes?View question
Q.3008·Miscellaneous·2022·EasyConsider the points A(2, 4, 6), B(–2, –4, –2), C(4, 6, 4) and D(8, 14, 12). Which of the following statements is/are correct? 1. The points are the vertices of a rectangle ABCD. 2. The mid-point of AC is the same as that of BD. Select the correct answer using the code given below:View question
Q.3009·Miscellaneous·2022·EasyA plane cuts intercepts 2, 2, 1 on the coordinate axes. What are the direction cosines of the normal to the plane?View question
Q.3010·Miscellaneous·2022·EasyConsider the following statements: 1. The direction ratios of y-axis can be <0, 4, 0> 2. The direction ratios of a line perpendicular to z-axis can be <5, 6, 0> Which of the statements given above is/are correct?View question
Q.3011·Miscellaneous·2022·EasyPQRS is a parallelogram. If PR = a and QS = b , then what is PQ equal to?View question
Q.3012·Miscellaneous·2022·EasyLet a and b are two unit vectors such that a + 2 b and 5 a – 4 b are perpendicular. What is the angle between a and b ?View question
Q.3013·Miscellaneous·2022·EasyThe position vectors of vertices A, B and C of triangle ABC are respectively j + k , 3 i + j + 5 k and 3 j + 3 k . What is angle C equal to?View question
Q.3014·Miscellaneous·2022·EasyLet z = [y] and y = [x] – x, where [.] is the greatest integer function. If x is not an integer but positive, then what is the value of z?View question
Q.3015·Miscellaneous·2022·EasyIf f(x) = 4x + 1 and g(x) = kx + 2 such that fog(x) = gof(x), then what is the value of k?View question
Q.3016·Miscellaneous·2022·EasyIf y = (x^x)^x, then which one of the following is correct?View question
Q.3017·Miscellaneous·2022·EasyWhat is the area of the region bounded by x – |y| = 0 and x – 2 = 0?View question
Q.3018·Miscellaneous·2022·EasyConsider the following statements: 1. The degree of the differential equation dy/dx + cos(dy/dx) = 0 is 1. 2. The order of the differential equation [(d²y/dx²)³ + cos(dy/dx)] = 0 is 2. Which of the statements given above is/are correct?View question
Q.3019·Miscellaneous·2022·EasyWhich one of the following rivers in India was not crossed by Alexander and his army?View question
Q.3020·Miscellaneous·2022·EasyWho among the following has described the medieval Indian postal system as of two kinds—the horse-post called ‘Uluq’ and the foot-post called ‘Dawa’?View question
Q.3021·Miscellaneous·2022·EasyAt which among the following Harappan sites are fire altars found?View question
Q.3022·Miscellaneous·2022·EasyWhat is the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis?View question
Q.3023·Miscellaneous·2022·EasyConsider the following statements on computation of density : Physiological density can be computed by dividing the total population by the net cultivable area. Agricultural density can be computed by dividing the total agricultural population by the net cultivable area. Population density can be computed by dividing the total population by the total area. How many of the above statements is/are correct?View question
Q.3024·Miscellaneous·2022·EasyWhat is the solution of the differential equation (dy – dx) + cos x(dy + dx) = 0?View question