Engineering Questions — JEE (Main)
81 solved questions with detailed explanations
Q.1. Consider the relation R on the set defined by if and only if . Then among the statements : I. The number of elements in R is 17 II. R is an equivalence relation
Q.74. At 298 K, the molar conductivity of x% (w/w) MX solution (aqueous) is 123.5 S cm mol. The conductance of same solution is S. The value of x is _______ . (Given : cell constant = 1.3 cm; molar m
Q.9. A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, is
Q.4. Let the set of all values of such that the equation , , has at least one solution, be the interval [, ]. Then is equal to:
Q.4. Let and . If , then equals :
Q.2. The number of values of , satisfying the equations and , is :
Q.13. If , , then the value of is :
Q.3. Let and be two distinct roots of the equation . Let the sets {a: and are the eccentricities of hyperbolas} = (, ), and {a: and are the eccentricities of an ellipse and a hyperbola, respecti
Q.74. The values of pressure equilibrium constant recorded at different temperatures for the following equilibrium reaction have been given below: A(g) B(g) + C(g) [Table: 1/T (K⁻¹) values 0.05, 0.06
Q.75. If the half life of a first order reaction is 6.93 minutes then the time required for completion of 99% of the reaction will be ________ minutes. (Given: log 2 = 0.3010)
Q.71. Consider the following species BrF₅, XeF₆, BF₃, ICl₄⁰, XeF₄, SF₄, NH₃, ClF₃, XeF₂, ICl₂⁰ Number of species having spd hybridized central atom is
Q.2. Consider the quadratic equation . Let be the minimum value of the product of its roots and be the maximum value of the sum of its roots. Then the sum of the first six terms of the G.P., whose f
Q.1. Let . Let be the roots of the equation . If and , then is equal to :
Q.9. A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one green ball is :
Q.4. The sum of all possible values of , for which the system of equations : has a non-trivial solution, is equal to :
Q.12. Let chord PQ of length of the parabola be such that the ordinates of points P and Q are in the ratio 1: 2. If the chord PQ subtends an angle at the focus of the parabola, then is equal to:
Q.6. The sum upto 10 terms is equal to :
Q.10. Let C be a circle having centre in the first quadrant and touching the x-axis at a distance 3 units from the origin. If the circle C has an intercept of length on y-axis, then the length of the
Q.73. One mole of phenol is treated with dilute HNO₃ at 298K to give a mixture of products. The mixture is separated by steam distillation. The seam volatile compound (X) is separated. The increase in
Q.13. Suppose the two chords, drawn from the point on the circle are bisected by the y-axis. If the other ends of these chords are R and S, and the mid point of the line segment RS is , then is equ