Engineering Questions — Mathematics — JEE (Main)

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.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

Q.11. Let O be the vertex of the parabola and its chords OP and OQ are perpendicular to each other. If the locus of the mid-point of the line segment PQ is a conic C, then the length of its latus rec

Q.2. Let the sum of the first n terms of an A.P. be . Then the sum of squares of the first 10 terms of the A.P. is:

Q.8. Let the mean and the variance of seven observations , , be 8 and 16 respectively. Then the quadratic equation whose roots are and is:

Q.7. A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of all these 10 observations is equal to :

Q.6. A candidate has to go to the examination centre to appear in an examination. The candidate uses only one means of transportation for the entire distance out of bus, scooter and car. The probabili

Q.25. Let y = y(x) be the solution of the differential equation (tanx)²dy = (sec³x - (tanx)²y)dx, 0 < x < , y() = . If y() = , then equals .......

Q.1. Let [] denote the greatest integer function. If the domain of the function is [, ), then is equal to:

Q.13. Let , and . Then is equal to:

Q.10. Let P be a moving point on the circle . Then, the maximum distance of P from the vertex of the parabola is equal to :

Q.7. A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of all these 10 observations is equal to :

Q.4. Consider the system of linear equations in x, y, z :,,,Where is a differentiable function. If this system has infinitely many solutions for all , then f

Q.3. If the system of linear equations : , , . has infinitely many solutions, then the value of equals.