Engineering Questions — Mathematics
131 solved questions with detailed explanations
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.18. The number of critical points of the function in the interval is equal to:
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.15. The square of the distance of the point of intersection of the lines , and from the origin is :
Q.22. Let and . If the number of points where g is not continuous and is not differentiable are and respectively, then is equal to ________.
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.19. The area of the region {(x, y) : , , } is :
Q.23. If , and be three vectors such that and , then is equal to ________.
Q.4. Let and . If and , then among the two statements : (S1): and (S2): , (1) only (S1) is correct (2) only (S2) is correct (3) both (S1) and (S2) are correct (4) both (S1) and (S2) are wrong
Q.11. In an equilateral triangle PQR, let the vertex P be at (3, 5) and the side QR be along the line . If the orthocentre of the triangle PQR is (, ), then is equal to :
Q.9. Let a focus of the ellipse E: be S(4,0) and its eccentricity be . If the point P(3, ) lies on E and O is the origin, then the area of is equal to :
Q.11. If the eccentricity of the hyperbola , passing through , satisfies , then the length of the latus rectum of the hyperbola is:
Q.13. The square of the distance of the point P(5, 6, 7) from the line is equal to :
Q.14. Let and . If is a vector such that and , then is equal to :
Q.14. If is the image of in the line , then the possible value(s) of is(are) :