Engineering Questions — Mathematics
122 solved questions with detailed explanations
Q.19. Let f: R R be a differentiable function such that for all x, y R and . Then the minimum value of the function , is
Q.16. The area of the region R = {(x,y): , } is equal to :
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.21. From a month of 31 days, 3 different dates are selected at random. If the probability that these dates are in an increasing A.P. is equal to , where and , then is equal to ________.
Q.20. The integral is equal to :
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: