Engineering Questions — Mathematics
131 solved questions with detailed explanations
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.6. The number of seven-digit numbers, that can be formed by using the digits 1, 2, 3, 5 and 7 such that each digit is used at least once, 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.18. The value of the integral is:
Q.15. Let and be unit vectors inclined at an acute angle such that . If . Then is equal to :
Q.6. The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8. If the first term of the A.P. is equal to the common ratio of the G.P. and the first term of th
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.20. The value of the integral is:
Q.10. Let an ellipse , , pass through the point and have eccentricity . Then the length of its latus rectum is :
Q.19. Let denote the greatest integer function. Then the value of is:
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.19. Let y = y(x) be the solution of the differential equation : , , satisfying . If , than is equal to :
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.17. If the curve passes through the point and satisfies the differential equation , , then is equal to :