Engineering Questions — Mathematics — JEE Main
67 solved questions with detailed explanations
Q.18. The number of critical points of the function in the interval is equal to:
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.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) :
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.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.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.19. Let y = y(x) be the solution of the differential equation : , , satisfying . If , than is equal to :