Engineering Questions — Mathematics — JEE (Main)
64 solved questions with detailed explanations
Q.6. Let . Then the sum of all elements of the matrix is equal to :
Q.11. The eccentricity of an ellipse E with centre at the origin O is and its directrices are . Let H: be a hyperbola whose eccentricity is equal to the length of semi-major axis of E, and whose len
Q.14. Let . Then is equal to:
Q.3. If the system of linear equations : , , . has infinitely many solutions, then the value of equals.
Q.2. The number of values of , satisfying the equations and , is :
Q.2. Let one root of the quadratic equation in x: be twice the other. Then the length of the latus rectum of the parabola is equal to:
Q.7. A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the 10th floor. The number of ways, in which any 4 persons exit at a floor an
Q.7. The first term of an A.P. of 30 non-negative terms is . If the sum of this A.P. is the cube of its last term, then its common difference is :
Q.12. Let be a directrix of an ellipse E, whose centre is at the origin and eccentricity is . Let , , be a focus of E and AB be a chord passing through P. Then the locus of the mid point of AB is :
Q.10. A bag contains coins – fair coins, and one coin with 'Head' on both sides. A coin is selected at random and tossed. If the probability of getting 'Head' is , then is equal to:
Q.10. If a straight line drawn through the point of intersection of the lines and , meet the co-ordinate axes at the points P and Q, then the locus of the mid point of PQ is:
Q.2. If the set of all solutions of is , then is equal to :
Q.12. The sum of all the integral values of p such that the equation , , has at least one solution, is :
Q.1. Consider the relation R on the set defined by if and only if . Then among the statements : I. The number of elements in R is 17 II. R is an equivalence relation
Q.9. A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, is
Q.4. Let the set of all values of such that the equation , , has at least one solution, be the interval [, ]. Then is equal to:
Q.4. Let and . If , then equals :
Q.2. The number of values of , satisfying the equations and , is :
Q.13. If , , then the value of is :
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