Engineering Questions — JEE (Main)

Q.4. The number of functions , which are not onto, is :

Q.69. Identify the correct statements A. Glucose exist in two anomeric forms. B. Anomers of glucose differ in configuration at C-1 in cyclic hemiacetal structure. C. Melting point of a-anomer of gluco

Q.1. Let be defined as . Then is:

Q.31. An object of uniform density rolls up the curved path with the initial velocity v as shown in the figure. If the maximum height attained by an object is (g = acceleration due to gravity), the o

Q.5. Let be a set of matrices. Then the number of matrices in S, for which the sum of the diagonal elements is equal to 4, is:

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.30. A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle . In the next 2 s it rotates through an angle . The ratio i

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.72. In an estimation of sulphur by Carius method 0.2g of the substance gave 0.6 g of BaSO₄. The percentage of sulphur in the substance is %. (Given molar mass in g mol⁰ S : 32, BaSO₄ : 231)

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 :