Practice/Question bank/JEE Main

JEE Main practice questions

NTA-style Physics, Chemistry and Maths MCQs with solutions. 2,688 questions in the bank.

1. 1The eccentricity of an ellipse whose center is at the origin is[IMAGE]. If one of its directrices is [IMAGE] then the equation of the…Mathematics· Ellipse· Easy· figure
2. 2If [IMAGE] then coordinates of point on the parabola [IMAGE] which is at shortest distance from theMathematics· Parabola· Moderate· figure
3. 3If [IMAGE] is tangent to parabola [IMAGE] and chord to circle [IMAGE] which passes through (2, 3) at the greatest distance from center of…Mathematics· Parabola· Moderate· figure
4. 4A line [IMAGE] through [IMAGE] cuts parabola [IMAGE] at A & B then which is falseMathematics· Parabola· Easy· figure
5. 5Let P be a point on the ellipse [IMAGE] in the [IMAGE] quadrant foci are [IMAGE] and [IMAGE]. Then the least possible value of the…Mathematics· Ellipse· Tough· figure
6. 6[IMAGE] is a point on the ellipse [IMAGE] If S and [IMAGE] are the focii of the ellipse, then the equation of the external bisector ofMathematics· Ellipse· Tough· figure
7. 7An equilateral triangle ABC is inscribed in the parabola [IMAGE] and one of the sides of the equilateral triangle has the gradient 2. If…Mathematics· Parabola· Tough· figure
8. 8A parabola whose axis is parallel to x-axis passes through three points (2, 0), (0, -1) and (6, 1) then area enclosed by the parabola and…Mathematics· Parabola· Moderate· figure
9. 9The locus of midpoint of all focal chords of the parabolaMathematics· Parabola· Moderate· figure
10. 10A hyperbola passes through the focus of the ellipse [IMAGE] and its transverse and conjugate axes coincide with the x & y -axis…Mathematics· Hyperbola· Tough· figure
11. 11If the tangents to the parabola [IMAGE] makes an angle of 45º with x- axis, then the point of contact isMathematics· Parabola· Easy· figure
12. 12Angle between two focal chords of a parabola [IMAGE] which are tangents to the circle [IMAGE] is [IMAGE] where a and b relatively prime…Mathematics· Parabola· Moderate· figure
13. 13Tangents are drawn from the point [IMAGE] to the hyperbola [IMAGE] and are inclined at angles [IMAGE] and [IMAGE] to the x- axis. If…Mathematics· Hyperbola· Moderate· figure
14. 14Rectangle ABCD has area 200sq. units. An ellipse with area [IMAGE] passes through A & C and has foci at B and D. Then the perimeter of the…Mathematics· Ellipse· Tough· figure
15. 15The eccentricity of ellipse [IMAGE] will be equal toMathematics· Ellipse· Easy· figure
16. 16If the focus of parabola [IMAGE] coincides with one of the foci of ellipse[IMAGE], then the eccentricity of the ellipse isMathematics· Ellipse· Moderate· figure
17. 17Radius of the circle that passes through origin and touches the parabola [IMAGE] at the point [IMAGE] is.Mathematics· Parabola· Tough· figure
18. 18Equation of the hyperbola whose axes are the axes of coordinates (focus lying on x-axis) and which passes through the point (-3, 1) and has…Mathematics· Hyperbola· Easy· figure
19. 19The line passing through the extremity A of the major axis and extremity "B" of the minor axis of the ellipse [IMAGE] meets its auxiliary…Mathematics· Ellipse· Tough· figure
20. 20A tangent and a normal are drawn at the point [IMAGE] of the parabola [IMAGE] which cut the axis of the parabola at the point A and B…Mathematics· Parabola· Moderate· figure
21. 21[IMAGE] is the equation of the chord [IMAGE] of [IMAGE] whose focus is S. If PS and QS meet the parabola again at R and T, respectively,…Mathematics· Parabola· Easy· figure
22. 22If [IMAGE] then [IMAGE] is equal toMathematics· Matrix and determinant· Moderate· figure
23. 23Let [IMAGE] and [IMAGE] for some real x. Then [IMAGE] is possible ifMathematics· Vectors· Moderate· figure
24. 24The diagonals of a parallelogram are [IMAGE] and [IMAGE] Its area isMathematics· Vectors· Easy· figure