Practice/Question bank/JEE Main

JEE Main practice questions

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

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  1. 1Equation of chord AB of circle x^2 + y^2 = 2 passing through the point P(2, 2) such that $\frac{PB}{PA} = \ 3$ is o`Ùk x^2 + y^2 = 2 dh…Mathematics· Circles· Moderate
  2. 2Equation of straight line $ax + by + c = 0$, where $3a\ + \ 4b\ + \ c\ = \ 0,$ which is at maximum distance from (1, -2), is tgk¡$3a\ + \…Mathematics· Straight Lines· Moderate
  3. 3Vertices of a variable triangle are (3, 4), (5cosθ, 5sinθ) and (5sinθ, - 5cosθ). Then locus of its orthocenter is,d pj f=Hkqt (3, 4),…Mathematics· Circles· Tough
  4. 4Consider vertices of $\Delta ABC,\ \ A(3,4),\ \ B(\beta,\alpha)$ and $C(7,7)$ and line$L:\alpha(3x + 6y - 37) - \beta(6x + 3y - 36) = 0$.…Mathematics· Straight Lines· Moderate
  5. 5A line of fixed length 2 units moves so that its one end is on the positive x-axis and other end on that part of the line x + y = 0 which…Mathematics· Circles· Moderate· figure
  6. 6If the point (p, 5) lies on the line parallel to the y-axis and passing through the intersection of the lines $2\left( a^{2} + 1 \right)x +…Mathematics· Straight Lines· Easy
  7. 7If the chord $y = mx + 1$ of circle $x^{2} + y^{2} = 1$ subtends an angle of measure 45° at the major segment of the circle, then the value…Mathematics· Circles· Moderate· figure
  8. 8Tangents are drawn to ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1$,from point $\left( \frac{25}{3},\sqrt{41} \right)$. These tangents…Mathematics· Conic Sections· Easy
  9. 9The area of the region defined by x^2 + y^2 ≤ π^2 and y ≥ sin x is$\frac{\pi^{3}}{\lambda}$. Find the value of$\lambda$…Mathematics· Circles· Moderate· figure
  10. 10Consider a circle C: x^2 + y^2 - 8y + 12 = 0 and an ellipse E: $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}$ = 1 (a > b and b < 2). If the…Mathematics· Conic Sections· Easy / Moderate/ Tough· figure
  11. 11If circles $x^{2} + y^{2} + 2gx + 2y + 2 = 0$ and $x^{2} + y^{2} + 2x + 2fy + 4 = 0$ intersect in two distinct points P and Q,and equation…Mathematics· Circles· Moderate
  12. 12If two different tangents of y^2 = 4x are normal chords to x^2 = 4by then y^2 = 4xMathematics· Conic Sections· Easy
  13. 13A circle intersects an ellipse$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}$ = 1 precisely at three points A, B, C as shown in the figure. AB…Mathematics· Conic Sections· Tough· figure
  14. 14The lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangent to the same circle. Find the radius of this circle. rc bl o`ÙkMathematics· Circles· Moderate
  15. 15Let tangents be drawn to the curve y^2 - 4(x + y) = 3 sin θ + 4 cos θ - 15, θ∈ R from the origin when the vertex of the curve is at the…Mathematics· Conic Sections· Tough
  16. 16If the equation $2x^{2} + 2hxy + 6y^{2} - 4x + 5y - 6 = 0$ represents a pair of straight lines then find the length of intercept on the…Mathematics· Straight Lines· Moderate
  17. 17If the normals to the curve y = x^2 at the points P, Q and R pass through the point $\left( 0,\frac{3}{2} \right)$, find the radius of the…Mathematics· Conic Sections· Moderate· figure
  18. 18If the tangent at point P on circle $x^{2} + y^{2} + 6x + 6y = 2$ meets straight line 5x - 2y + 6 = 0 at point Q on y-axis then find length…Mathematics· Circles· Easy· figure
  19. 19P is a point in first quadrant lying on the ellipse$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}$ = 1, tangent at point P meets x-axis at T.…Mathematics· Conic Sections· Easy· figure
  20. 20Find the distance of point (4, 5) from the straight line joining the points (1, 2) and (-2, 3) measured parallel to the line x + y + 1 = 0…Mathematics· Straight Lines· Easy
  21. 21Find the number of integer values of k for which the equation $x^{2} + y^{2} + (k - 1)x - ky + 5 = 0$ represents a circle whose radius…Mathematics· Circles· Moderate
  22. 22Normal at the point P to the parabola y^2 = 4x, intersects the circle with SP as diameter at Q also. If PQ = 2 units (given that point S is…Mathematics· Conic Sections· Easy· figure
  23. 23P, Q, R lie on the parabola y^2 = 4ax, such that PQR is an equilateral triangle. Locus of centroid of triangle PQR is λy^2 = 4ax - 32a^2,…Mathematics· Conic Sections· Moderate
  24. 24If a variable line has intercepts of e_1 and e_2on the co-ordinate axes, where $\frac{e_{1}}{2}\&\frac{e_{2}}{2}$are the eccentricities of…Mathematics· Conic Sections· Tough
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