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JEE Main practice questions

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

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  1. 1One of the diameters of circle circumscribing the rectangle ABCD is 4x+7. If A and B are the points (-3,4) and (5,4) respectively and…Mathematics· Circles· Easy· figure
  2. 2AB is any chord of the circle $x^{2} + y^{2} - 6x - 8y - 11 = 0$ which subtends an angle$\frac{\pi}{2}$at $(1,2)$. If locus of midpoint of…Mathematics· Circles· Tough· figure
  3. 3Let $A_{1},A_{2},A_{3},\ldots\ldots,A_{14}$be a regular polygon with 14 side inscribed in a circle of radius R. If $\left( A_{1}A_{3}…Mathematics· Properties of triangle· Moderate· figure
  4. 4Tangents are drawn to the ellipse $x^{2} + 2y^{2} = 2$. The locus of the midpoint of the intercept made by tangents between the axes is…Mathematics· Ellipse· Moderate· figure
  5. 5If two perpendicular tangents can be drawn from the origin to the circle $x^{2} - 6x + y^{2} - 2py + 17 = 0$then the value of $p^{2}$ is;fn…Mathematics· Circles· Easy
  6. 6In $\Delta ABC$, if r=1, R=3 and S=5, then the value of $a^{2} + b^{2} + c^{2}$ is $\Delta ABC$ r=1, R=3 rFkk S=5] rc $a^{2} + b^{2} +…Mathematics· Properties of triangle· Easy
  7. 7The eccentricity of ellipse 14x^2- 4xy + 11y^2= 60 will be equal to nh?kZo`Ùk 14x^2- 4xy + 11y^2= 60Mathematics· Ellipse· Moderate
  8. 8Two lines (L_1 and L_2) are drawn from point $(\alpha,\alpha)$ making an angle 45º with the lines $L_{3} \equiv x + y - f(\alpha) = 0$ and…Mathematics· Straight Lines· Moderate· figure
  9. 9If the eccentricity of the hyperbola $x^{2} - y^{2}\sec^{2}\alpha = 5\ is\ \sqrt{3\ }$times the eccentricity of the ellipse…Mathematics· Hyperbola· Easy / Moderate/ Tough
  10. 10Given A (0,0) and B(x,y) with x∈(0,1) and y>0. Let the slope of the line AB equals m_1 point C lies on the line x = 1 such that slope of BC…Mathematics· Properties of triangle· Easy
  11. 11The equation of the common tangent touching the circle $(x - 3)^{2} + y^{2} = 9\ $and the parabola y^2 =4x above the X-axis isMathematics· Parabola· Moderate
  12. 12Equation of the circle which circumscribes the square formed by the lines xy-9x-2y+18 = 0 and xy - 5x - 6y + 30 = 0 isMathematics· Circles· Moderate
  13. 13Let ABC be a triangle with $\angle BAC = \frac{2\pi}{3}$ and AB= x such that (AB) (AC) =1. If x varies then the longest possible length of…Mathematics· Properties of triangle· Moderate· figure
  14. 14All the vertices of a trapezium lie on the parabola y^2 = 4x. Its diagonals pass through (1, 0) and have a length $\frac{25}{4}$ units…Mathematics· Conic Sections· Moderate· figure
  15. 15The equation of the circle, which is the mirror image of the circle, $x^{2} + y^{2} - 2x = 0$ in the line $y = 3 - x$ is ml o`Ùk dk…Mathematics· Circles· Moderate
  16. 16Let Y_1 and Y_2 be the foot of the perpendiculars on the auxiliary circle from the foci upon any tangent at P on the ellipse. The tangent…Mathematics· Conic Sections· Tough
  17. 17Let O be the origin, A(1, 0) and B(0, 1) and P(x, y) are points such that xy > 0 and x + y < 1, then ekuk O ewy fcUnq gS A(1, 0) > 0Mathematics· Straight Lines· Easy
  18. 18Variable ellipses are drawn with x = -4 as a directrix and origin as corresponding foci. The locus of extremities of minor axes of these…Mathematics· Conic Sections· Moderate· figure
  19. 19If equation $4y^{3} - 8a^{2}yx^{2} - 3ay^{2}x + 8x^{3} = 0$ represents three straight lines, two of which are perpendicular to each other,…Mathematics· Straight Lines· Moderate
  20. 20Let PQ and RS be 2 perpendicular focal chords of a rectangular hyperbola, which are not parallel to its axes, then Ekkuk PQ o RS,d nks…Mathematics· Conic Sections· Moderate· figure
  21. 21Quadrilateral formed by points of intersection of pair of lines ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 with coordinate axes is cyclic if…Mathematics· Circles· Easy / Moderate/ Tough
  22. 22P is a point on the circle x^2 + y^2 = 1. Line OP, where O is origin, and x = 1 meet at Q. L_1 is a line parallel to x-axis drawn from Q. A…Mathematics· Conic Sections· Moderate· figure
  23. 23Equation of circle touching the line $x + y = 4$at (1, 3) and intersecting the circle $x^{2} + y^{2} = 4$orthogonally, is gksxk tks o`Ùk…Mathematics· Circles· Easy
  24. 24Let A ≡ (- 2, 0) and B ≡ (2, 0), then the number of integral values of a, a $\in$ for which line segment AB subtends an acute angle at…Mathematics· Circles· Easy
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