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. 1Let normal's at two points on the parabola y^2 =4x intersects on the parabola. If the line joining these two points passes through the…Mathematics· Parabola· Tough
  2. 2If the straight line ax + by + p =0 and xcosα + ysinα = p enclosed an angle of$\frac{\pi}{4}$and the line xsinα - ycosα = 0 meets them at…Mathematics· Straight Lines· Moderate· figure
  3. 3In a triangle ABC, let D be the midpoint of BC. If angle ADB is 45° and angle ACD is 30° then angle BAD will be equal to ? f=Hkqt ABC esa…Mathematics· Properties of triangle· Moderate· figure
  4. 4If tangent at (1,2) to the circle $c_{1}:x^{2} + y^{2} = 5\ $intersects the circle $c_{2}:x^{2} + y^{2} = 9\ at\ A\& B$and tangents at A& B…Mathematics· Circles· Moderate· figure
  5. 5In an acute angled ∆ABC, r_2 + r_3 = r + r_1 and $\angle B > \frac{\pi}{3}$then U;wudks.k ∆ABC esa, r_2 + r_3 = r + r_1rFkkMathematics· Properties of triangle· Moderate
  6. 6Line L touches circles C_1, C and C_2 having radii r_1, r, r_2 respectively. These circle pair wise touch each-other externally. If r_1 =…Mathematics· Circles· Easy· figure
  7. 7If $C_{1}:x^{2} + y^{2} = (3 + 2\sqrt{2})^{2}$is a circle and PA and PB are a pair of tangents on C_1,where P is any point on the director…Mathematics· Circles· Tough· figure
  8. 8Let (m, n) to be a point from which two perpendicular tangents can be drawn to the ellipse 4x^2 + 5y^2 = 20. If E=4m + 3n, thenMathematics· Ellipse· Moderate
  9. 9A variable chord PQ of y^2= 4ax subtends a right angle at its vertex then the locus of point of intersection of normals at P and Q will be…Mathematics· Parabola· Tough· figure
  10. 10In an equilateral $\Delta ABC,r,R,r_{1}$, form (where symbols have usual meanings) leckgq f=Hkqt $\Delta ABC,$ $r,R,r_{1}$,Mathematics· Properties of triangle· Easy
  11. 11If $\frac{x^{2}}{r^{2} - r - 6} + \frac{y^{2}}{r^{2} - 6r + 5} = 1$will represents the ellipse, then set of all positive values of r is ä…Mathematics· Ellipse· Easy
  12. 12Find the latus rectum of the conic (3x+4y-4)^2=4(4x-3 y+1). 'kkado (3x+4y-4)^2=4(4x-3 y+1)Mathematics· Conic Sections· Easy
  13. 13Find the shortest distance between line y=x-2 & the parabola y=x^2+3x+2.Mathematics· Parabola· Moderate· figure
  14. 14The gradient of the common tangent to the two curves, y=x^2 - 5x+ 6 and x^2 + x+1 is nks oØksa y=x^2 - 5x + 6 rFkk y = x^2 + x + 1Mathematics· Conic Sections· Moderate
  15. 15The gradient of the common tangent to the two curves, y=x^2 - 5x + 6 and y = x^2 + x + 1is nks oØksa y=x^2 - 5x + 6 rFkk y = x^2 + x + 1Mathematics· Parabola· Easy· figure
  16. 16Let ABC be a triangle such that the coordinates of the vertex A are (-3,1). Equation of the median through B is 2x + y -3 =0 and equation…Mathematics· Straight Lines· Tough· figure
  17. 17One of the diameter of the circle circumscribing the rectangle ABCD is 4y = x + 7. If A and B are the points (-3, 4) and (5, 4)…Mathematics· Circles· Moderate
  18. 18If minimum distance between $y^{2} = 4x\ and\ x^{2} + y^{2} - 4x - 16y + 63 = 0\ is\ \sqrt{p}$ then value of $\frac{1111}{100}p$ is U;qure…Mathematics· Conic Sections· Easy· figure
  19. 19A circle is inscribed (i.e. touches all four sides ) into a rhombous ABCD with one angle 60°. The distance from the centre of the circle to…Mathematics· Circles· Moderate· figure
  20. 20Consider a ∆ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C respectively AD be a median of the ∆ABC.…Mathematics· Properties of triangle· Tough· figure
  21. 21Line 2y + x =8 cuts the parabola y^2 = 4x at point A and B. Now normal at A and B cuts at point P. Another normal from P (not passing…Mathematics· Parabola· Moderate· figure
  22. 22The centers of two circles C_1and C_2 each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line…Mathematics· Circles· Moderate· figure
  23. 23In a ∆ABC, b=12 units, c=5 units and ∆ =30 square units. If d is the distance between vertex A and in center of the triangle then the value…Mathematics· Properties of triangle· Moderate
  24. 24If circles $x^{2} + y^{2} = c\ $with radius $\sqrt{3}\ and\ x^{2} + y^{2} + ax + by + c = 0$with radius [IMAGE] intersect at two points A…Mathematics· Circles· Moderate· figure
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