Practice questions
88551 published questions with worked solutions.
- If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a...
- If the 2^ nd , 5^ th and 9^ th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is
- If the sum of the first ten terms of the series (1 3 5 )^2 + (2 2 5 )^2 + (3 1 5 )^2 + 4^2 + (4 4 5 )^2 + , is 16 5 m, then m is...
- Let p = _ x 0^+ (1 + ^2 x )^ 1 2x then log p is equal to
- For x ∈ R, f(x) = |log 2 – sinx| and g(x) = f(f(x)), then :
- Consider f(x) = ^ -1 ( 1 + x 1 - x ), x (0, 2 ). A normal to y = f(x) at x = 6 also passes through the point :
- A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = x units and a circle of...
- The integral 2x^ 12 + 5x^9 (x^5 + x^3 + 1)^3 dx is equal to - (where C is an arbitrary constant)
- _ n ( (n + 1)(n + 2) 3n n^ 2n )^ 1 n is equal to -
- The area (in sq. units) of the region (x, y) : y^2 2x and x^2 + y^2 4x, x ≥ 0, y ≥ 0 is -
- If a curve y = f(x) passes through the point (1, –1) and satisfies the differential equation, y(1 + xy)dx = x dy, then f (- 1 2 )...
- Two sides of a rhombus are along the lines, x – y + 1 = 0 and 7x – y – 5 = 0. If its diagonals intersect at (–1, –2), then which...
- If one of the diameters of the circle, given by the equation, x^2 + y^2 - 4x + 6y - 12 = 0, is a chord of a circle S, whose...
- The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to...
- The distance of the point (1, –5, 9) from the plane x – y + z = 5 measured along the line x = y = z is :
- If the line, x - 3 2 = y + 2 -1 = z + 4 3 lies in the plane, ℓx + my – z = 9, then ^2 + m^2 is equal to :
- Let a , b and c be three unit vectors such that a ( b c ) = 3 2 ( b c ). If b is not parallel to c , then the angle between a and...
- If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true ?
- Let two fair six-faced dice A and B be thrown simultaneously. If E_1 is the event that die A shows up four, E_2 is the event that...
- If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x + cos 3x + cos 4x = 0, is :Not in JEE Main syllabus