Mathematics questions
18011 published questions with worked solutions.
- Let M and m respectively be the maximum and minimum values of the function f(x) = ^ -1 (sinx+cosx) in [0, 2 ], then the value of...
- Each of the persons A and B independently tosses three fair coins. The probability that both of them get the same number of heads...
- A differential equation representing the family of parabolas with axis parallel to y-axis and whose length of latus rectum is the...
- If two tangents drawn from a point P to the parabola y^2=16(x-3) are at right angles, then the locus of point P is :
- The equation of the plane passing through the line of intersection of the planes r .( i + j + k )=1 and r .(2 i +3 j + k )+4=0...
- If the solution curve of the differential equation (2x-10y^3)dy+ydx=0, passes through the points (0, 1) and (2, ), then is a root...
- Let A (a, 0), B(b, 2b + 1) and C(0, b), b 0, |b| 1 be points such that the area of triangle ABC is 1 sq. unit, then the sum of...
- Let [ ] be the greatest integer less than or equal to . The set of all values of for which the system of linear equations x + y +...
- The set of all values of k > –1, for which the equation (3x^2+4x+3)^2-(k+1)(3x^2+4x+2)(3x^2+4x+3)+k(3x^2+4x+2)^2=0 has real...
- A box open form top is made from a rectangular sheet of dimension a × b by cutting squares each of side x from each of the four...
- Let Z be the set of all integers, A = (x,y) Z Z : (x-2)^2+y^2 4 , B = (x,y) Z Z : x^2+y^2 4 and C = (x,y) Z Z : (x-2)^2+(y-2)^2 4...
- The area of the region bounded by the parabola (y-2)^2=(x-1), the tangent to it at the point whose ordinate is 3 and the x-axis...
- If y(x)= ^ -1 ( 1+ x + 1- x 1+ x - 1- x ), x ( 2 , ) then dy dx at x = 5 6 is :
- Two poles, AB of length a metres and CD of length a + b (b ) metres are erected at the same horizontal level with bases at B and...
- The value of the integral _0^1 xdx (1+x)(1+3x)(3+x) is :
- If _ x ( x^2-x+1 -ax)=b, then the ordered pair (a, b) is
- Let S be the sum of all solutions (in radians) of the equation ^4 + ^4 - =0 in [0, 4 ]. Then 8S is equal to ———Not in JEE Main syllabus
- Let S be the mirror image of the point Q(1, 3, 4) with respect to the plane 2x – y + z + 3 = 0 and let R(3, 5, ) be a point of...
- The probability distribution of random variable X is given by : X: 1,2,3,4,5; P(X): K,2K,2K,3K,K. Let p = P (1 < X < 4| X < 3)....
- Let Z_1 and Z_2 be two complex numbers such that arg(Z_1-Z_2) = 4 and Z_1, Z_2 satisfy the equation |Z – 3| = Re(z). Then the...