Mathematics questions
18011 published questions with worked solutions.
- If the x-intercept of a focal chord of the parabola y^2=8x+4y+4 is 3, then the length of the chord is equal to __________.
- Let + + = 1 be the equation of a plane passing through the point (3, –2, 5) and perpendicular to the line joining the points (1,...
- The line x = 8 is the directrix of the ellipse E : x^2 a^2 + y^2 b^2 =1 with the corresponding focus (2, 0). If the tangent to E...
- Number of integral solutions to the equation x + y + z = 21, where x 1, y 3, z 4, is equal to __________.
- Let the sixth term in the binomial expansion of ( 2^ _2(10-3^x) + [5] 2^ (x-2) _23 )^m, in the increasing powers of 2^ (x-2) _23...
- The sum of the common terms of the following three arithmetic progressions. 3, 7, 11, 15, …, 399, 2, 5, 8, 11, …, 359 and 2, 7,...
- The total number of six digit numbers, formed using the digits 4, 5, 9 only and divisible by 6, is __________.
- If _0^ 5^ x (1+ x 3x+ ^2x+ ^3x 3x) 1+5^ x dx= k 16 , then k is equal to __________.
- If the orthocenter of the triangle, whose vertices are (1, 2), (2, 3) and (3, 1) is ( , ), then the quadratic equation whose...
- The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3, 5, then the sum of cubes of the...
- If the centre and radius of the circle | z-2 z-3 |=2 are respectively ( , ) and , then 3( + + ) is equal to
- If y = y(x) is the solution curve of the differential equation dt dx +y x=x x, 0 x 3 , y(0) = 1, then y ( 6 ) is equal to
- The sum to 10 terms of the series 1 1+1^2+1^4 + 2 1+2^2+2^4 + 3 1+3^2+3^4 + is
- The combined equation of the two lines ax + by + c = 0 and a'x + b'y + c' = 0 can be written as (ax + by + c) (a'x + b'y + c') =...
- Let S be the set of all solutions of the equation ^ -1 (2x)-2 ^ -1 ( 1-x^2 )= , x [- 1 2 , 1 2 ]. Then _ x S 2 ^ -1 (x^2-1) is...
- The value of 1 1!50! + 1 3!48! + 1 5!46! + + 1 49!2! + 1 51! is :
- Let S denote the set of all real values of such that the system of equations x+y+z=1, x+ y+z=1, x+y+ z=1 is inconsistent, then _...
- For a triangle ABC, the value of cos2A + cos2B + cos2C is least. If its inradius is 3 and incentre is M, then which of the...Not in JEE syllabus
- Let f(x) = vmatrix 1+ ^2x& ^2x& 2x ^2x&1+ ^2x& 2x ^2x& ^2x&1+ 2x vmatrix , x [ 6 , 3 ]. If and respectively are the maximum and...
- The area enclosed by the closed curve C given by the differential equation dy dx + x+a y-2 =0, y(1) = 0 is 4 . Let P and Q be the...