Mathematics questions
18011 published questions with worked solutions.
- If y = y(x) is the solution of the differential equation 5+e^x 2+y dy dx +e^x=0 satisfying y(0) = 1,then a value of y( _e13) is :
- A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of...
- The product of the roots of the equation 9x^2-18|x|+5=0, is
- If (e^ 2x +2e^x-e^ -x -1)e^ (e^x+e^ -x ) dx=g(x)e^ (e^x+e^ -x ) +c, where c is a constant of integration, then g(0) is equal to :
- If the minimum and the maximum values of the function f: [ 4 , 2 ] R, defined by : f( )= vmatrix - ^2 &-1- ^2 &1 - ^2 &-1- ^2 &1...
- Let R. The system of linear equations 2x_1-4x_2+ x_3=1 x_1-6x_2+x_3=2 x_1-10x_2+4x_3=3 is inconsistent for :
- Is S is the sum of the first 10 terms of the series ^ -1 ( 1 3 )+ ^ -1 ( 1 7 )+ ^ -1 ( 1 13 )+ ^ -1 ( 1 21 )+ , then tan(S) is...
- If the four complex number z, z , z -2Re( z ) and z-2Re(z) represent the vertices of a square of side 4 units in the Argand...
- The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14, then the absolute...
- If (a, b, c) is the image of the point (1, 2, – 3) in the line, x+1 2 = y-3 -2 = z -1 , then a + b + c is equal to
- The value of _ - /2 ^ /2 1 1+e^ x dx is
- If 2^ 10 +2^9 3^1+2^8 3^2+ +2 3^9+3^ 10 =S-2^ 11 , then S is equal to :
- If the co-ordinates of two points A and B are ( 7 ,0) and (- 7 ,0) respectively and P is any point on the conic, 9x^2+16y^2=144,...
- If is the positive root of the equation, p(x)=x^2-x-2=0, then _ x ^+ 1- (p(x)) x+ -4 is equal to
- Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five,...
- If the line. 2x – y + 3 = 0 is at a distance 1 5 and 2 5 from the lines 4x – 2y + = 0 and 6x – 3y + = 0, respectively, then the...
- The natural number m, for which the coefficient of x in the binomial expansion of (x^m+ 1 x^2 )^ 22 is 1540, is _______.
- The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word...
- Let f(x)=x [ x 2 ], for – 10 < x < 10, where [t] denotes the greatest integer function. Then the number of points of...
- If the system of linear equations x+y+3z=0 x+3y+k^2z=0 3x+y+3z=0 has a non-zero solution (x, y, z) for some k ∈ R, then x+ ( y z...