Mathematics questions
18011 published questions with worked solutions.
- A survey shows that 63% of the people in a city read newspaper A whereas 76% read newspaper B. If x% fo the people read both the...
- Let f(x) = |x – 2| and g(x) = f(f(x)), x ∈ [0, 4]. Then _0^3(g(x)-f(x)) ,dx is equal to :
- Let x_0 be the point of local maxima of f(x)= a ( b c ), where a =x i -2 j +3 k , b =-2 i +x j - k and c =7 i -2 j +x k . Then...
- Two vertical poles AB = 15 m and CD = 10 m are standing apart on a horizontal ground with points A and C on the ground. If P is...Not in JEE syllabus
- Let x^2 a^2 + y^2 b^2 =1 (a > b) be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value...
- If 1+(1-2^2 1)+(1-4^2 3)+(1-6^2 5)+ +(1-20^2 19)= -220 , then an ordered pair ( , ) is equal to :
- The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then...
- Let f(x)= x (1+x)^2 dx (x ≥ 0). Then f(3) – f(1) is equal to :
- If the equation of a plane P, passing through the intersection of the planes, x + 4y – z + 7 = 0 and 3x + y + 5z = 8 is ax + by +...
- Let (2x^2+3x+4)^ 10 = _ r=0 ^ 20 a_rx^r. Then a_7 a_ 13 is equal to _______.
- Suppose a differentiable function f(x) satisfies the identity f(x + y) = f(x) + f(y) + xy^2 + x^2y. for all real x and y. If _ x...
- If the system of equations x-2y+3z=9 2x+y+z=b x-7y+az=24, has infinitely many solutions, then a – b is equal to __________.
- The probability of a man hitting a target is 1 10 . The least number of shots required, so that the probability of his hitting...
- In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two...
- Let 0 be in R. If and are the roots of the equation, x^2-x+2 =0 and and are the roots of the equation, 3x^2-10x+27 =0, then is...
- Let x = 4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is 1 2 . If P(1, ), > 0 is a point on...
- If the system of equations x+y+z=2 2x+4y-z=6 3x+2y+ z= has infinitely many solutions, then :
- The area (in sq. units) of the largest rectangle ABCD whose vertices A and B lie on the x-axis and vertices C and D lie on the...
- If a and b are real numbers such that (2+ )^4=a+b , where = -1+i 3 2 , then a + b is equal to :
- The solution of the differential equation dy dx - y+3x _e(y+3x) +3=0 is : (where C is a constant of integration.)