Mathematics questions
18011 published questions with worked solutions.
- If ^1P_1+2.^2P_2+3.^3P_3+ +15 ^ 15 P_ 15 =^qP_r-s, 0 s 1, then ^ q+s C_ r-s is equal to _________.
- The area of the region S = (x, y) : 3x^2 4y 6x+24 is _________.
- The locus of a point, which moves such that the sum of square of its distances from the points (0,0), (1,0), (0,1) (1,1) is 18...
- If y = y(x) is an implicit function of x such that _e(x+y)=4xy. then d^2y dx^2 at x = 0 is equal to _________.
- The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is...
- Let a, b R, b 0, Define a function f(x)= cases a 2 (x-1), & for x 0 2x- 2x bx^3 , & for x>0 cases If f is continuous at x = 0,...
- If vectors a_1 =x i - j + k and a_2 = i +y j +z k are collinear, then a possible unit vector parallel to the vector x i +y j +z k...
- Let f:R R be defined as f(x)= cases 2 (- x 2 ), & x<-1 |ax^2+x+b|, & -1 x 1 ( x), & x>1 cases If f(x) is continuous on R, then a...
- For x > 0, if f(x)= _1^x _et (1+t) dt, then f(e)+f ( 1 e ) is equal to
- A natural number has prime factorization given by n = 2^x3^y5^z, where y and z are such that y + z = 5 and y^ -1 +z^ -1 = 5 6 , y...
- Let f(x) = ^ -1 x and g(x) = x^2-x-2 2x^2-x-6 If g(2) = _ x 2 g(x), then the domain of the function fog is
- The triangle of maximum area that can be inscribed in a given circle of radius 'r' is :Not in JEE syllabus
- Let L be a line obtained from the intersection of two planes x + 2y + z = 6 and y + 2z = 4. If point P( , , ) is the foot of...
- Let F_1(A,B,C)=(A B) [ C (A B)] A and F_2(A,B)=(A B) (B A) be two logical expressions. Then :Not in JEE syllabus
- If the locus of the mid-point of the line segment from the point (3, 2) to a point on the circle, x^2+y^2=1 is a circle of radius...
- Consider the following system of equations : x + 2y – 3z = a, 2x + 6y – 11z = b, x – 2y + 7z = c, where a, b and c are real...
- If 0 < a, b < 1, and ^ -1 a+ ^ -1 b= 4 , then the value of (a+b)- ( a^2+b^2 2 )+ ( a^3+b^3 3 )- ( a^4+b^4 4 )+ is :
- Let A(1, 4) and B(1, –5) be two points. Let P be a point on the circle (x-1)^2+(y-1)^2=1 such that (PA)^2+(PB)^2 have maximum...
- If the mirror image of the point (1, 3, 5) with respect to the plane 4x – 5y + 2z = 8 is ( , , ), then 5( + + ) equals :
- Let f(x)= _0^xe^tf(t)dt+e^x be a differentiable function for all x R. Then f(x) equals :