Mathematics questions
18011 published questions with worked solutions.
- Let P be the image of the point (3,1,7) with respect to the plane x-y+z=3. Then the equation of the plane passing through P and...
- Let a,b R and f: R R be defined by f(x)=a (|x^3-x|)+b|x| (|x^3+x|). Then f is
- Let f: R (0, ) and g: R R be twice differentiable functions such that f'' and g'' are continuous functions on R . Suppose...
- Let a,b R and a^2+b^2 0. Suppose S= z C :z= 1 a+ibt ,t R ,t 0 , where i= -1 . If z=x+iy and z S, then (x,y) lies on
- Let a, , R . Consider the system of linear equations ax+2y= 3x-2y= Which of the following statement(s) is(are) correct?
- Let u =u_1 i +u_2 j +u_3 k be a unit vector in R ^3 and w = 1 6 ( i + j +2 k ). Given that there exists a vector v in R ^3 such...
- If 2x-y+1=0 is a tangent to the hyperbola x^2 a^2 - y^2 16 =1, then which of the following CANNOT be sides of a right angled...
- If a chord, which is not a tangent, of the parabola y^2=16x has the equation 2x+y=p, and midpoint (h,k), then which of the...
- Let [x] be the greatest integer less than or equals to x. Then, at which of the following point(s) the function f(x)=x ( (x+[x]))...
- Let f: R (0,1) be a continuous function. Then, which of the following function(s) has(have) the value zero at some point in the...
- Let a, b, x and y be real numbers such that a-b=1 and y 0. If the complex number z=x+iy satisfies Im ( az+b z+1 )=y, then which...
- Let X and Y be two events such that P(X)= 1 3 , P(X|Y)= 1 2 and P(Y|X)= 2 5 . Then
- For how many values of p, the circle x^2+y^2+2x+4y-p=0 and the coordinate axes have exactly three common points?
- Let f: R R be a differentiable function such that f(0)=0, f ( 2 )=3 and f'(0)=1. If g(x)= _x^ 2 [f'(t) cosec t- t cosec t ,f(t)]...
- For a real number , if the system bmatrix 1 & & ^2 & 1 & ^2 & & 1 bmatrix bmatrix x y z bmatrix = bmatrix 1 -1 1 bmatrix of...
- Words of length 10 are formed using the letters A, B, C, D, E, F, G, H, I, J. Let x be the number of such words where no letter...
- The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its...
- The equation of the plane passing through the point (1,1,1) and perpendicular to the planes 2x+y-2z=5 and 3x-6y-2z=7, is
- Let O be the origin and let PQR be an arbitrary triangle. The point S is such that OP OQ + OR OS = OR OP + OQ OS = OQ OR + OP OS...Not in JEE syllabus
- If y=y(x) satisfies the differential equation 8 x ( 9+ x )dy= ( 4+ 9+ x )^ -1 dx, x>0 and y(0)= 7 , then y(256)=