List of top Mathematics Questions

The dot product of a vector with the vectors i+ j-3 k, i+3 j-2 k, 2 i+ j+4 k are 0,5 and 8 respectively. The vector is
If the line through the points A(k,1,-1) and B(2k,0,2) is perpendicular to the line through the points B and C(2+2k,k,1), then the value of k is
The angle between the lines whose intercepts on the axes are (a,-b) and (b,-a) respectively, is
An urn contains five balls. Two balls are drawn and found to be white. The probability that all the balls are white is
If beginvmatrix p & q-y & r-z
p-x & q & r-z
p-x & q-y & r endvmatrix=0, then the value of (p)/(x)+(q)/(y)+(r)/(z) is
If R(t)= beginpmatrix cos t & sin t
-sin t & cos t endpmatrix, then R(s)R(t) equals
Let a, b, c be non-coplanar unit vectors equally inclined to one another at an acute angle θ. Then | a+ b+ c| in terms of θ is equal to
If int xlog(1+(1)/(x))dx = f(x)log(x+1)+g(x)x²+Lx+C, then
2¹/4·2²/8·2³/16·2⁴/32⋯ is equal to
If sumᵣ=0ⁿ(-1)ʳfracⁿCᵣⁿ+3Cᵣ=(3)/(a+3), then a-n is equal to
If f(z)=dfrac7-z1-z², where z=1+2i, then |f(z)| is equal to
A cylindrical gas container is closed at the top and open at the bottom. If the iron plate of the top is (5)/(4) times as thick as the plate forming the cylindrical sides, find the ratio of the radius to the height of the cylinder using minimum material for the same capacity.
If f(x)=cos⁻1[(1-(log x)²)/(1+(log x)²)], then the value of f'(e) is equal to
Statement–1: A five digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 with repetition. The total number formed are 216. Statement–2: If sum of digits of any number is divisible by 3 then the number must be divisible by 3.
The equation of one of the common tangents to the parabola y²=8x and the circle x²+y²=12x+4 is
If f(x)= begincases (xlog(cos x))/(log(1+x²)), & x≠ 0
0, & x=0 endcases then f(x) is
The area under the curve y=|cos x-sin x|, 0≤ x≤ (π)/(2), above the x-axis is
The number of roots of the equation cos 3θ=0 for 0≤θ\le2π is
The maximum value of z=3x+2y subject to x+2y\ge2, x+2y\le8, x,y\ge0 is
If f(x)=xˣ, then f(x) is increasing in interval
The value of cot⁻17+cot⁻18+cot⁻118 is
If x is a real number, then (x)/(x²-5x+9) must lie between
If int (cos x-1)/(sin x+eˣ)dx is equal to
The value of limₓtₒᵢₙfty(fraca₁¹/x+a₂¹/x+⋯+aₙ¹/xn)ⁿx, aᵢ>0 is
An equilateral triangle is inscribed in the circle x²+y²=a² with one of the vertices at (a,0). What is the equation of the side opposite to this vertex?