If ax + by + c = 0 is normal to xy = 1, then determine if a and b are less than, greater than, or equal to zero.
Find the general solution of the differential equation: cosx (1 + cosy) dx - siny (1 + sinx) dy = 0
Three vectors a, b and c are given. Find the equation of a vector that lies in the plane of vector a and vector b and whose projection on vector c is 1/√3.
What is the number of solutions of tanx + secx = 2 cosx if x belongs to (0, 2π)?
Find the coordinates of the point where the line through A (9, 4 , 1) and B (5, 1, 6) crosses X axis ?
\( \int \frac{dx}{\sin(x) + \cos(x)} = ? \)
Find ∫(cos√x) dx=?
∫\(\frac {e^x}{(2+e^x)(e^x +1)}\)dx = (where C is a constant of integration.)
Two numbers are selected at random from the first six positive integers. If X denotes the larger of two numbers, then Var (X) =?
If the lines 2x – 3y = 5 and 3x – 4y = 7 are the diameters of a circle of area 154 sq. units, then equation of the circle is (Taken π=\(\frac {22}{7}\))
If the slope of one of the lines given by ax2 + 2hxy + by2 = 0 is two times the other, then
If matrix A =\(\begin{bmatrix} 1 & 2 \\ 4 & 3 \end{bmatrix}\) is such that AX = I, where I is 2 x 2 unit matrix, then X =
If the position vectors of the points A and B are 3\(\hat {i}\) + \(\hat {j}\) + 2\(\hat {k}\) and \(\hat {i}\) -2\(\hat {j}\) -4\(\hat {k}\) respectively, then the equation of the plane through B and perpendicular to AB is
Let cos (α + β) = \(\frac {4}{5}\) and sin (α - β) = \(\frac {5}{13}\), where 0 < α, β < \(\frac {π}{4}\) , then tan 2α=?
If y = sec–1\((\frac {x + x^{-1}}{x - x^{-1}})\), then \(\frac {dy}{dx}\) =?
A random variable X has the following probability distribution then P (X ≥ 2) =?
lim(x→0)\((\frac {1+tanx}{1+sinx})^{cosec x}\) = ?
The second derivative of a sin 3t w.r.t. a cos 3t at t =π/4 is
