List of top Questions asked in BCECE

If A and B are events with P(A ∪ B) = \(\frac{3}{4}\), P(A') = \(\frac{2}{3}\) and P(A ∩ B) = \(\frac{1}{4}\) then P(B) is

Two dices are thrown simultaneously. The probability of obtaining a total score of 5 is

The equation of the plane which bisects the line joining (3, 0, 5) and (1,2,-1) at right angles is

The equation of the line passing through the point (5, 3, 2) and perpendicular to the lines \(\frac{x-2}{1}=\frac{y-3}{-1}=\frac{z-4}{1}\) and \(\frac{x-1}{2}=\frac{y-1}{1}=\frac{z+1}{0}\) is

The angle between two diagonals of a cube is

If ω is an imaginary cube root of 1, then the value of 1(2 - ω) (2 - ω²)+ 2(3 - ω) (3 - ω²)+ … + (n-1)(n - ω) (n - ω²) is

The equation of the tangent and normal to the ellipse x² + 2y² + 2x - 4y - 14 = 0 at (2, -1) is

If the line \(2x+\sqrt6y=2\) touches the hyperbola x² - 2y² = 4, then the point of contact is

The imaginary part of conjugate of \((\frac{1+i}{1-i})^5\) is

If \(\sin^{-1}(\frac{x}{5})+\cosec^{-1}(\frac{5}{4})=\frac{\pi}{2},\) then the value of x

The general solution of \(\sqrt3\cos x+\sin x=\sqrt2\), for any integer “n” is

The value of \(4\tan^{-1}(\frac{1}{5})-\frac{\pi}{4}=\)

The area enclosed between the parabolas y² = 16x and x² = 16y is

The solution of y' = e^x-y + x²e^-y is

If the function f(x) defined by
\(f(x)=\frac{x^{100}}{100}+\frac{x^{99}}{99}+...+\frac{x^2}{2}+x+1,\)
then f'(0)=

The value of the integral \(\int\limits^{\pi}_{-\pi}\frac{\cos^2x}{1+a^x}dx,\)
a > 0 is

The value of the integral
\(\int\frac{e^x(x^2+1)}{(x+1)^2}\ dx=\)

The value of the integral
∫e^x{f(x) + f'(x)} dx is

A man 6' tall moves away from a source of light 20′ above the ground level, his rate of walking being 4 m.p.h. At what rate is the tip of his shadow moving ?

The maximum area of a rectangle that can be inscribed in a circle of radius 2 units is

If \(\cos^{-1}(\frac{y}{b})=\log(\frac{x}{n})^x\), then x²y₂ + xy¹ =

The angle between the curves
x² + y² = 25 and
x² + y² - 2x + 3y - 43 = 0 at (-3, 4) is

If \(y=x^{x^x}\), then y' =

If \(f(x)=\begin{cases} xe^{-(\frac{1}{|x|}+\frac{1}{x})}; & \text{if } x\ne0 \text{ then} \\ 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ ; & \text{if }x=0\end{cases}\)
which of the following is correct ?

If \(y=\sin^{-1}\frac{1}{2}(\sqrt{1+x}+\sqrt{1-x})\) then y' =