If \(f(x)={ Cx }^{ 2 }={ cx }^{ 2 },0 is the p.d.f, of x then c is _____________

The population p of a certain bacteria decreases at a rate proportional to the population p. The differential equation corresponding to the above statement is __________.

The solution of \(\frac{dy}{dx}+y\) cot x = sin 2x is ___________

Which of the following is a statement?

Which of the following is a contradiction?

If u = log (x³ + y³ + z³ - 3xyz) then \(\frac { { \partial }u }{ \partial { x } } +\frac { { \partial }u }{ { \partial y } }+ \frac { { \partial }u }{ \partial z } \) = _____________

The statement "If f has a local extremum at c and if f'(c) exists then f'(c) = 0" is ________

A binary operation on a set S is a function from

The value of \(\int _{ -4 }^{ 4 }{ \left[ { tan }^{ -1 }\left( \frac { { x }^{ 2 } }{ { x }^{ 4 }+1 } \right) +{ tan }^{ -1 }\left( \frac { { x }^{ 4 }+1 }{ { x }^{ 2 } } \right) \right] dx } \) is

A circular template has a radius of 10 cm. The measurement of radius has an approximate error of 0.02 cm. Then the percentage error in calculating area of this template is

A rod of length 2l is broken into two pieces at random. The probability density function of the shorter of the two pieces is
\(f(x)=\left\{\begin{array}{ll} \frac{1}{l} & 0< x < l \\ 0 & l <x<2l \end{array}\right.\)
The mean and variance of the shorter of the two pieces are respectively.

The solution of \(\frac{d y}{d x}+p(x) y=0\) is

The volume of a sphere is increasing in volume at the rate of 3 πcm³ / sec. The rate of change of its radius when radius is \(\frac { 1 }{ 2 } \) cm

The angle between the planes 2x + y - z = 9 and x + 2y + z = 7 is_____________

The area of the parallelogram having diagonals \(\overset { \rightarrow }{ a } =3\overset { \wedge }{ i } +\overset { \wedge }{ j } -2\overset { \wedge }{ k } \) and \(\overset { \rightarrow }{ b } =\overset { \wedge }{ i } -3\overset { \wedge }{ j } +\overset { \wedge }{ 4k } \) is ____________

The director circle of the ellipse \(\frac { { x }^{ 2 } }{ 9 } -\frac { { y }^{ 2 } }{ 5 } =1\) is ____________

\(cot\left( \frac { \pi }{ 4 } -{ cot }^{ -1 }3 \right) \)

For real x, the equation \(\left| \frac { x }{ x-1 } \right| +|x|=\frac { { x }^{ 2 } }{ |x-1| } \) has ________

The number of solutions of the system of equations 2x+y = 4, x - 2y = 2, 3x + 5y = 6 is ____________

If \(\vec{a}\) and \(\vec{b}\) are parallel vectors, then \([\vec { a } ,\vec { c } ,\vec { b } ]\) is equal to

The equation of the circle passing through (1, 5) and (4, 1) and touching y-axis is x² + y² − 5x − 6y + 9 + \(\lambda\)(4x + 3y − 19) = 0 where λ is equal to

The value of sin^-1 (cos x), \(0\le x\le\pi\) is

A zero of x³ + 64 is

iⁿ+iⁿ⁺¹+iⁿ⁺²+iⁿ⁺³ is