questions
Integration
* Integrate
e^{x^(1/3)}dx
* evaluate
integral of [e^(x) +1] ^2
*evaluate
∫ (sin 3x)^4 dx with limits
0 to pi
*the
integral of (1+x) /[ x *sqrt(x2)]
* evaluate
the integral of sqrt(tan x)
*
evaluate
integral of { sqrt{1+(x^2)} } / {x^2}
using
integration by parts
*∫
sec³x dx using integration
by parts
*integral
of (e^(ax) ) cosbx using integration
by parts
*∫
arc(tan4x)
using integration by parts
*evaluate
the integral of coshx cosx by integration by part
method
*evaluate
.∫ (x²) sin x dx using integration by parts
*evaluate
.∫ x ²cos(mx) dx using integration by parts
*integral
of log(sin x) from 0 to pi/2 (where the log is of
base e)
Area using integral
* evaluate
the area of an ellipse (x² /a²) +
(y²/b²) =1 using integration
* find
the area between y² = x and x² =y
* find
the area bounded b y =x² and y = 3x
Differential equation
*solve
x(dy/dx) + (1+x)y =2
Differentiation
differentiation from first principles
*differentiate
sqrt(x) from first principle
*if
y = x sinx , find dy/dx from first
principles
*find
the derivative of f(x) =1/x at x=3 using the
lim {f(x)f(a)} / {xa} as x>a
*derivative
of ln(x + sqrt(x^21))
Implicit differentiation
*find
dy/dx if sqrt(x) +sqrt(y)
= 8
*if
xy + y^2 =1 , find dy/dx
*if
√(xy) = x  2y, find dy/dx using implicit
differentiation
Differentiation using trigonometric substitution
*differentiate.
arctan
√ [(1x)/(1+x)] w.r.t..x using trigonometric
substitution
Application
of differential calculus
* power
series expansion for y = arctan(x) in powers of x
*find
the maclaurin series for sec x
Boolean Algebra
*show
that (p v q) → r ≡ (p → r) ^ (q→ r)
Mathematical Induction
*Prove
that
[1/(1x2) ]+[1/(2x3)]+...+ [1/( n(n+1) )] = n/n+1
using mathematical induction)
*prove
by mathematical induction
that 1^3 +2^3 + 3^3 +...+ n^3 = [ ( n
(n+1) ) /2 ] ^2
Partial fraction
*put
into partial fraction 1 / { (x^3) + 1 }
Algebra
*When
a polynomial p(x) is divided by (x+1), the remainder is
4.
And when it is divided by (x2), it's remainder is 3.
What is the remainder when p(x) is divided by
x²x2
*Express
the recurring decimal 0.484848... as a fraction
using the concept of geometric series
*If
the sum of two consecutive odd integers is 20,
find the numbers
*Factorise
2(x^3)  3 (x^2)  3x +2
*Person
A takes 6 days less than the time taken by the person
B to finish a particular piece of work. If both A and
B work
together , they can finish it in 4 days. Find the time
that B
would take to finish this work by himself
*form
a quadratic equation whose roots are
3 and 4
* Complex
Number
Notes on complex numbers, concept of the imaginary unit i,
powers of i,
general form of a complex number, modulus, amplitude etc.
* Progression
Arithmetic progression(A.P.),
Geometric progression (G.P), Harmonic progression
(H.P) ,
nth term , sum of n terms, of A.P. and G.P sum
of infinite number of terms of a G.P
, sum of the first n natural numbers,
sum of the squares of the first n natural numbers and
sum of the cubes of the first n natural numbers
* Trigonometry
formula
trigonometry identity, trigonometry formulae,
trigonometric
ratio/value of standard angle
*Analytical
Geometry
The distance formula, section formula, midpoint formula,
various equations of
straight line like point slope,two point, intercept form,
equation of circle, condition
for orthogonal circle, equation of tangent to a circle are
given.
*Vector
vector dot product, cross product,magnitude or modulus
of a vector, unit vector
scalar triple product [S.T.P], vector triple
product[V.T.P]
*list
of differentiation formula
list of differentiation formula like power rule,
trigonometric function
*integral
calculus integration formula
list of formula used for integration of functions,
integral calculus
*correlation
coefficient equation of regression line
Carl pearson correlation coefficient, equation of the
line of regression
of y on x and the regression line of x on y
*Indeterminate
forms, LHospital's rule, Permutation and Combination
the list of indeterminate forms, how to evaluate limits of
the form 0/0 and infinity/ infinity using
l hospital's rule, the concept of permutation and
combination
*square
root without using calculator by using long division
method
method of finding the square root by long division without
using calculator
*Hyperbolic
function
Definition of hyperbolic functions sinh x, cosh x ,tanh
x , coth x, cosech x, sech x
and some identities of hyperbolic functions.
*Laplace
Transform Inverse laplace transform
Laplace transform and inverse laplace transform of some
standard functions
for b.tech, be students.
* Graph
Theory definitions
This page contains some of the most basic definitions from
the subject of
graph theory, which might be useful to the students of
computer science.

