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Browse our library of Math concepts, absolutely free
Level 1 - Class 6,7 & 8
Ratio and Proportional Relationships
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To find the ratio of ages of father and son.
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Application of ratio and proportion using unitary method.
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To find the percentage based on given conditions.
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To find the percentage decrease based on given conditions.
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To calculate the amount and compound interest compounded half
yearly.
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To compare simple interest and compound interest based on given
conditions.
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To find the distance a loaded truck travels ,with the help of given
data using the concept of direct proportion.
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To find the number of machines required in a factory with the help
of given data using the concept of inverse proportion.
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Compare the populations of two states of a country.
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To calculate the original borrowed sum for a given interest rate.
Geometry
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To find the kind of triangle using angle sum property.
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Find the angle measure using angle sum property.
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Find the angle measure between hands of a clock.
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Application of perimeter of plane figures.
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To find the remaining part of land on a square flower bed.
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To find the number of tiles using the concept of perimeter of
rectangle.
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How to draw chords of a circle and construct the perpendicular
bisectors.
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How to draw angle measure of 135 degrees and bisect it.
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To find the angle measure in the given figure.
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To find the number of sides of a regular polygon if the measure of
an exterior angle is given.
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To find the value of the unknowns x, y and z by considering the
given parallelogram.
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To construct a quadrilateral when two adjacent sides and three
angles are known.
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To construct a quadrilateral when three sides and two included
angles are known.
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How to find the values of x, y, z in the given figure using the concept
of supplementary and complementary angles.
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Find the angles in the given figure.
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Find the value of an unknown interior angle x in a triangle.
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Find the values of the unknown angles in a given triangle.
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Is the sum of four sides of a quadrilateral less than twice the sum of
its diagonals?
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Using Pythagoras theorem find the original height of a broken tree
if some parameters are given.
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To prove that the bisector of the vertical angle of an isosceles
triangle bisects the base.
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How to construct an isosceles right triangle?
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How to find the area and height of a given triangle?
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How to calculate the distance covered by a minute hand of a circular
clock?
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How to find the area of crossroads in a rectangular path?
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How to find the number of revolutions made by a wheel of a car?
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What cross sections do we get if some solids are cut horizontally or
vertically?
Statistics and probability
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How to draw temperature time graph.
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To draw a bar graph and answer questions on it.
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To find the mean, median and mode for the given data.
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To plot a double bar graph for a temperature problem.
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To find the probability in tossing of an unbiased coin.
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To find the number of outcomes of an event by using the given
data (in dice problem).
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To find the probability of the occurrence of a particular event using
the given data.
The Number System
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To find the total distance covered in a particular time.
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Cost problem based on distributive law of multiplication.
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To find consecutive composite numbers less than 100.
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Find the missing number in the given factor tree.
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To find the H.C.F by prime factorization.
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Simplify using distributive laws.
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A problem on comparing unlike fractions.
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Complete the addition and subtraction box using sum and difference
of fraction.
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Weight problem based on addition and subtraction of decimals.
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Express the given decimals as fractions.
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By what integer should 100 be divided to obtain a particular integer?
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Count the number of steps moved.
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Compare perimeters of a rectangle and a square.
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Compare who bought more fruits in decimals.
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To find five rational numbers between two given fractions.
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To find the square root of the given number by prime factorization
method.
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Using long division method, to find the side of a square whose
area is given.
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To find the smallest number by which the given number may be
divided to obtain a perfect cube.
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To find the cube root of a given number by prime factorization
method.
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To find the value of the given expression using laws of exponents.
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To find the given expression using laws of exponents.
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To find the values of unknown constants A and B.
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To find the value of x using divisibility tests.
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How to compare two given fractions?
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How to simplify and express the given expression in exponential
form?
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How to find the value of x in a given expression using properties
of exponents?
Expressions and Equations
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How to find the number of oranges in large and small boxes using
variables?
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Form an equation for the given riddle.
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Solve the given linear equation in one variable.
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Application of simple linear equations to a practical situation.
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To find the three consecutive integers using given conditions.
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To find a two digit number using given conditions.
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To solve the given linear equation.
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To add two given algebraic expressions.
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To subtract first algebraic expression from the second algebraic
expression.
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To simplify the given polynomial expression.
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To find the given square using suitable identity.
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To factorize the given expression using a suitable identity.
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To factorize the given expression as directed.
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To find and correct the errors in the given mathematical statement.
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To draw a graph for the given data and check if it is linear or not.
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How to find the value of an unknown variable 'a' if x is equal to 0
in the given expression
Level 2 - Class 9 & 10
Number and Quantity
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To find three rational numbers between two given rational numbers.
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Representing irrational numbers on the number line.
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Rationalizing the denominator.
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Using Euclid's division lemma to find the HCF of two given numbers.
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Expressing given numbers as the product of their prime factors.
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To prove that the given number is irrational.
Algebra
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Using remainder theorem to check whether a given polynomial is the
factor of the other polynomial.
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Factorization of a polynomial involving three terms (by splitting the
middle term).
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Factorization of a polynomial involving four terms.
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Application of algebraic identity.
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Framing a linear equation in two variables.
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Finding a quadratic polynomial whose zeroes are given.
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Divide two polynomials and verify the result using division algorithm.
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To find the zeroes of a quadratic polynomial and to verify the
relationship between the zeroes and the coefficients.
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To solve the system of equations using cross multiplication method.
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To solve the system of linear equations (in age problem) using
substitution method.
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Using elimination method, find the number if the sum of digits of
that number is given along with the some other data.
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To solve a system of equations by reducing it to pairs of linear
equations.
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To solve the given quadratic equation by factorization.
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To solve the given problem (distance speed problem) using the
concept of quadratic equation.
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To find the solution of the given quadratic equation by completing
the square.
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To solve an age problem by using middle term splitting method.
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In an arithmetic progression, find the nth term from the end.
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To find the number of terms and common difference if the first term,
last term and the sum is given.
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To find the sum of first n multiples of a given number.
Functions
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To evaluate the given trigonometric expression using trigonometric
ratios of angles.
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To find the values of two unknown variables using trigonometric
ratios of angles.
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To find the angle measure using trigonometric ratios of
complementary angles.
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To prove the given identity (involving acute angles).
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To prove the given identity (involving acute angles).
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To find the height of the building using the given data (involving
angle of elevation) using trigonometric ratios of angles.
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To find the distance between two places using the given data
(involving angle of depression) using trigonometric ratios of angles.
Geometry
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Locating given points in the Cartesian plane.
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Finding angle measure using given conditions.
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Finding angle measure using given conditions, based on parallel
lines.
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Finding angle measure using properties of parallel lines and angle
sum property.
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Finding angle measures using properties of triangles
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Finding angle measure using angle sum property of quadrilaterals.
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Application of midpoint theorem.
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Application of the theorem, triangles and parallelograms on the
same base and between same parallel lines are equal in area.
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Application of area of parallelogram.
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To find the perpendicular bisector of the given line.
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To find angle measure using given data and theorems based on
circles.
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Steps of construction to form an equilateral triangle whose altitude
measure is given.
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Finding area of a triangle using Heron's formula
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To find the depth of the trapezium if area of trapezium and length of
its two sides are given.
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To find the lateral and total surface areas of cube and cuboids.
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To find the height of a right circular cylinder if the area and radius of
the cylinder are given.
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Comparing the surface areas of two spheres (the moon and the
earth).
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To find the volume of a cuboids using given data.
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To find the volume of sphere using given data.
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To check whether the two given quadrilaterals are similar or not.
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To show that the two given triangles are similar.
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To prove the given result using Pythagoras theorem.
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To find a point on x-axis using given data by distance formula.
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To find the coordinates of a point using section formula.
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To find the area of a triangle provided coordinates of the three
vertices are given.
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To find the area of the shaded region in the given figure.
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To find the curved surface area of the frustum of a cone.
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To find the volume of a cuboids when volume of two cubes joined
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To find the height of the cylinder when the sphere of the given
radius is converted to form a cylinder.
Statistics and probability
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Finding mean, median and mode.
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Tossing two coins simultaneously and finding the probability of two
heads coming up.
Level 3 - Class 11 & 12
Number and Quantity
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Finding argument and modulus of a given complex number.
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Solving quadratic equation with complex roots.
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Find the product of multiplication of given matrices.
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Verify the given expression using the required operations
(transpose and addition) on matrices.
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Find the inverse of the given functions using elementary
transformation.
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Prove the given identity using basic properties of determinants.
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Find the area of a triangle for which coordinates of its vertices are
given.
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Solving linear equations using matrix method.
Geometry
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Finding slope of a line with help of given conditions.
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To find the equation of a line with the help of given conditions.
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To find the equation of a circle with the help of given conditions.
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To find the equation of a parabola with the help of given conditions.
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To find the equation of an ellipse with the help of given conditions.
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To find the equation of a hyperbola with the help of given conditions.
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Prove that the given points are collinear.
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Finding the ratio in which a given plane intersects a
given line segment.
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Find the values of x and y if 2 equal vectors are given.
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Find the unit vector in the direction of given vector.
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Find the angle between two given vectors.
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Find the projection of one vector on another vector.
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Find the value of λ based on given conditions.
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Find the value of x for the given unit vector.
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Find the direction cosines.
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Find the direction cosines if direction ratios are given.
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Find the equation of the line which passes through the given point
and is parallel to the given vector.
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Find the angle between the given pair of lines.
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Find the shortest distance between two lines whose vector
equations are given.
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Find the coordinates of the foot of the perpendicular drawn from the
origin.
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Find the intercepts cut off by the given equation of the plane.
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Find the distance of a point from the given plane.
Statistics and probability
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How many different words can be formed using the letters of a
single word.
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To find the number of ways in which a particular card can
be selected from a deck of 52 playing cards with the help of given
conditions.
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To find mean deviation about median for the given data.
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To find variance and standard deviation for given data.
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To find the conditional probability with the help of given data.
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Find the probability using the concept of independent events.
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Find the probability using the concept of multiplication theorem.
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Find the probability using Bayes Theorem.
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Find the probability distribution of the given event.
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Find binomial distribution if mean and standard deviation is given.
Discrete Mathematics
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Verify the given condition using basic operation of sets.
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Solve the given practical problem using Venn diagram.
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Solve the given linear programming problem graphically
(minimization problem).
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Solve the given linear programming problem graphically
(maximization problem).
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Practical problem on linear programming.
Functions
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Find the domain and range of the given function.
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Prove the given identity by using basic trigonometric formulas.
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Solve the given trigonometric equation.
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Finding limit of the given function.
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Find the derivative of the given expression by first principle.
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Find the inverse of the given function.
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Find the principle value of the given function.
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Simplify the given expression using properties of inverse
trigonometric functions.
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Check the continuity of the given function at a given point.
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Find the derivative of the given function.
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Find the derivative of the given implicit function.
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Find the derivative of the given logarithmic function.
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Find the derivative of the given function in parametric form.
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Verify the mean value theorem for the given function using given
conditions.
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Practical problem on rate of change of quantities.
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Find the intervals of x where function is increasing or decreasing.
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Find the slope of the given function at a given point.
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Practical problem on maxima and minima.
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Find the integration of the given function.
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Find the integration of the given function using substitution method.
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Find the integration of the given function using trigonometric
identities.
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Find the integration of the given function by parts.
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Find the definite integration of the given function.
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Find the definite integration of the given function using substitution
method.
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Find the definite integration using its properties.
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Find the area of the region bounded by a curve and a line.
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Find the area between two given curves.
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Find the solution of differential equations using variable separable
method.
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Find the solution of the given homogenous differential equations.
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Find the solution of the given linear differential equation.
Algebra
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Solving a simple linear in equation.
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Practical problem on linear in equation.
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Finding middle term of the binomial expansion.
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Finding last term of an AP if sum is given.
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How to select three terms of a GP.
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