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Worked Maths
Приєднався 22 лис 2024
Sometimes unconventional and always fully worked out and simple solutions to math problems from the JEE Main and Advanced previous year papers, illustrating approaches requiring a minimum amount of rote learning. While working out the problems yourself can have immense benefits, latest research shows that it is equally, if not more, important to go through worked solutions for knowledge retention and transfer (www.tandfonline.com/doi/full/10.1080/01443410.2023.2273762).
JEE Derivatives 2022 - Find limit of an expression involving (eᵃˣ-1) terms
In this question from the 2022 paper we are asked to find the values of two variable in an equation involving a limit which includes terms of the form (eᵃˣ-1) in both the numerator and the denominator. We show how to solve this problem without having to expand the eᵃˣ terms.
Переглядів: 6
Відео
JEE Derivatives 2023 - Find limit of an expression with polynomials raised to the 6th power
Переглядів 93 дні тому
In this question from the 2023 main paper we are asked to find the limit of a fairly complicated expression involving polynomials raised to the power of 6 in both the numerator and the denominator. We show how to solve this problem without having to expand out the 6th powers of these polynomials.
JEE Derivatives 2011 - Find variable in an equation involving a limit in the 1 infinity form
Переглядів 34 дні тому
In this question from the 2011 paper we are given an equation where the left side of the equation is a limit in the one to the power of infinity form, and we have to find an angle θ involved in the equation, given that another real variable b involved in the equation is greater than 0.
JEE Derivatives 2024 - Find k given a limit involving k is in the 1 to the power of infinity form
Переглядів 104 дні тому
In this limits question from the 2024 advanced paper we are given that a particular limit involving the variable k, which is in the 1 to the power of infinity form, is equal to e⁶, and we are asked to find the value of k for which the equation holds.
JEE Integrals 2006 - Integral using multiple substitutions
Переглядів 115 днів тому
In this question from the 2006 paper we are asked to evaluate an indefinite integral involving polynomials in x in the numerator and the denominator. The problem can be solved in a few different ways using different substitutions. We illustrate a method involving multiple substitutions.
JEE Derivatives 2000 - Find limit where expression is raised to the power of x
Переглядів 135 днів тому
In this question from the 2000 paper we are asked to find the limit of the expression ((x-3)/(x 2))ˣ, as x tends to infinity. We illustrate two methods for solving the problem - one without using any formula and a shorter method that uses the formula for the limit of (1 1/x)ˣ. We also show how you can drive this formula.
JEE Derivatives 2002 - Find the limit of an expression raised to the power 1/x
Переглядів 26 днів тому
In this question from the 2002 paper we are asked to evaluate the limit of an expression raised to the power 1/x. This immediately suggest that we should do a substitution and take log and then try and find the limit.
JEE Integrals 1995 - Indefinite integral involving squares, cubes and 4th power of sines and cosines
Переглядів 116 днів тому
In this problem from the 1995 paper we are asked to compute an indefinite integral involving the squares, cubes, 4th and 5th powers of cosines and sines. The problem requires first doing a substitution and then decomposing the resulting algebraic expression into partial fractions and then computing the integral.
JEE Derivatives 1983 - Proof of a special case of the L'Hospital's rule
Переглядів 57 днів тому
In this simple question from the 1983 paper we are asked to find the limit of an indeterminate expression which immediately suggests using the L'Hospital's rule. We also work out a short proof of the L'Hospital's rule for the special case where the functions in the numerator and denominator are differentiable at the limit point.
JEE Derivatives 2003 - Find limit of an expression indeterminate at the limit point
Переглядів 127 днів тому
In this question from the 2003 paper we are asked to find the limit of an expression involving a function in numerator and a denominator which is indeterminate at the limit point, and where the value of the derivative is given at two other points.
JEE Derivatives 2012 - Find the value of some constants in an expression whose limit is given
Переглядів 78 днів тому
In this question from the 2012 paper we are given an expression involving two constants a and b, and whose limit is given as 4 as x tends to infinity, as we are asked to determine the values of these two constants.
JEE Trigonometry 1988 - Find the value of √3cosec(20°) - sec(20°)
Переглядів 128 днів тому
In this old trigonometry question from the 1988 paper we are asked to compute the value of √3cosec(20°) - sec(20°), where two of the given options don't involve sines and cosines and the other two options do.
JEE Trigonometry 1995 - Find value of an expression involving sines and cosines of a variable x
Переглядів 79 днів тому
In this question from the 1995 paper we are given a relatively complicated looking expression involving different power of the sines and cosines of a variable x and we are asked to find the value of this expression. Instead of taking a tedious approach and trying to simplify the expression, we show a shortcut for solving such problems.
JEE Trigonometry 1998 - Find which trigonometric expression is rational
Переглядів 179 днів тому
In this question from the 1998 paper we are given 4 trigonometry expressions involving the sines and cosines of 15 degrees and 75 degrees and we are asked to find which of these expressions is a rational number.
JEE Trigonometry 2001 - Find tan(α) given equations involving three angles α, β and γ
Переглядів 2010 днів тому
In this question from the 2001 paper we are given two equations α β = 90 degrees and β γ = α and we have to find the value of tan(α) in terms of tan(β) and tan(γ) and select the from the given options.