The slope of the tangent to a curve C: y = y(x) at any point (x, y) on it is . If C passes through the points and Then is equal to Solution: Tip for solving this question: Use the formula of the slope of the tangent. On integration, find the value of y. Then […]

## Mean and Variance of a binomial distribution are 24 and 128

If the sum and the product of the mean and variance of a binomial distribution are 24 and 128, respectively, then the probability of one or two successes is : Solution: Tip for solving this question: Firstly find the mean and variance of the binomial distribution. Make an equation according to the question and solve […]

## Line with slope greater than 1 passes A(4, 3) and intersects x–y=2 at B

A line with a slope greater than 1 passes through point A(4, 3) and intersects the line x – y – 2 = 0 at point B. If the length of the line segment AB is , then B also lies on the line 2x + y = 9 3x – 2y = 7 x […]

## General Solution of differential equation (x – y^2)dx +y(5x + y^2)dy

The general solution of the differential equation is: Solution: Find the general solution of a given differential equation using the substitution method. Given, … (1) Let On differentiation, we get Then, equation (1) becomes … (2) Now, Substitute t = vx On differentiation, we get Then, equation (2) becomes … (3) Now, integrate equation (3) […]

## Absolute maximum value of the function (x^2 – 2x + 7)e^(4x^3 – 12x^2 – 180x + 31)

If the absolute maximum value of the function , then Solution: Tip for solving this question: Find differentiation of f(x) The absolute maximum value of x Step 1 of 2: Given, Take Now, differentiate For critical points, Here, From the above values, we see that the absolute maximum is 22 and it occur at x […]

## Lim n →∞, sqrt(n2-n-1)+nα+β=0 then 8(α+β)

If is equal to (A) 4 (B) –8 (C) –4 (D) 8 Solution: Tip for solving this question: Simplify the limit Find value of Step 1 of 3: Given, On rationalisation, we get Step 2 of 3: In Here, Now, Here, Step 3 of 3: Now, Final Answer: Hence, Option (C) is correct.

## Number of elements where n belongs to N and Sn Intersection Tn is phi

For , Let and Then the number of elements in the set is (A) 0 (B) 2 (C) 3 (D) 4 Solution: Tip for solving this question: Firstly Identify the given sets According to the set type, apply intersection properties to find no. of elements. Step 1 of 2: Let z = x + iy […]

## α^2021 + β^2021 + γ^2021 + δ^2021 for x^4 + x^3 + x^2 + x + 1 = 0

JEE Mains 2022 July 25th Shift 1 Mathematics Question Paper Solution to α^2021 + β^2021 + γ^2021 + δ^2021 for x^4 + x^3 + x^2 + x + 1 = 0

## The total number of functions, f: {1, 2, 3, 4} → {1, 2, 3, 4, 5, 6} such that f(1) + f(2) = f(3), is equal to

The total number of functions, f: {1, 2, 3, 4} → {1, 2, 3, 4, 5, 6} such that f(1) + f(2) = f(3), is equal to (A) 60 (B) 90 (C) 108 (D) 126 Solution: Tip for solving this question: First, find f(3) at different values. Calculate the number of ways at different values […]

## For theta Belonging to 0, 4Pi the linear equations with no solutions

The number of for which the system of linear equations has no solution, is (A) 6 (B) 7 (C) 8 (D) 9 Solution: Tip for solving this question: By converting linear equations into matrix form, find the determinant of the matrix. Also, check out What is Determinant of Matrix in detail here. Then using properties […]