Identify myths and facts about substance abuse among adolescents.

Enumerate commonly abused drugs, their routes of administration and harmful effects

Elucidate the North-South Politics in climate change negotiations.

Analyse the impacts of climate change on women and children.

Discuss the impacts of climate change on the seven dimensions of human security, with special reference to developing countries.

 Climate change poses significant challenges to vulnerability assessment in various sectors, including human health, infrastructure, agriculture, and biodiversity. Explain.

Find one root of the equation:

x³ - 2x 5 = 0

in the interval [3,2] using Birge-Vieta method. Perform only one iteration.

How many terms n be chosen in Maclaurin’s expansion for  e^x with an error less than  

Using the third order Taylor’s series method, find the solution of the initial value problem:

at x = 0.1 taking h = 0.1

 From the following data, calculate the population in the year 1985:

 If 

f(x) = e^ax  , 

show that

 Estimate the eigen values of the matrix:

using the Gerschgorin bounds. Also, draw the rough sketch of the region in which the eigen values lie.

Find the first term of the series whose second and subsequent terms are ,0,3,8 − 0,1 using difference table.

 Using synthetic division method, check whether α = 3 is a root of the polynomial equation:

x⁴ +  x³ - 13x² - x + 12 = 0

Solve the system of equations:

x + 2y + z = 3

3x − 2y − z4 = −2

2x + 3y − z = −6

using Gauss-Elimination method.

Given the data: 

f(3) = 168,

f(7) = 120

and f(9) = 72 

If  f(k) is estimated as 138 using the Newton’s form of the interpolating polynomial, then find the value of .k

Using Runge-Kutta fourth order method with h = 0.1, find an approximation value of y(0.1) for the initial value problem:

b) Evaluate the integral:

using composite trapezoidal rule with h = ,2.0 compare with the exact value.

Use the Euler’s method to solve numerically the initial value problem: 

with h = 2.0 on the interval [0, 1].

Using the data sin (0.1) = 0.09983 and sin (0.2) = 0.19867, find an approximate value of sin (0.15) by Lagrange’s interpolation. Also obtain a bound on the truncation error.

Use secant method to determine the root of the equation cos x - xe^x = 0. Take the initial approximation as x₀ = 0, x₁ = 1 and perform two iterations of the method.