Using properties of determinants prove that -

(b+c)^{2}....a^{2}........a^{2}

b^{2}.....(c+a)^{2.}.....b^{2} =2abc(a+b+c)^{3}

c^{2}.....c^{2}.......(a+b)^{2}

In this ques.. i just want to know tht after applying C_{1}→ C_{1}-C_{2}, C_{2}→ C_{2}-C_{3}

in this ques how can i take (a+b+c) common from C_{1} and C_{2}.

show that the function f: R ---->R given by f(x)=x^{3 }+ x is a bijection.

Use matrix multiplication to divide rs. 30,000 in two parts such that the total annual interest at 9% on the first part and 11% on the second part amounts rs. 3060.

differentiate wrtx

1)log(a+ bsinx)/(a-bsinx)

2)log_{7}(log_{7}x)

3)(e^{x}+e^{-x})/(e^{x}-e^{-x})

if y= [log(x+root x^{2}+1)]^{2 }show that (1+x^{2}) d^{2}y/dx^{2} +xdy/dx =2

Using properties of determinats, prove that

a^{2 } 2ab b^{2}

b^{2 }a^{2 } 2ab

2ab b^{2 }a^{2 }

= (a^{3} + b^{3})^{2}

If x^{p}.y^{q} = (x+y)^{p+q }, Prove that

(i) dy/dx = y/x

(ii) d^{2}y/dx^{2} = 0

Using properties of determinants prove that -

(b+c)

^{2}....a^{2}........a^{2}b

^{2}.....(c+a)^{2.}.....b^{2}=2abc(a+b+c)^{3}c

^{2}.....c^{2}.......(a+b)^{2}In this ques.. i just want to know tht after applying C

_{1}→ C_{1}-C_{2}, C_{2}→ C_{2}-C_{3}in this ques how can i take (a+b+c) common from C

_{1}and C_{2}.(a) balls are replaced before the second draw

(b) the balls are not replaced before the second draw

show that the function f: R ---->R given by f(x)=x

^{3 }+ x is a bijection.^{-1}x-cos^{-1}y=cos^{-1}{xy+whole root over(1-x^{2)}(1-y^{2})^{}}x - 1/ x + 1.

Use matrix multiplication to divide rs. 30,000 in two parts such that the total annual interest at 9% on the first part and 11% on the second part amounts rs. 3060.

K, x = pi/4 is continuous at x = pi/4

differentiate wrtx

1)log(a+ bsinx)/(a-bsinx)

2)log

_{7}(log_{7}x)3)(e

^{x}+e^{-x})/(e^{x}-e^{-x})if y= [log(x+root x

^{2}+1)]^{2 }show that (1+x^{2}) d^{2}y/dx^{2}+xdy/dx =2Using properties of determinats, prove that

a

^{2 }2ab b^{2}b

^{2 }a^{2 }2ab2ab b

^{2 }a^{2 }= (a

^{3}+ b^{3})^{2}5.Three schools A, B and C want to award their selected students for the values of honesty, regularity and hard work. Each school decided to award a sum of Rs. 2500, Rs. 3100, Rs. 5100 per student for the respective values. The number of students to be awarded by the three schools as given below:A = 50500, 40800, 41600

If x

^{p}.y^{q}= (x+y)^{p+q }, Prove that(i) dy/dx = y/x

(ii) d

^{2}y/dx^{2}= 0Q. 16. Find the value of ${a}_{23}+a{}_{32}$ in the matrix

A = ${\left[{a}_{ij}\right]}_{3x3}where{a}_{ij}=\left\{\begin{array}{l}\left|2i-j\right|ifij\\ -i+2j+3ifij\end{array}\right.$