Differentiation to Solve Modified Sum of Binomial Coefficients

Q. x+2y-z=3; 3x-y+2z=1; 2x-2y+3z=2 by using crammer rule

Q. 7. for perabola xx+yy+2xy-6x-2y+3=0, the focus is

Q. 10. If z=3-4i then z-3z-3z+99z-95= option A)5 B)6 C)-5 D)-4

Q.

Find the remainder when $7^{98}$ is divided by 5.

__

Q. 3. If x=asinpt. y=bcospt Than show (a2 - x2)ydy2/dx2 + b2 = 0

Q. The value of $\sum _{r=2}^{10}{}^r{C}_2\cdot {}^{10}{C}_r$ is not divisible by

1. $10$
2. $5$
3. $7$
4. $3$

Q. Find an anti derivative (integral) of the following function: sin2x - 4e^3x

Q. 143.Summation, k=1 to 2015 ipower 1/(4m+k) where mN

Q. Let P(n) be the statement : 2ⁿ ≥ 3n. If P(r) is true, show that P(r + 1) is true. Do you conclude that P(n) is true for all n ∈ N?

Q. If a, b, c, d are in G.P., prove that:

(i) $\frac{ab-cd}{b^2-c^2}=\frac{a+c}{b}$

(ii) (a + b + c + d)² = (a + b)² + 2 (b + c)² + (c + d)²

(iii) (b + c) (b + d) = (c + a) (c + d)

Q. if the function f:R, A is given by f(x)=x^2/x^2+1 is surjection , then A=

Q.

Find the value of ${}^n{C}_1+2^n{C}_2+3^n{C}_3.........n^n{C}_n$

1. $n\cdot 2^n$

2. $(n-1{)}^{2n}$

3. $(n-1)2^{n-1}$

4. $n\cdot 2^{n-1}$

Q. Remainder when $(2{)}^{1004}$ is divided by 17 is

1. 14
2. 16
3. 7
4. 10

Q. find the derivative using first principle e^{root x}