Cramer's Rule

Q. If Z = 2197 and R = 729, how would J be written in that code? J=125 how

Q.

For which of the following ordered pairs $(\mu ,\delta )$, the system of linear equations

$$\begin{gathered} x+2y+3z=1 \\ 3x+4y+5z=\mu \\ 4x+4y+4z=\delta \end{gathered}$$is inconsistent?

1. $\left(4,6\right)$

2. $\left(3,4\right)$

3. $\left(1,0\right)$

4. $\left(4,3\right)$

Q. if im(z)=2 and z1=1+i then minimum value of |z-z1| is

Q. If p^a = q^b = r^c and pqr= 1 prove that 1/a +1/b+1/c = 0.

Q. What is ib

Q.

Find the solution for the pair of inequations $x>1$ and $x<-1$

1. $x<-1$

2. $-1<x<1$

3. $x>1$

4. No solution

Q. What is a Gamma Function?

Q. if |z1|=1, |z2|=1, |1/z1+1/z2|=3/2, then find 2|z1+z2|

Q. Insert GM between 0.008 and 0.2

Q. Solve the equation }z^3=\overline z(z≠0)

Q. Differentiate sec5x w.r.t. x using first principle.

Q. The system of equations
$x+y-2z=0$
$2x-3y+z=0$
$x-5y+4z=k$ is consistent for

1. $k=0$ only
2. all non-zero real values of $k$
3. all real values of $k$
4. two real values of $k$

Q. consider the system of equations px+qy=0 rx+sy=0 where p, q, r, s∈0 and 1 only. find the probability that the system of equations has a unique solution.

Q. Integrate the following: ʃ[x²dx/(x-a)(x-b)(x-c)]

Q. The number of integer solution for the equation x+y+z+t=20, where x, y, z, t are all ≥-

Q.

How do you know when a system of equations is inconsistent?

Q. If z1 = 0, z2 = 3, z3 = 4i and z4 = 5 + 12 i then minimum value of |z – z1| + |z – z2| + |z – z3| + |z – z4| is equal to

Q. d(tanx) /dx where x=pi/4

Q.

The system of linear equations $x+y+z=6,x+2y+3z=10,$
$x+2y+2z=4$ will have

1. non trivial solution

2. trivial solution

3. infinite solutions

4. no solutions

Q. If the system of linear equations
$2x+py+6z=8$
$x+2y+qz=5$
$x+y+3z=4$
has infinitely many solutions, then a possible pair of $p$ and $q$ is

1. $p=3,q=3$
2. $p\ne 2,q\ne 3$
3. $p\ne 2,q=3$
4. $p=2,q\ne 3$

Q. Let $S$ be the set of all real values of $k$ for which the system of linear equations
$x+y+z=22x+y-z=33x+2y+kz=4$
has a unique solution. Then $S$ is

1. an empty set
2. equal to $\left\{0\right\}$
3. equal to $R$
4. equal to $R-\left\{0\right\}$

Q. What will be the value of dy/dx, when y=e^x-e^-x/e^x-e^-x

Q. Evaluate: ∫sin^7x dx

Q. X belongs to natural number such that X is less than 5, it is infinite or finite set

Q. 2[x] = 4{x} + x

Q.

1. -1

2. 

3. 1

4. 1/2

Q.

The system of equations

X+2y+3z=4

2x+3y+4z=5

3x+4y+5z=6 has

1. Many solutions

2. No solution

3. Unique solution

4. Atmost two solutions

Q.

Let a, b, c, be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x= cy +bz, y=az + cx and z = bx +ay. Then , a² + b²+ c²+ 2abc is equal to

1. 2

2. -1

3. 0

4. 1

Q.

1. 1

2. 10

3. 0

4. 9

Q. Cos^-1(cos4)=