A+B+C=N (N Fixed)

Q. Find the value of c for which the system
cx + 3y = c - 3, 12x + cy = c has infinitely many solutions.

1. 4
2. 2
3. None of these
4. 6
5. 8

Q. Two teachers from each stream are to be included?

1. 210
2. 145
3. 180
4. None of these
5. 96

Q. Find the number of possible integral solution of |x|+|y|=10

Q.

I. (3x-2)/y=(3x+6)/(y+16)
II. (x+2)/(y+4)=(x+5)/(y+10)

1. if x > y
   

2. if x < y
   

3. if x = y or relation cannot be established between 'x' and 'y'.

4. if x $\ge$ y
   

5. if x $\le$ y
   

Q. Determine the no. of terms in the expansion of (a + b + c + d)${}^5$ and (1 + a + a${}^2$ + a${}^3$)${}^5$

1. 56, 16
2. 32, 24
3. 165, 32
4. 32, 32
5. 16, 14

Q.

I. (x+3)(y+2)=12
II.2xy+4x+5y=11

1. if x > y
   

2. if x < y
   

3. if x $\ge$ y
   

4. if x $\le$ y
   

5. if x = y or relation cannot be established between 'x' and 'y'.

Q. The number of ways in which mn students can be distributed equally among n sections is-

1. $\frac{\left(mn\right)!}{(m!{)}^{n}n!}$
2. $(mn{)}^n$
3. $\frac{\left(mn\right)!}{(m!{)}^n}$
4. $\frac{\left(mn\right)!}{m!}$

Q. Find the number of ways in which $12$ students can be distributed among $3$ groups?

1. $3245$
2. $5775$
3. $6001$
4. none of these

Q. Out of 14people 12 said that it was not the case that they watched television but not listen to the radio also 9 people said it was not the case they dont watch TV and dont listen radio finally 7 people either watch TV or radio but not both Now let A number of people who watch TV and B be the number of people who listens radio find A and B

Q. Calculate the number of ways in which 10 different students can be divided into two groups under two different teachers containing 6 and 4 students respectively.

1. 
2. 
3. ¹⁰C₆*¹⁰C₄
4. 
5. none of these

Q.

I. $x^2+20x+4=50-25x$
II. $y^2-10y-24=0$

1. if x > y
   

2. if x < y
   

3. if x = y or relation cannot be established between 'x' and 'y'.

4. if x $\ge$ y
   

5. if x $\le$ y
   

Q. If $2^x-2^{x-1}=4$, then $x^3$ equals

1. $1$
2. $3$
3. $27$
4. $5$

Q. The equation has

1. 3 solutions
2. >3 solutions
3. no solution
4. 1
5. 2 solutions

Q. Find all the real solutions to the logarithmic equation
$\ln (x+1)-\ln \left(x\right)=2$

1. $1$
2. $e^2$
3. $\frac{1}{(e^2-1)}$
4. $\frac{1}{\left(\ln \right(2)-1)}$
5. no real solutions