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Let and be the roots of equation is equal to:

• Option 1)

6

• Option 2)

-6

• Option 3)

3

• Option 4)

-3

3

All the pairs ( x, y ) that satisfy the inequality

also satisfy the equation :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

=>  &  So, correct option is (4). Option 1) Option 2) Option 3) Option 4)

If  are three consecutive terms of a non-constant

G.P. such that the equations   and

have a common root , then  is equal to :

• Option 1)

0

• Option 2)

• Option 3)

• Option 4)

are in G.P. =>  For equation,                  Hence, roots are equal & equals to  Since, given equation have common roots , hence   must be root of                     Option 1) 0 Option 2) Option 3) Option 4)

If  denotes the greatest integer  , then the system

of linear equations

• Option 1)

Have infinitely many solutions if  and has a unique solution if .

• Option 2)

has a unique solution if

• Option 3)

has a unique solution if  and have infinitely many solutions if

• Option 4)

infinitely many solutions if

linear equations  &                              For infinite many solution, i.e. ...................(1) * when                         so,     * when                         so,     *when   *when                          Option 1) Have infinitely many solutions if  and has a unique solution if . Option 2) has a unique solution if  Option 3) has a unique solution if  and have infinitely many...

Let   with   and  it satisfies

for some natural number n . Then :

• Option 1)

n = 20 and Re(z) = -10

• Option 2)

n = 40 and Re(z) = 10

• Option 3)

n = 40 and Re(z) = -10

• Option 4)

n = 20 and Re(z) = 10

,  ,  Option 1)  n = 20 and Re(z) = -10 Option 2)  n = 40 and Re(z) = 10 Option 3)  n = 40 and Re(z) = -10 Option 4)  n = 20 and Re(z) = 10

A value of , for which

, is:

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Option 1)       Option 2) Option 3) Option 4)

A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to :

• Option 1)

28

• Option 2)

27

• Option 3)

25

• Option 4)

24

atleast one boy & one girl :  ( 1B & 2G) + ( 2B & 1G)   As, n cannot be -ve so, n = 25 Option 1) 28 Option 2) 27 Option 3) 25 Option 4) 24

If  is the inverse of a  matrix A, then the sum of all values of  for which det  is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Option 1) Option 2) Option 3) Option 4)

The equation  represents :

• Option 1)

• Option 2)

• Option 3)

the line through the origin with slope

• Option 4)

the line through the origin with slope

The line through the origin with slope 1Option 1)a circle of radius .  Option 2)a circle of radius Option 3)the line through the origin with slope Option 4)the line through the origin with slope

if  are roots of the equation  then  is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Option 1) Option 2) Option 3) Option 4)

If A is a syymmetric matrix and B is a skew-symmetrix matrix such that , then AB is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

A is symmetric matrix  B is skew-symmetrix (1) + (2)  Option 1) Option 2) Option 3) Option 4)

Let a,b and c be in G.P. with common ratio r , where  and

. If  3a , 7b and 15c are the first three terms of an A.P.,

then the 4th term of this A.P. is :

• Option 1)

• Option 2)

5 a

• Option 3)

• Option 4)

a

Since a,b,c are in G.P. with common ratio r then  b = ar ,  Also 3a, 7b and 15c are in A.P. =>  =>  =>  =>  =>  =>  =>  So, terms are                         or                         =>    or    So, 4th term     or    So, option (4) is correct.   Option 1) Option 2) 5 a Option 3) Option 4) a

The sum of the real roots of the equation

, is equal to :

• Option 1)

6

• Option 2)

0

• Option 3)

1

• Option 4)

-4

=>  =>  Root of equation (-3,1,2) So, Sum of real root of equation = -3+1+2=0 So, option (2) is correct.Option 1)6Option 2)0Option 3)1Option 4)-4

Let  be a real number for which the system of linear equations

has infinitely many solutions. Then  is a root of the quadratic equation :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

linear equations             Now, using cramers law for infinite solution   all will be zero      Now put  in options and check for the correct one  (1) (2) (3) (4) So, option (4) is correct.     Option 1) Option 2) Option 3) Option 4)

If  and  are two complex numbers such that

and   then :

• Option 1) • Option 2)

• Option 3)

• Option 4)

and  Let    =>                                                                  Option 1)Option 2)Option 3)Option 4)

If  and  are the roots of the quadratic equation,

, then

is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

and  are the roots of the equation  Now,                                                                                                                                                                   correct option (2) Option 1) Option 2) Option 3) Option 4)

If the system of linear equations

x + y + z = 5

x + 2y + 2z = 6

x + 3y +  z =  , (,  ) , has infinitely

many solutions, then the value of  +  is :

• Option 1)

12

• Option 2)

9

• Option 3)

7

• Option 4)

10

x + 3y +  z -  = p ( x + y + z - 5) + q ( x + 2y + 2z - 6 )  On comparing the coefficients  p + q = 1   and    p + 2q = 3 => ( p , q ) = ( -1 , 2 ) Hence, x + 3y +  z -  = x + 3y + 3z - 7  =>  =>  So, option (4) is correct. Option 1) 12 Option 2) 9 Option 3) 7 Option 4) 10

If a>0 and  , has magnitude  ,

then  is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

given that  Option (1) is correct. Option 1) Option 2) Option 3) Option 4)

If   and

,  ; then

for all

• Option 1)

• Option 2)

• Option 3)

• Option 4)

So,  So, option (4) is correct.Option 1)Option 2)Option 3)Option 4)

If the system of equations   has a non-trivial solution   , then    is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

for non-trivial solution  A=0   so       Option 1) Option 2) Option 3) Option 4)
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