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Statement 1: The system of linear equati...

Statement 1: The system of linear equations `x+(sinalpha)y+(cosalpha)z=0x+(cosalpha)y+(sinalpha)z=0x-(sinalpha)y-(cos\ alpha)z=0` has a non-trivial solution for only value of `alpha` lying the interval `(0,\ pi/2)` Statement 2: The equation `in\ alpha` `|cosalphas in\ alphacosalphasinalphacosalphasinalphacosalpha-sinalpha-cosalpha|=0` has only one solution lying in the interval `(0,\ pi/2)` Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true

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Statement I: If (log)_(((log)_5x))5=2,\ t h n\ x=5^(sqrt(5)) Statement II: (log)_x a=b ,\ if\ a >0,\ t h e n\ x=a^(1//b) Statement 1 is True: Statement 2 is True, Statement 2 is a correct explanation for statement 1. Statement 1 is true, Statement 2 is true;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false. Statement 1 is false, statement 2 is true

Statement I: cos e s^(-1)(cos e c9/5)=pi-9/5dot Statement II: cos e c^(-1)(cos e c x)=pi-x :\ AAx in [pi/2,(3pi)/2]-{pi} Statement I is True: Statement II is True; Statement II is a correct explanation for statement I. Statement I is true, Statement II is true; Statement II not a correct explanation for statement I. Statement I is true, statement II is false. Statement I is false, statement II is true

Consider the system of equations x-2y+3z=1;-x+y-2z=; x-3y+4z=1. Statement 1: The system of equations has no solution for k!=3. Statement2: The determinant |1 3-1-1-2k1 4 1|!=0,\ for\ k!=3. Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true

Statement I: If a=y^2,\ b=z^2, c=x^2,\ t h e n8(log)_a x^3dot(log)_b y^3dot(log)_c z^3=27 Statement II: (log)_b adot(log)_c b=(log)_c a ,\ also (log)_b a=1/("log"_a b) Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1. Statement 1 is true, Statement 2 is true;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true

Statement I The system of linear equations x+(sin alpha )y+(cos alpha )z=0 x+(cos alpha ) y+(sin alpha )z=0 -x+(sin alpha )y-(cos alpha )z=0 has a not trivial solution for only one value of alpha lying between 0 and pi . Statement II |{:(sin x, cos x , cos x),( cos x , sin x , cos x) , (cos x , cos x , sin x ):}|=0 has no solution in the interval -pi//4 lt x lt pi//4 .

Let F(x) be an indefinite integral of sin^(2)x Statement-1: The function F(x) satisfies F(x+pi)=F(x) for all real x. because Statement-2: sin^(2)(x+pi)=sin^(2)x for all real x. A) Statement-1: True , statement-2 is true,statement-2 is correct explanation for statement-1 (b) statement-1 true, statement-2 true and Statement -2 is not a correct explanation for statement -1 c) Statement-1 is True, Statement -2 is False. D) Statement-1 is False, Statement-2 is True.

If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha) , then show that sinalpha+cosalpha=sqrt(2)costheta .

Let lambda "and" alpha be real. Let S denote the set of all values of lambda for which the system of linear equations lambda x+(sinalpha)y+(cos alpha)z=0 x+(cos alpha) y+(sin alpha) z=0 -x+ (sin alpha) y-(cos alpha) z=0 has a non- trivial solution then S contains

The system of equations alphax+y+z=alpha-1, x+alphay+z=alpha-1 x+y+alphaz=alpha-1 and has no solution if alpha is

If A(alpha)=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}] then prove that A(alpha)A(-alpha)=I .

ALLEN -DETERMINANTS-All Questions
  1. Let a,b,c, be any real number. Suppose that there are real numbers x,y...

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  2. Let a,b,c be such that b(a+c) ne 0. If |{:(a,a+1,a-1),(-b,b+1,b-1)...

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  3. Consider the system of linear equations; x1 +2x2+x3=3 2x1+3x2+x3=3 3x1...

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  4. The number of value of k for which the linear equations 4x+k y+2z=0,k ...

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  5. If the trivial solution is the only solution of the system of equation...

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  6. The number of values of k, for which the system of equations (k""+""...

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  7. If a ,b ,c are sides of a scalene triangle, then value of {:|(a, b, c)...

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  8. If the system of linear equations x1+2x2+3x3=6,\ x1+3x2+5x3=9,\ 2x2+5x...

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  9. Statement 1: The system of linear equations x+(sinalpha)y+(cosalpha)z=...

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  10. Consider the system of equations x+a y=0,\ y+a z=0\,z+a x=0.\ Then th...

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  11. If f(n)=alpha^n+beta^n then show that |{:(3,1+f(1),1+f(2)),(1+f(1),...

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  12. The set of all values of lamda for which the system of linear equation...

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  13. The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-lambd...

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  14. The number of distinct real roots of the equation |cosx s in x s in x ...

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  15. Test the consistency and solve them when consistent the following s...

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  16. If a,b,c are real numbers such that 3(a^(2)+b^(2)+c^(2)+1)=2(a+b+c+ab...

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  17. The number of values of k for which the system of the equations (k+1)x...

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  18. The value of lambda for which the system of equations 2x-y-2z=2,x-2y +...

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  19. Statement I: cos e s^(-1)(cos e c9/5)=pi-9/5dot Statement II: cos e ...

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  20. The number of all possible values of theta\ w h e r e\ 0<theta<pi,\ f...

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