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: 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

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: 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

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.

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 equation (log)_(1/(2+|"x"|))(5+x^2)=(log)_((3+x^ 2))(15+sqrt(x)) has real solutions. Because Statement II: (log)_(1//"b")a=-log_b a\ (w h e r e\ a ,\ b >0\ a n d\ b!=1) and if number and base both are greater than unity then the number is positive. a. A b. \ B c. \ C d. D

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: consider D= |a_1a_2a_3 b_1b_2b_3 c_1c_2c_3| let B_1, B_2,\ B_3 be the co-factors \ b_1, b_2, a n d\ b_3 respectively then a_1B_1+a_2B_2+a_3B_3=0 because Statement II: If any two rows (or columns) in a determinant are identical then value of determinant is zero a. A b. \ B c. \ C d. D

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 ,\ \ b , c in R\ a n d a!=b!=c\ a n d\ x ,\ y ,\ z are non zero. Then the system of equations a x+b y+c z=0,b x+c y+a z=0,c x+a y+b z=0 has infinite solutions. because Statement II: If the homogeneous system of equations has non trivial solution, then it has infinitely many solutions. a. A b. \ B c. \ C d. D

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: Consider the system of equations 2x+3y+4z=5, x+y+z=1, x+2y+3z=4 This system of equations has infinite solutions. because Statement II: If the system of equation is e_1: a_1x+b_1y+c_1-d_1=0 e_2: a_2x+b_2y+c_2z-d_2=0 e_3: e_1+lambdae_2=0,\ w h e r e\ lambda\belongs to R\ &(a_1)/(a_2)!=(b_1)/(b_2) Then such system of equations has infinite solutions. a. A b. \ B c. \ C d. D

Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A^2=""I . Statement 1: If A!=I and A!=""-I , then det A""=-1 . Statement 2: If A!=I and A!=""-I , then t r(A)!=0 . (1) Statement 1 is false, Statement ( 2) (3)-2( 4) is true (6) Statement 1 is true, Statement ( 7) (8)-2( 9) (10) is true, Statement ( 11) (12)-2( 13) is a correct explanation for Statement 1 (15) Statement 1 is true, Statement ( 16) (17)-2( 18) (19) is true; Statement ( 20) (21)-2( 22) is not a correct explanation for Statement 1. (24) Statement 1 is true, Statement ( 25) (26)-2( 27) is false.