Statement 1: Let `f(x)=sin(cos x) \ i n \ [0,pi/2]`. Then `f(x)` is decreasing in `[0,pi/2]`
Statement 2: `cosx` is a decreasing function `AAx in [0,pi/2]`
a) Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation for Statement 1.
b) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1.
c) Statement 1 is true, Statement 2 is false.
d) Statement 2 is true, Statement 1 is false.

Statement 1: A plane passes through the point A(2,1,-3)dot If distance of this plane from origin is maximum, then its equation is 2x+y-3z=14. Statement 2: If the plane passing through the point A( vec a) is at maximum distance from origin, then normal to the plane is vector vec a (a) Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation for Statement 1. (b) Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is true , Statement 2 is false. (d) Statement 2 is true, Statement 1 is false.

STATEMENT 1: int_0^(pi/4)log(1+t a ntheta)d theta=pi/8log2. STATEMENT 2: int_0^(pi/2)logsin theta d theta =-pilog2. (a) statement 1 is true, statement 2 is true, Statement 2 is the correct explanation for statement 1. (b) statement 1 is true, statement 2 is true, Statement 2 is not correct explanation for statement 1. (c) statement 1 is true, statement 2 is not true. (d) statement 2 is true, statement 1 is not true.

Statement 1 : The number of circles passing through (1, 2), (4, 8) and (0, 0) is one. Statement 2 : Every triangle has one circumcircle (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1. (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

Statement 1: Mass of O^16 nucleus is less than the sum of masses of 9 protons and 8 neutrons. Statement 2: Some internal energy is needed to keept the protons and neutrons bound in the nucleus. (A) Statement 1 is true, Statement 2 is true. Statement 2 is not a correct explanation for statement 1. (B) Statement 1 is true, Statement 2 is true. Statement 2 is 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: For f(x)=sinx ,f^(prime)(pi)=f^(prime)(3pi) Statement 2: For f(x)=sinx ,f(pi)=f(3pi)dot a. Statement 1 and Statement 2, both are correct and Statement 2 is the correct explanation for Statement 1 b. Statement 1 and Statement 2, both are correct and Statement 2 is not the correct explanation for Statement 1 c. Statement 1 is correct but Statement 2 is wrong. d. Statement 2 is correct but Statement 1 is wrong.

Statement 1: If the parabola y^2=4a x and the circle x^2+y^2+2b x=0 touch each other externally, then the roots of the equation f(x)=x^2-(b+a+1)x+a=0 are real. Statement 2: For parabola and circle touching externally, a and b must have the same sign. (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1. (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

Statement 1: ""^m C_r+ ""^m C_(r-1)(""^nC_1)+ ""^mC_(r-2)(""^n C_2)+....+ ""^n C_r=0 , if m+n lt r Statement 2: ""^n C_r=0 , if n lt r (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1. (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

Statement 1 : The circle having equation x^2+y^2-2x+6y+5=0 intersects both the coordinate axes. Statement 2 : The lengths of xa n dy intercepts made by the circle having equation x^2+y^2+2gx+2fy+c=0 are 2sqrt(g^2-c) and 2sqrt(f^2-c) , respectively. (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1. (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

Statement 1: There are no common tangents between the circle x^2+y^2-4x+3=0 and the parabola y^2=2xdot Statement 2:Given circle and parabola do not intersect. (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1. (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.