Statement 1: The number of positive integral solutions of `a b c=30` is 27.
Statement 2: Number of ways in which three prizes can be distributed among three persons is `3^3`
(a) Statement 1 and Statement 2 , both are correct. Statement 2 is 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 correct but Statement 2 is not correct.
(d) Statement 2 is correct but Statement 1 is not correct.

Statement 1: Through (lambda,lambda+1) , there cannot be more than one normal to the parabola y^2=4x , if lambda (a) Statement 1 and Statement 2 , both are correct. Statement 2 is 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 correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

Consider two circles x^2+y^2-4x-6y-8=0 and x^2+y^2-2x-3=0 Statement 1 : Both the circles intersect each other at two distinct points. Statement 2 : The sum of radii of the two circles is greater than the distance between their centers. (a) Statement 1 and Statement 2 , both are correct. Statement 2 is 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 correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

Statement 1: let E={1,2,3,4}a n dF={a ,b} Then the number of onto functions from EtoF is 14. Statement 2: Number of ways in which four distinct objects can be distributed into two different boxes is 14 if no box remains empty. (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 correct but Statement 2 is not correct. (d) Both Statement 1 and Statement 2 are not correct.

Statement 1: the number of ways of writing 1400 as a product of two positive integers is 12. Statement 2: 1400 is divisible by exactly three prime factors. (a) Statement 1 and Statement 2 , both are correct. Statement 2 is 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 correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

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: Number of terms in the expansion of (x+y+z+w)^(50) is ""^(53)C_3 Statement 2: Number of non-negative solution of the equation p+q+r+s=50 is ""^(53)C_3 (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 correct but Statement 2 is not correct. (d) Both Statement 1 and Statement 2 are not correct.

Statement 1 : The area of the triangle formed by the points A(1000 ,1002),B(1001 ,1004),C(1002 ,1003) is the same as the area formed by the point A^(prime)(0,0),B^(prime)(1,2),C^(prime)(2,1) Statement 2 : The area of the triangle is constant with respect to the translation of axes. (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 correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

Statement 1 : Slopes of tangents drawn from (4, 10) to the parabola y^2=9x are and 1/4 and 9/4 . Statement 2 : Two tangents can be drawn to a parabola from any point lying outside the parabola. (a) Statement 1 and Statement 2 , both are correct. Statement 2 is 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 correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

Statement-1: The point (sin alpha, cos alpha) does not lie outside the parabola y^2 + x-2=0 when alpha in [pi/2,(5pi)/6] uu [pi,(3pi)/2] Statement-2: The point (x_1, y_1) lies outside the parabola y^2= 4ax if y_1^2-4ax_1 > 0 . (a) Statement 1 and Statement 2 , both are correct. Statement 2 is 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 correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

Statement 1: Number of ways in which Indian team (11 players) can bat, if Yuvraj wants to bat before Dhoni and Pathan wants to bat after Dhoni is 11!/3! . Statement 2: Yuvraj, Dhoni, and Pathan can be arranged in batting order in 3! ways. (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 correct but Statement 2 is not correct. (d) Both Statement 1 and Statement 2 are not correct.