Statement 1: For `-1

Statement 1: For a singular square matrix A ,A B=A C B=Cdot Statement 2; |A|=0,t h e nA^(-1) does not exist.

Each question has four choices a,b,c and d out of which only one is correct. Each question contains Statement 1 and Statement 2. Make your answer as: If both the statements are true and Statement 2 is the correct explanation of statement 1. If both the statements are True but Statement 2 is not the correct explanation of Statement 1. If Statement 1 is True and Statement 2 is False. If Statement 1 is False and Statement 2 is True. Statement 1: sinpi/(18) is a root of 8x^3-6x+1=0 Statement 2: For any theta in R ,sin3theta=3sintheta-4sin^3theta

Read the given statements and select the correct option. Statement 1: Major reservoirs of phosphorus are phosphate rocks and fossil bone deposits laid down in the past geological ages. Statement 2: During weathring of rocks, minute amounts of these phosphates dissolve in soil solution and are absorbed by the roots of the plants. A. Both statements 1 and 2 are correct. B. Statement 1 is correct but statement 2 is incorrect. C. Statement 1 is incorrect but statement 2 is correct. D. Both statement 1 and 2 are incorrect.

Statement 1: Sum of the series 1^3-2^3+3^3-4^3++11^3=378. - Statement 2: For any odd integer ngeq1,n^3-(n-1)^3++(-1)^(n-1)1^3=1/4(2n-1)(n+1)^2dot

Statement 1 : If -2h=a+b , then one line of the pair of lines a x^2+2h x y+b y^2=0 bisects the angle between the coordinate axes in the positive quadrant. Statement 2 : If a x+y(2h+a)=0 is a factor of a x^2+2h x y+b y^2=0, then b+2h+a=0 Both the statements are true but statement 2 is the correct explanation of statement 1. Both the statements are true but statement 2 is not the correct explanation of statement 1. Statement 1 is true and statement 2 is false. Statement 1 is false and statement 2 is true.

Each question has four choices a, b, c, and d, out of which only one is correct. Each question contains STATEMENT 1 and STATEMENT 2. a. Both the statements are TRUE and statement 2 is the correct explanation for Statement 1. b. Both the statements are TRUE but Statement 2 is NOT the correct explanation for Statement 1. c. Statement 1 is TRUE and Statement 2 is FALSE. d. Statement 1 is FALSE and Statement 2 is TRUE. A vector has components p and 1 with respect to a rectangular Cartesian system. The axes are rotted through an angel alpha about the origin the anticlockwise sense. Statement 1: IF the vector has component p+2 and 1 with respect to the new system, then p=-1. Statement 2: Magnitude of the origin vector and the new vector remains the same.

Let C_1 be the circle with center O_1(0,0) and radius 1 and C_2 be the circle with center O_2(t ,t^2+1),(t in R), and radius 2. Statement 1 : Circles C_1a n dC_2 always have at least one common tangent for any value of t Statement 2 : For the two circles O_1O_2geq|r_1-r_2|, where r_1a n dr_2 are their radii for any value of tdot