Let `O` be the origin and `P -= (a, a^2)`. (1) If `P(a, a^2)` lies in the first quadrant between the lines `y=x and y=2x`, then `1ltalt2`. (2) Slope of `OP` is `a`.
(A) Both 1 and 2 are true and 2 is the correct explanation of 1
(B) Both 1 and 2 are true and 2 is not a correct explanation of 1
(C) 1 is true but 2 is false
(D) 1 is false but 2 is true

Assetion: a_1,a_2,a_3,…………. an are not in G.P. Reason: a_(n+1)=a_n (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion: a^2,b^2,c^2 are in A.P., Reason: 1/(b+c), 1/(c+a), 1/(a+b) are in A.P. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Statement-1: The area of the region R={(x,y) : |x| le |y| and x^2+y^2 le 1} is pi/4 sq. units.Statement-2: Curves |y|=|x| and x^2+y^2=1 symmetric about both x and y-axis. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement-1: int_0^([x]) 4^(x-[x])dx=(3[x])/(2log2) ,Statement-2: int_0^([x]) a^(x-[x])dx=[x]int_0^1 a^(x-[x])dx (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Let P, Q, R be three non-collinear points having rational coordinatse. (1) Coordinates of incentre of DeltaPQR are rational (2) Incentre of a triangle is the point of intersection of internal bisectors of angle of the triangle. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Let C_1 and C_2 be two circles with C_2 lying inside C_1 . A circle C lying inside C_1 touches C_1 internally and C_2 externally. Statement : 1 Locus of centre of C is an ellipse. Statement (2) The locus of the point which moves such that the sum of its distances from two fixed points is a constant greater than the distance between the two fixed points is an ellipse. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement-1: Let a,b,c be non zero real numbers and f(x)=ax^2+bx+c satisfying int_0^1 (1+cos^8x)f(x)dx=int_0^2(1+cos^8x)f(x)dx then the equation f(x)=0 has at least one root in (0,2) .Statement-2: If int_a^b g(x)dx vanishes and g(x) is continuous then the equation g(x)=0 has at least one real root in (a,b) . (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement-1: The area bounded by the curves y=ln|x| , y-axis and y=1-|x| is 2 sq. units.Statement-2: Both the curves y=log|x| and y=1-|x| are symmetric about y-axis. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement 1: The equation of the common tangent to the curves y^2 = 8x and xy= -1 is y=x+2 . Statement 2: Curves y^2 = 8x and xy=-1 intersect at (1/2, -2) . (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

x-y+b=0 is a chord of the circle x^2 + y^2 = a^2 subtending an angle 60^0 in the major segment of the circle. Statement 1 : b/a = +- sqrt(2) . Statement 2 : The angle subtended by a chord of a circle at the centre is twice the angle subtended by it at any point on the circumference. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true