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In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion(A) :If a 2 x 2 matrix commutes with every 2 x 2 matrix, then it is a scalar matrix.
Reason(R) :A 2 x 2 scalar matrix commutes with every 2 x 2 matrix.
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
The area, in square unit, of the region bounded by the curve x^{2} = 4y , the line x = 2 and the xaxis is
The radical axis of the circles, belongs to the coaxial system of circles whose limiting points are (1,3) and (2,6) is
If z₁ and z₂ are any two complex numbers then z₁ + z₂^{2} + z₁  z₂^{2} =
If the line 2x  y + k = 0 is a diameter of the circle x^{2} + y^{2} + 6x 6y + 5 =0, then k is equal to
The complex equation z + 1 − i = z + i − 1 represents a
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer
Assertion (A): Three vectors
Reason (R): The coplanar vectors are linearly independent
In the following question, a Statement1 is given followed by a corresponding Statement2 just below it. Read the statements carefully and mark the correct answer
Consider the system of equations
x  2y + 3z = 1
 x + y  2z = k
x  3y + 4z = 1
Statement1:
The system of equations has no solution for k ≠3.
Statement2:
The determinant
Twelve students compete for a race. The number of ways in which first three prizes can be taken is
The tangents at the points a on the parabola are at right angles if
Points (0,0), (2,1) and (9,2) are vertices of a triangle, then cosB =
The angle between the lines (x  1)/1 = (y  1)/1 = (z  1)/2 and (x  1)/( √3  1) = (y  1)/(√3  1) = (z  1)/4 is
If function ƒ(x) = x^{3} + ax^{2} + bx + c is monotonically increasing ∀ x ∈ R, where a & b are prime numbers less than 10, then number of possible ordered pairs (a,b) is
a, b ∈ {2, 3, 5, 7}
ƒ '(x) = 3x^{2} + 2ax + b ≥ 0 ∀ x ∈ R
D ≤ 0
4a^{2} – 12b ≤ 0
4(a^{2} – 3b) ≤ 0
a = 2 b = 2,3,5,7
a = 3 b = 3,5,7
a = 5 No solution
a = 7 No solution
Ordered pairs (a,b) are (2,2), (2,3), (2,5), (2,7), (3, 3), (3,5) & (3,7)
Suppose that ƒ is differentiable for all x such that ƒ'(x) ≤ 2 for all x. If ƒ(1) = 2 and ƒ(4) = 8 then ƒ(2) has the value equal to 
Let y = g(x) be the inverse of a bijective mapping f : R → R, f(x) = 3x^{3} + 2x. The area bounded by graph of g(x), the xaxis and the ordinate at x = 5 is 
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