Suppose the cube x3– px + q has three distinct real roots where p > 0 and q > 0. Then which one of the following holds?
The cubic has minima at and maxima at –
The cubic has minima at – and maxima at
The cubic has minima at both and-
The cubic has minima at both and-
The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is
(x – 2)y′2 = 25 – (y – 2)2
(y – 2)y′2 = 25 – (y – 2)2
(y – 2)2y′2= 25 – (y – 2)2
(y – 2)2y′2= 25 – (y – 2)2
Let A be a square matrix all of whose entries are integers. Then which one of the following is true?
If det A = ± 1, then A–1 exists but all its entries are not necessarily integers
If detA ≠ ± 1, then A–1 exists and all its entries are non-integers
If detA = ± 1, then A–1 exists and all its entries are integers
If detA = ± 1, then A–1 exists and all its entries are integers
Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x = cy + bz, y = az + cx and z = bx + ay. Then a2 + b2 + c2 + 2abc is equal to
2
-1
0
0
The vector lies in the plane of the vectors and bisects the angle between .Then which one of the following gives possible values of α and β?
α = 2, β = 2
α = 1, β = 2
α = 2, β = 1
α = 2, β = 1
The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz−plane at the point . Then
a = 2, b = 8
a = 4, b = 6
a = 6, b = 4
a = 6, b = 4
In a shop, there are five types of ice-creams available. A child buys six ice-creams.
Statement -1: The number of different ways the child can buy the six ice-creams is 10C5.
Statement -2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A’s and 4 B’s in a row.
Statement −1 is false, Statement −2 is true
Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1
Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.
Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.
A.
Statement −1 is false, Statement −2 is true
x1 + x2 + x3 + x4 + x5 = 6
5 + 6 – 1C5 – 1 = 10C4.