For each t ∈R, let [t] be the greatest integer less than or equal to t. Then
does not exist (in R)
is equal to 0
is equal to 15
is equal to 120
If the tangent at (1, 7) to the curve x2 = y – 6 touches the circle x2 + y2 + 16x + 12y + c = 0 then the value of c is
95
195
185
85
If α, β ∈ C are the distinct roots, of the equation x2 -x + 1 = 0, then α101 + β107 is equal to
2
-1
0
1
PQR is a triangular park with PQ = PR = 200 m. A T.V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q and R are respectively 45o, 30o and 30o, then the height of the tower (in m) is
50√2
100
50
100√3
Tangents are drawn to the hyperbola 4x2 – y2 = 36 at the points P and Q. If these tangents intersect at the point T(0, 3) then the area (in sq. units) of △PTQ is
36√5
45√5
54√3
60√3
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is
At least 750 but less than 1000
At least 1000
Less then 500
At least 500 but less than 750
Two sets A and B are as under:
A = {(a-b)∈ RxR:|a-5|<1 and |b-5|<1}
B = {(a,b)∈ Rx R: 4(a-6)2 + 9 (b-5)2 ≤ 36},then
Neither A ⊂ B nor B ⊂ A
B ⊂ A
A ⊂ B
A ∩ B = ∅
Tangent and normal are drawn at P(16, 16) on the parabola y2 = 16x, which intersect the axis of the
parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and,∠CPB = θ then a value of tan θ is
4/3
1/2
2
3
The Boolean expression ~ (p v q )v (-p ∧q ) is equivalent to
~q
~ p
p
q
B.
~ p
~ (p v q )v (p ∧q )
By property (-~ p ∧- q )v (-p ∧ q )
~p