Mathematics - Online Test
Q1. The number of points on X axis which are at a distance of c units ( c < 3 ) from ( 2 , 3 ) is
Answer : Option B
Explaination / Solution:
Let (x,0) be the point.
Then (by distance formula,
(x-2)2 +32 = c2
x2 -4x +4 + 9 - c2 = 0
x2 - 4x +13 - c2 = 0
x will be real if the b2 - 4ac 0
i.e; 16 - 4(13 - c2) 0
i.e; c2 - 9 0
i.e; |c| 3
Hence there is no point.
Q2. Let p and q be two propositions. Then the implication p↔∼q is true ,when
Answer : Option C
Explaination / Solution:
| p | q | ||
| T | T | F | F |
| T | F | T | T |
| F | T | F | T |
| F | F | T | F |
Q3. For any three propositions p , q , and r , the proposition (p∧q)∧(q∧r) is true , when
Answer : Option C
Explaination / Solution:
hence p=T , q=T, r=T
Q4.
The area bounded by the curves and is equal to
Answer : Option D
Explaination / Solution:
Eliminating y, we get:
Required area:
Required area:
Q5. If is a non zero vector of magnitude ‘a’ and a non zero scalar, then is a unit vector if
Answer : Option B
Explaination / Solution:
is a unit vector if and only if is equal to .
Q6. dx is equal to
Answer : Option B
Explaination / Solution:
Q7.
Domain of f(x) =
Answer : Option A
Explaination / Solution:
,
Q8. A and B are two distinct points, Locus of a point P satisfying |PA| + | PB | = 2k, a constant is
Answer : Option A
Explaination / Solution:
Since the value of k is not specified, we cannot get a specific equation.
Q9.
In a , a = 4, b = 3 and A = ; then c is a root of the equation
Answer : Option C
Explaination / Solution:
Q10. For is divisible by
Answer : Option A
Explaination / Solution:
When n = 1 we get 64. When n = 2 we get 704 which is divisible by 64......... By the principle of mathematical induction it is divisible by 64.
