Mathematics - Online Test
Q1. Negation of the statement q∨∼(p∧r) is
Answer : Option C
Explaination / Solution:
∼(q∨∼(p∧r)) Since ∼(q∨r)≡∼q∧∼r
∼q∧(p∧r)
Q2. If ∫ f(x) dx = f (x), then
Answer : Option B
Explaination / Solution:
It implies that the function remains same after integrating or differentiating it. So the function must be ex
Q3. Magnitude of the vector 
is
is
Answer : Option C
Explaination / Solution:
Q4. The z-Transform of a sequence x[n] is given as X(z) = 2z+4-4/z+3z2. If y[n] is the first
difference of x[n], then Y(z) is given by
Answer : Option A
Explaination / Solution:
y(n) is first difference of x(n) So
g(n)=x(n)-x(n-1)
Q5. If = ,then x =
Answer : Option C
Explaination / Solution:
Q6. Let f be a function satisfying f(x + y) = f(x) + f(y) for all x, y then f ‘ (x) =
Answer : Option B
Explaination / Solution:
Q7. Which of the following lines is a normal to the circle
Answer : Option A
Explaination / Solution:
comparing the above equation with we get center as (1,2)
putting (1,2) in L.H.S of above line ,we get 1+2=3=R.H.S
=> it satisfies center satisfies the equation of line or the line passes through center
and the line passing through the centre is normal.
Q8.
cot = sin 2 n , n integer) if equals
Answer : Option B
Explaination / Solution:
sin2θ=cotθ⇒2sinθcosθ=sinθcosθ⇒cosθ(2sinθ−1sinθ)=0⇒−cosθ(1−2sin2θ)=0⇒−cosθ.cos2θ=0⇒cosθ=cosπ20rcos2θ=cosπ2⇒θ=π2,π4[∵θ≠nπ,nϵZ]
Q9.
If is divisible by x – k for all n belongs to natural numbers N , then the least positive integral value of k is :
Answer : Option A
Explaination / Solution:
since we have x - 1 as a factor of xn - 1n.
Q10. 8 coins are tossed at a time. The probability of getting 6 heads up is
Answer : Option B
Explaination / Solution:
Total ways of getting 6 heads out of 8 toss of coins is 28.
Total number of outcome is 28 = 256
Therefore probability is
