Mathematics - Online Test
Q1. If a∈R, then the roots of the equation tan x = a are in G.P for what values of a
Answer : Option C
Explaination / Solution:
Q2. If the mean of numbers 27,31,89,107,156 is 82 , then the mean of 130,126,68,50,1 is :
Answer : Option B
Explaination / Solution:
mean=130+126+68+50+15=3755=75
Q3. The binary operation * defined on the set of integers as a∗b=|a−b|−1is
Answer : Option D
Explaination / Solution:
Here * is commutative as b*a = |b−a|−1=|a−b|−1=a∗b.
Because ,|−x|=|x|for all x∈R.
Q4. Solution set of the equation 
Answer : Option B
Explaination / Solution:
Q5. Two points ( a , 0 ) and ( 0 , b ) are joined by a straight line. Another point on this line is
Answer : Option A
Explaination / Solution:
The slope of the line joining the points (a,0) and (0,b) is [b-0]/[0-a] = -(b/a)
Hence the equation of the line is y = (-b/a)x +b
i.e; ay = -bx +ab
Substituting the x coordinate 3a in the place of x in the above equation we get y = -2b
Hence (3a,-2b) is another point on the line.
Q6. (p∧∼q)∧(∼p∨q) is
Answer : Option D
Explaination / Solution:
Since
F V F = F Since
Hence contracdiction
Q7. dx is equal to
Answer : Option A
Explaination / Solution:
∫cos((x−a)+a)cos(x−a)dx=∫cos(x−a)cosa−sin(x−a)sinacos(x−a)dx=∫{cosa−sinatan(x−a)}dx.xcosa+sinalog|cos(x–a)|+C
Q8. In the figure which are the Equal vectors?
Answer : Option B
Explaination / Solution:
are equal vectors , because they have equal magnitude and same direction.
are equal vectors , because they have equal magnitude and same direction.
Q9. If P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find P(A|B)
Answer : Option B
Explaination / Solution:
We have ,
P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4
P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4
Q10. If then is equal to
Answer : Option C
Explaination / Solution:
sin−1x+cos−1x=π2cos−1x=π2−sin−1x=π2−π5=3π10.
