Mathematics - Online Test
Q1.
The middle term in the expansion of is
Answer : Option D
Explaination / Solution:
Q2. If A and B are sets , then A ∩ ( B – A ) is
Answer : Option C
Explaination / Solution:
Q3. is equal to
Answer : Option B
Explaination / Solution:
Q4. A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. What number of rackets and bats must be made if the factory is to work at full capacity?
Answer : Option B
Explaination / Solution:
Let number of rackets made = x
And number of bats made = y
Therefore , the above L.P.P. is given as :
Maximise , Z = x +y , subject to the constraints : 1.5x +3y ≤ 42 and. 3x +y ≤ 24, i.e.0.5x + y ≤ 14 i.e. x +2y ≤ 28 and 3x +y ≤ 24 , x, y ≥ 0.
Corner points | Z = x + y |
O( 0 , 0 ) | 0 |
D(0,14 ) | 14 |
A(8,0) | 8 |
B(4,12) | 16…………………(Max.) |
Here Z = 16 is maximum. i.e Maximum number of rackets = 4 and number of bats = 12.
Q5. Tangents to the curve at the points (1, 1) and ( – 1, – 1) are
Answer : Option D
Explaination / Solution:
Q6. Solve the system of inequalities :
Answer : Option C
Explaination / Solution:
Hence the solution of the system will be
Q7. If a, b, c, d are in H.P., then ab + bc + cd is
Answer : Option D
Explaination / Solution:
using the property of H.M
multiplying the above equations, we get
now dividing by bc,
Q8. If the variance of the data is V, then its S.D. is
Answer : Option D
Explaination / Solution:
standard deviation have the same units as the data but variance is mean of the square of differences.
Q9. The area of the figure bounded by y = and the straight line x = 1 is
Answer : Option D
Explaination / Solution:
Q10. A relation R on a non-empty set A is said to be an equivalence relation if
Answer : Option A
Explaination / Solution:
A relation R on a non empty set A is said to be reflexive if xRx for all x A . .
A relation R on a non empty set A is said to be symmetric if x Ryy Rx, for all x , y A .
A relation R on a non empty set A is said to be transitive if x Ry and y Rzx Rz, for all x,y,z A.
An equivalence relation satisfies all these three properties.
A relation R on a non empty set A is said to be symmetric if x Ryy Rx, for all x , y A .
A relation R on a non empty set A is said to be transitive if x Ry and y Rzx Rz, for all x,y,z A.
An equivalence relation satisfies all these three properties.
