Mathematics - Online Test
Q1. General solution of is
Answer : Option B
Explaination / Solution:
Q2. The value of is
Answer : Option A
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Q3. The coefficient of xn in the expansion of (1+x)(1−x)n is
Answer : Option C
Explaination / Solution:
Q4. If A and B be two sets such that n( A ) = 70 , n ( B ) = 60 , and n ( A ∪ B ) = 110 . Then n ( A ∩ B ) is equal to
Answer : Option D
Explaination / Solution:
Q5. is equal to
Answer : Option C
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Q6. A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?
Answer : Option B
Explaination / Solution:
Let number of packages of nuts produced = x
And number of packages of bolts produced = y
Therefore , the above L.P.P. is given as :
Maximise , Z = 17.50x +7y , subject to the constraints : x +3y ≤ 12 and. 3x +y ≤ 12, x, y ≥ 0.
Corner points | Z =17.50 x +7 y |
O( 0 , 0 ) | 0 |
D(4,0 ) | 70 |
A(0,4) | 28 |
B(3,3) | 73.50…………………(Max.) |
Here Z = 73.50 is maximum.
i.e 3 packages of nuts and 3 packages of bolts;
Maximum profit = Rs 73.50.
Q7. Solve the system of inequalities − 2 < 1 − 3x < 7
Answer : Option B
Explaination / Solution:
Q8.
Tangents to the curve at the points (1, 1) and ( – 1, 1)
Answer : Option D
Explaination / Solution:
therefore , slope of tangent at (1,1) = - 1 and the slope of tangent at ( - 1 ,1 )= 1 .
Now product of the slopes=1.-1= -1
Hence , the two tangents are at right angles.
Q9. The number of numbers between 105 and 1000 which are divisible by 7 is
Answer : Option B
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Q10. If the median = (mode + 2 mean) μ, then μ is equal to
Answer : Option C
Explaination / Solution:
