Mathematics - Online Test
Q1. If z = x + yi ; x ,y R, then locus of the equation
Answer : Option B
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which is a straight line
Q2. Differential equation of the family of circles touching the y-axis at origin is
Answer : Option A
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Q3. If in the binomial expansion of the sum of 5th and 6th terms are 0, then is
Answer : Option A
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Q4. Let A = { a ,b ,c } , B = { a, b } , C = { a, b, d } , D = { c , d } and E = { d } . Then which of the following statement is not correct ?
Answer : Option C
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Q5. If x = f(t) and y = g (t), then is qual to
Answer : Option D
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Q6. The corner points of the feasible region determined by the following system of linear inequalities:2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5). Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is
Answer : Option A
Explaination / Solution:
Here Z = px +qy , subject to constraints :
2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0
As it is given that Z is maximum at ( 3 ,4 ) and ( 0, 5 ).
Therefore , 3p + 4q = 0p + 5q , which gives 3p = q .
2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0
As it is given that Z is maximum at ( 3 ,4 ) and ( 0, 5 ).
Therefore , 3p + 4q = 0p + 5q , which gives 3p = q .
Q7. Solve : 3x + 5 < x − 7, when x is a real number
Answer : Option D
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Q8.
If a, b, c, d , e are in G. P., then equals
Answer : Option D
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Q9. The mean and S.D. of 1,2,3,4,5,6 is
Answer : Option C
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Q10. The function f (x) = has a
Answer : Option A
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