Mathematics - Online Test
Q1. Equation of a plane which is at a distance d from the origin and the direction cosines of the normal to the plane are l, m, n is.
Answer : Option D
Explaination / Solution:
In Cartesian co – ordinate system Equation of a plane which is at a distance d from the origin and the direction cosines of the normal to the plane are l, m, n is given by : lx + my + nz = d.
Q2. The distance between the planes 
Answer : Option B
Explaination / Solution:
No Explaination.
Q3. 
Answer : Option C
Explaination / Solution:
Q4. The number of all numbers that can be formed by using some or all of the digits 1, 3, 5, 7, 9 (without repetitions) is
Answer : Option C
Explaination / Solution:
Number of ways of forming 5 digit numbers=
Number of ways of forming 4 digit numbers=
Number of ways of forming 3 digit numbers=
Number of ways of forming 2 digit numbers=
Number of ways of forming 1 digit numbers= 5
Hence the total number of ways = 120+ 120 + 60+ 20+ 5 = 325
Q5.
For the differential equationfind the solution curve passing through the point (1, –1).
Answer : Option D
Explaination / Solution:
Q6. Arg. ( x ) , x ∈ R and x < 0 is
Answer : Option A
Explaination / Solution:
Given x R and x 0, therefore the number is and this will be a point inthe second quadrant as x is negative
We have arg(=
We have in the second quadrant the principal value of argument=
Hence Arg. ( x ) , x R and x 0 is
Q7.
In the expansion of the sum of coefficients of odd powers of x is
Answer : Option C
Explaination / Solution:
Q8. If A, B and C are any three sets , then A ∩ ( B ∪C ) is equal to
Answer : Option B
Explaination / Solution:
Q9. The equation of the tangent to the curve at the point (0, 1) is
Answer : Option B
Explaination / Solution:
Q10. The derivative of with respect to is
Answer : Option A
Explaination / Solution:
