Mathematics - Online Test
Q1. In a LPP, the linear inequalities or restrictions on the variables are called
Answer : Option C
Explaination / Solution:
In a LPP, the linear inequalities or restrictions on the variables are called Linear constraints.
Q2. The range of the function f(x) = x – [x] is
Answer : Option C
Explaination / Solution:
Since [x] ≤ x, therefore , x – [x] ≥ 0. Also, x – [x] <1,∴0⩽x−[x]<1. Therefore ,Range of f = [0,1).
Q3. If is the identity matrix of order 3 , then is
Answer : Option C
Explaination / Solution:
Because , the inverse of an identity matrix is an identity matrix itself.
Q4. The line ( p + 2q ) x + ( p – 3q ) y = p - q for different values of p and q passes through the fixed point
Answer : Option C
Explaination / Solution:
Expanding the given equation
px+2qx+py-3qy = p-q
px+py+2qx-3qy = p-q
p(x+y) -q(-2x+3y) = p-q
Equating the coeffiecients of like terms
x+y=1 and -2x+3y=1
On solving both the equations we get,
x = 2/5 and y = 3/5
Hence the line passes through the fixed point (2/5.3/5)
Q5. The area of the quadrilateral formed by the lines | x | + | y | = 1 is
Answer : Option A
Explaination / Solution:
Equations of the lines are
x0, y0, then x+y=1
x0, y0, then x+y=-1
x0, y0, then x-y = 2
x0 , y0, then x-y=-2
Clearly these lines form a square, whose coordinates are (1,1),(1,-1),(-1,-1),(-1,1)
Hence its area is 4 x [1/2]1 x 1= 2 sq units
Q6. Which of the following is a proposition ?
Answer : Option C
Explaination / Solution:
it is a statement which is F.Hence it is a proposition.Other options are open sentences which are not propositions
Q7.
The area bounded by the angle bisectors of the lines
Answer : Option B
Explaination / Solution:
The angle bisectors of the line given by are x = 0 , y = 1. Required area : =
Q8. If a unit vector makes angles , then the components of are
Answer : Option D
Explaination / Solution:
Let,, then ,
Putting these values in (1) , we get :
Putting these values in (1) , we get :
Q9. is equal to
Answer : Option A
Explaination / Solution:
Q10. 4tan−1(15)−tan−1(1239)=
Answer : Option C
Explaination / Solution:
