Mathematics - Online Test
Q1. Area of the region bounded by the curves y = , x = a , x = b and the x- axis is given by
Answer : Option A
Explaination / Solution:
Required area
∫abexdx=[ex]ba=eb−ea
Q2. The matrix 
is decomposed into a product of a lower triangular
matrix [L] and an upper triangular matrix [U]. The properly decomposed [L] and
[U] matrices respectively are
is decomposed into a product of a lower triangular
matrix [L] and an upper triangular matrix [U]. The properly decomposed [L] and
[U] matrices respectively are
Answer : Option D
Explaination / Solution:
[A] = [L][U] Option D is correct
Q3. The direction cosines of any normal to the XY plane are
Answer : Option D
Explaination / Solution:
Concept used - Parellel lines have same direction cosines
Explanation We know Z axis is perpendicular to XY plane and direction cosines of Z axis are <0,0,1>
and as any normal to XY plane will be parallel to Z axis and parellel lines have same direction cosines so answer is <0,0,1>
Q4. If P is of order 2 × 3 and Q is of order 3 × 2, then PQ is of order
Answer : Option B
Explaination / Solution:
Here, matrix P is of order and matrix Q is of order , then , the product PQ is defined only when : no. of columns in P = no. of rows in Q. And the order of resulting matrix is given by : rows in P x columns in Q.
Q5. In case of strict decreasing functions, slope of tangent and hence derivative is
Answer : Option B
Explaination / Solution:
In case of a strict decreasing function , slope of tangent and hence derivative is either negative or zero because decreasing function change sign from positive to negative and making obtuse angle measured clockwise.Hence negative and will be zero at peak.
Q6. If A and B be any two sets , then (A∪BA∪B)′ is equal to
Answer : Option D
Explaination / Solution:
Q7. is equals to
Answer : Option C
Explaination / Solution:
Q8. A square matrix A is invertible iff det A is equal to
Answer : Option D
Explaination / Solution:
Only non-singular matrices possess inverse.
Q9.
If the coefficients of and in the expansion of are equal then n =
Answer : Option A
Explaination / Solution:
Q10.
Answer : Option D
Explaination / Solution:
