Mathematics - Online Test
Q1. If the angles of a triangle be in the ratio 1 : 4 : 5, then the ratio of the greatest side to the smallest side is
Answer : Option A
Explaination / Solution:
Q2.
The area of the figure bounded by the curve , the x – axis and the straight line x = e is
Answer : Option D
Explaination / Solution:
Required area :
$= = - = 1
$= = - = 1
Q3. The radius of the sphere through the points ( 4 ,3 , 0 ) , ( 0 , 4 , 3 ) ,( 0 , 5 , 0 ) and ( 4 , 0 , 3 ) is
Answer : Option A
Explaination / Solution:
we know that general equation of sphere is
since sphere passing through the points ( 4 ,3 , 0 ) , ( 0 , 4 , 3 ) ,( 0 , 5 , 0 ) and ( 4 , 0 , 3 ) so putting these values one by one in given equation , we get
16+ 9+ 8g + 6f + c=0 =>8g +6f +c = -25 -------------1)
16 +9 +8f +6h +c=0 =>8f + 6h +c= -25 -----------2)
25 + 10f +c = 0 -----------------------3)
16+ 9+ 8g + 6h +c=0 =>8g +6h +c= -25 -------------4)
by 2) - 4 ) we have f = g
using this in 1) we have 16f +c = -25 -------5)
Now solving 3) and 5) we get f=0
using value of f we have g= 0 , h= 0 , c= -25
Now radius = = =5
Q4. The order of [x y z] is
Answer : Option A
Explaination / Solution:
= . ( where ; matrix A denotes the product of three given matrices.)
Q5. The function f(x) = is
Answer : Option A
Explaination / Solution:
f′(x)=ddx(tan−1x)
Therefore , f is strictly increasing on R
Q6. If A and B are two sets , then A∪B=A∩BA∪B=A∩B iff
Answer : Option C
Explaination / Solution:
Q7. If are non real complex numbers such that are real numbers , then
Answer : Option A
Explaination / Solution:
Q8. The maximum value of F(x) = x3 – 9x2 + 24x + 5 in the interval [1, 6] is
Answer : Option C
Explaination / Solution:
Q9. If A ,B andC be the three square matrices such that A = B + C , then Det A is equal to
Answer : Option C
Explaination / Solution:
Because , if A=B+C then |A|=|B+C|
Q10. The term containing in the expansion of is
Answer : Option B
Explaination / Solution:
