1) If two rows or two columns of a determinant are identical then value of the determinant is:
A) 0 B) 2 C) -1 D) 1
2) The value of tan(π/2 - tan⁻¹1/3) is equal to
A) 1/3 B) 3 C) 2/3 D) 3/2
3) The domain for which the functions f(x)= 3x² - 2x and g(x)= 3(3x -2) are equal, will be..
A){1,2/3} B) {1,3} C) {2/3,3} D) {2/3,0}
4) If y= tan⁻¹{(5-x)/(1+5x)}, then value of dy/dx=?
A) -1/(1+x²) B) 1/(1+x²) C) 5 D) 5/(1+x²).
5) Solve: 2 sin⁻¹x= cos⁻¹x, 0<x<1.
A) 1/2 B) 1/3 C) 1 D) none
6) Let A={1,2,3}. Define a relation (on A) which is reflexive and symmetric but not transitive.
A) (2,2),(3,3),(2,3),(1,2),(2,1)
B) (1,1),(2,2),(3,3),(2,3),(1,2),(2,1)
C) (1,1),(2,2),(3,3),(2,3),(1,2)
D) (1,1),(2,2),(3,3),(1,2)
7) If A= 8 0 & B= 2 -2
4 -2 -5 1 find another matrix X where 2A + 3X = 5B.
A) 2 10/3 B) -2 10/3
11 3 -11 3
C) -2 -10/3 D) -2 -10/3
-11 3 11 -3
8) If 2 3 = x 3
4 5 2x 5. Find the value of x.
A) 0 B) 1 C) -2 D) 2
9) If y= sin⁻¹{2x/(1+x²) then dy/dx
A) 1/(1+x²) B) -1/(1+x²) C) 2/(1+x²) D) -2/(1+x²)
10) f(x)= 5 - | x - 1 |. Find the maximum value of f(x). Also find the value of x for which f(x) is maximum.
A) -5, -1 B) 5, 1 C) 1, 5 D) -1,-5
11) If R₁ and R₂ are two equivalence relation defined on set A(≠ 0), then R₁∩R₂ is an
A) one-one function
B) onto function
C) equivalence relation
D) none
12) If tan⁻¹x + tan⁻¹y + tan⁻¹z=π/2 and x+y+ z =√3, then.
A) x=y≠z B) x≠y≠z C) x≠y=z D) x= y=z.
13) 1 2 2
If A= 2 1 2
2 2 1 then A²-4A= ?
A) 5 B) 4 C) 3 D) 1
14) Solve: 3x+y+z=20; 3x+y-z= 0; 5x- 9y= 1;
A) 1,2,3 B) 2,1,3 C) 3,2,1 D) 1,3,2
15) If cos y= x cos(a+y), (a≠0), then dy/dx is
A) cos{(a+y)}/sin a
B) cos a/sin (a +y)
C) cos²{(a+y)}/sin a
D) sin²{(a+y)}/cos a
16) If x= sin t, y= sin kt (k≠0, constant) then (1-x²) d²y/dx² - x dy/dx =?
A) - ky B) -ky² C) -k²y D)- k²y²
17) Find maximum and minimum values of (x²-x+1)/(x²+x+1).
A) -3, 1/3 B) -3, -1/3 C) 3, -1/3 D) 3, 1/3
