Day-2
1) The differential coefficient of tan⁻¹ {(sinx + cosx)/(sinx - cosx) is
a) -1 b) 0 c) 1 d) none
2) eʸ = eˣ, then dy/dx is
a) logx b) xˣ c) log(ex) d) none
3) If y= 4cos³x - 3cosx, find d²y/dx² at x=0.
4) If f(x)= tan⁻¹{√(1+ x²) - 1}/x , then f'(0) is
a) 0 b) 1 c) 1/2 d) none
5) If y= f(x)= (2x+3)/(3x+5), find the inverse function of f(x).
6) If xʸ = yˣ, find dy/dx
7) f(x)= logx, then f"(1) is equal to
a) -1 b) 1 c) e d) none
8) Show that the derivative of an odd function is always an even function.
9) y= sin⁻¹(cosx), find dy/dx.
10) The differential coefficient of tan⁻¹(Secx+ tanx) is
a) 0 b) Secx - tanx c) 1/2 d) 2
11) tan⁻¹{2x/(1- x²)} w.r.t cos⁻¹{(1- x²)/(1+ x²)}.
12) If y= x - x²/2 + x³/3- x⁴/4+.....∞, show dy/dx= 1/(1+ x)
13) The derivative of f(logx) w.r.t.x where f(x)= logx, is
a) x/logx b) logx/x c) 1/(x logx) d) none
Day -1
1) Evaluate:
a) sin{2tan⁻¹(1/5) + tan⁻¹(5/12)}.
b) tan[sin⁻¹(1/3) + coa⁻¹(1/√3)}.
2) If A=1 0 2 & Adj A= 5 a -2
-1 1 -2 1 1 0
0 2 1 -2 -2 b then the values of a and b.
A) a=-4, b=1 B) a=-4, b=-2 C) a= 4, b=1 D) a= 4 b= -1
3) If A= -1 0
0 2 then the value of A³ - A² is
A) I B) A C) 2A D) 2I
4) If A= -x -y
z t then the transpose of adj A is ?
5) Find the value of x of following determinant
x 2 -1
2 5 x. = 0
-1 2. x
A) -3,1 B) 3,-1 C) 3,1 D) -3,-1
6) Value of Determinant: 1+ a 1 1
1 1+b 1
1 1 1+ c
7) If A= 2 -1
-1 2 then value of A² is
8) find the Inverse Matrix of 2 1
7 4
9) If D= 1 a a²- bc
1 b b²- ca
1 c c²- ab then D is
A) 0 B) independent of a C) independent of b D) independent of c
