Jr. MATHEMATICS Jr. then dy dx 92. If ya 76. The number of points of non-differentiability for 83. If y1+ and x+y-+ TC in 1) 0 the function f(x)=x|+cos.x+ tan*+ 2)2 -y 4) 3) 1) the interval (-1, 2) is 93. * 84. Let D be the domain of a twice differentiable function f. For all xe D.f"(x)+ f(x)3D0 and f(x)=[g(x)dx+constant. If h(x)- f(x) +(g and h (0) = 5 then h (2015)- h (2014) = 3) 0 I) 1 2) 2 3) 3 4) 4 ther d'y 77. If y=e, then dxdy? is equal to 1) I)nex 2) ne-nx 3)1 4)-ne-x 2) 3 4)1 1) 5 78. Let f(x)= x|x,g(x)%3 sin x and h(x)3D(gof)(x). Then d'y 94. If at t is 85. If x = at and y = 2at, then dx 2 1) 1) h(x) is not differentiable at x = 0 2) h(x) is differentiable at x = 0, but h'(x) -2 1) a 4. 2) 8. 3) 4) a. 2) %3D is not continuous at x = 0 dy %3D 31 3) h'(x) is continuous at x = 0 but it is not 86. x/1+ y+yV1+x =03D> %3D dt differentiable at x 0 1 -1 1 4) 1+x2 4) h'(x) is differentiable at x 0 1) (1+ x) 2) (1+x)2 3) 95. t 79. Let f,g:R R be two functions defined 87. If A(x)=g(x) and g'(x)=-f(x) for all x and (2) = 4 =(2) then f(24) + g(24) is x sin f(x)= ARS %3D by . and 1) 32 3) 64 4) 48 0, g(x) = x f(x) GMT.224D f(l+x) -0 f(1) 3) Se 4) e2 GNM 88. If (1)=3, A(1)=6 then Lt Statement I: f is a continuous function at x = 0 %3D Statement II: g is a differentiable function at x = 0 1) 0 2) 1 1) both statements I and II are false 2) both statements I and II are true dy 89. dx 3) statements I is true, statements II is fasle 4) statements I is false, statements II is true 96. 7x-y 1) x-7y 7y-x 7y-x 3) 2x-7y 7x+y 4) x+7y 2) 1-Vy y-7x 80. If x , then (x+1)dy 3/y+1)dv then (x+1)+ 90. The function f(x) = sin(tanx) is not differen- 1+Vy 2) 0 dx2 Vy dx tiable at 1)-2y 3)-y 4) y 1) x 0 2) x=-/6 3) x 1/6 4) x 1/4 97. 81. If x+y=r+ and x+y=r+ then Vi+x+Vi-x Vi+-Vi+x 2. 91. If f(x)=Tan for dx 1) -1 2) -2 3) 4) xy