`x+x+x+ .......(y\ t i m e s)=\ `

Write each of the following in exponential form: (i) a\ x\ a\ x\ a\ x\ a\ x\ a\ x\ a\ x\ a (ii) a\ x\ a\ x\ a\ x\ a ..10\ t i m e s (iii) 17\ "x"\ x\ "x"\ x\ "x"\ x\ y\ "x"\ y\ "x"\ y (iv) y\ x\ y\ x\ y\ x\ y\ x\ y ..20\ t i m e s (v) 7\ x\ a\ x\ a\ x\ b\ x\ b\ x\ b\ x\ c (vi) 13\ x\ p\ x\ p\ x\ p\ x .7\ t i m e s\ x\ q\ x\ q\ x\ q .12\ t i m e s

Which of the following quantities vary inversely as each other? The number of x men hired to construct a will and the time y takes to finish the job. The length x of a journey by bus and price y of the ticket Journey (x\ k m) undertaken by a car and the patrol (y\ l i t r e s) consumed by it.

The complex number which satisfies the condition |(i+z)/(i-z)|=1\ lies on a. c i r c l e\ x^2+y^2=1 b. t h e\ x-a xi s c. t h e\ y-a xi s d. t h e\ l in e\ x+y=1

Show that f\ : NvecN ,\ given by f(x)={x+,\ \ \ \ \ \ \ \ \ \ \ \ \ if\ x\ i s\ od dx-1,\ \ if\ x\ i s\ e v e n is both one-one and onto.

The area bounded by the curves y=x e^x ,y=x e^(-x) and the line x=1 is 2/e s qdotu n i t s (b) 1-2/e s qdotu n i t s 1/e s qdotu n i t s (d) 1-1/e s qdotu n i t s

Solution of (dy)/(dx)+2x y=y is (a) ( b ) (c) y=c (d) e^( e ) (f) x-( g ) x^((( h )2( i ))( j ) (k))( l ) (m) (n) (b) ( o ) (p) y=c( q ) e^( r ) (s) (t) x^((( u )2( v ))( w )-x (x))( y ) (z) (aa) (c) ( d ) (e) y=c( f ) e^(( g ) x (h))( i ) (j) (k) (d) ( l ) (m) y=c (n) e^( o ) (p)-( q ) x^((( r )2( s ))( t ) (u))( v ) (w) (x)

The area enclosed between the curves y=(log)_e(x+e),x=(log)_e(1/y), and the x-axis is (a) 2s qdotu n i t s (b) 1s qdotu n i t s (c) 4s qdotu n i t s (d) none of these

The x and y coordinates of the particle at any time are x = 5t - 2t^(2) and y = 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at I = 2s is

A wave pulse is travelling along +x direction on a string at 2 m//s . Displacement y (in cm ) of the parrticle at x=0 at any time t is given by 2//(t^(2)+1) . Find (i) expression of the function y=(x,t),i.e., displacement of a particle at position x and time t. Draw the shape of the pulse at t=0 and t=1 s.

A particle moves in xy plane such that v_(x)=50-16 t and y=100-4t^(2) where v_(x) is in m/s and y is in m. It is also known that x=0 when t=0 . Determine (i) Acceleration of particle (ii) Velocity of particle when y=0 .