Free mock test for NDA Sequence and Series Conic Section Ray Optics(Physics) Differentiation + Ray Optics(Physics) Application of Derivative + Electrostatic Application of Derivative + Electricity Complex Number

Start the test Question no. 1 If a positive charge is shifted from a low potential region to a high potential region , the electric potential energy decreases   increases   remains the same   may decrease / increase Question no. 2 Work done in moving a unit positive charge through a distance of x metre on an equipotential surface is   x joule   1/x joule   0 x 2 Question no. 3 f(x) = cos x is monotonic decreasing under which one of the following condition ? (0 , π/2) only   (π/2 , π) only   (0 , π)   (0 , 2π) Question no. 4 A wire 34 cm long is to be bent in the form of a quadrilateral of which each angle is 90 degree. What is the maximum area which can be enclosed inside the quadrilateral ? 68 cm 2   70 cm 2   71.25 cm 2   72.25 cm 2 Question no. 5 What are the points on the curve x 2 +...

Start the test Question no. 1 If x = cost , y = sint , then what is equal to ? y -3   y 3   -y -3   -y 3 Question no. 2 What is the derivative of (log tanx cotx)(log cotx tanx) -1 at x = π/4 ?   -1   0   1   1/2 Question no. 3 What is the derivative of log 10 (5x 2 + 3) with respect to x ? (xlog 10 e)/(5x 2 + 3)   (2xlog 10 e)/(5x 2 + 3)   (10xlog 10 e)/(5x 2 + 3)   (10xlog e 10)/(5x 2 + 3) Question no. 4 Let f(x) = [|x| -|x-1|] 2 , What is f'(x) equal to when x > 1 ?   0   2x-1   4x - 2   8x - 4 Question no. 5 let f(x+y) = f(x)f(y) for all x and y . then what is f'(5) equal to ?   f(5)f'(0)   f(5) - f'(0)   f(5)f(0)   f(5) + f'(0) Question no. 6 y = ln(√tanx) , then what is the value of dy/dx at x = π/4 ?   0   -1   1/2 ...

Start the test Question no. 1 The laws of reflection are valid for :   only for plane surface   only for curved surface   both plane and curved surface   neither of them Question no. 2 Consider the two statements : 1) if reflected rays intersect , virtual image is formed . 2) if reflected rays diverge after reflection , real image is formed. Which of the following statements are correct ?.   only 1   only 2   both   neither Question no. 3 Consider the following statements virtual images 1) can be formed on screen . 2) always erected and not always magnified   only 1   only 2   both   neither Question no. 4 The working principle of optics fibre is   Scattering   Polarization   Total internal reflection   Dispersion of light Question no. 5 When an object is placed under a transparent medium , it appears to be raised. The upward ...

Differentiation Common Standard formula Product rule In this rule , we can differentiate two or more functions which are mulitplied together. Example : Find the derivative of y = xsinx Video lecture : Divide rule / Quotient Rule In this rule , we can differentiate two or more functions which are divided or in the rational fractional form ( in numerator and denominator form). Example : Find the derivative of y = (xsinx)/(1+tanx) Chain Rule In this rule , we can differentiate a function which is function of others function (e.g. Fog(x) or f(g(x)) Example : Differentiate w.r.t to another function In this rule , we can differentiate a function f(x) with respect to another function g(x) not with respect to x. Example : Find the derivative of the ln(x+sinx) with respect to (x+sinx). miscellaneous Case 1 : if function is in form [f(x)] g(x) Example : y = sinx logx take the log to the both the sides. log y = log sinx l...

Start the test Question no. 1 If any point on a hyperbola is (3tanθ , 2secθ) , then what is the eccentricity of the hyperbola ?   3/2   5/2   √11 / 2   √13/2 Question no. 2 The curve y 2 = -4ax (a>0) lies in   first and fourth quadrants   first and second quadrants   second and third quadrants   third and fourth quadrants Question no. 3 What is the maximum number of the parabolas that can be drawn through these points as end points of latusrectum ?   only one   two   four   infinite Question no. 4 The sum of the focal distance of a point on an ellipse is constant and equal to   length of minor axis   length of major axis   length of latus rectum   sum of the lengths of semi major and semi minor axis. Question no. 5 Two parabolas y 2 = 4ax and x 2 = 4ay intersect   at two points on the line y =x   only at t...