Practice questions
88551 published questions with worked solutions.
- Let f : R → R be a polynomial function of degree four having extreme values at x = 4 and x = 5. If _ x 0 f(x) x^2 = 5, then f(2)...
- For t > – 1, let _t and _t be the roots of the equation ((t+2)^ 1/7 -1 )x^2 + ((t+2)^ 1/6 -1 )x + ((t+2)^ 1/21 -1 ) = 0. If _ t...
- The sum of the series 2 1 ^ 20 C_4 - 3 2 ^ 20 C_5 + 4 3 ^ 20 C_6 - 5 4 ^ 20 C_7 + + 18 17 ^ 20 C_ 20 , is equal to _______.
- If the function f(x) = ( x) - ( x) x - x is continuous at x = 0, then f(0) is equal to ______.
- The unit of 2I _0 c is : (I = intensity of an electromagnetic wave, c : speed of light)
- Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) :...
- Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The...
- The dimension of _0 _0 is equal to that of : ( _0 = Vacuum permeability and _0 = Vacuum permittivity)
- A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass water contact angle ≈ 0°) with...
- Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) :...
- Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The...
- A photoemissive substance is illuminated with a radiation of wavelength _i so that it releases electrons with de-Broglie...
- An object with mass 500 g moves along x-axis with speed v = 4 x m/s. The force acting on the object is :
- Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The...
- Which one of the following forces cannot be expressed in terms of potential energy ?
- A mirror is used to produce an image with magnification of 1 4 . If the distance between object and its image is 40 cm, then the...
- The equation of a wave travelling on a string is y = sin [20πx + 10πt], where x and t are distance and time in SI units. The...
- The electric field in a region is given by E = (2 i +4 j +6 k ) 10^3 N/C. The flux of the field through a rectangular surface...
- An inductor of reactance 100 Ω, a capacitor of reactance 50 Ω, and a resistor of resistance 50 Ω are connected in series with an...
- Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratios of lengths, radii and thermal...