We know `log_(2)32 = 5` . Show that we get the same answer by writing 32 as `64/2` and then using the product rule. Verify your answer .

We have log_(2)32 = 5 . Show that we get the same result by writing 32 = 2^(5) and then using power rules. Verify the answer.

We know that log_(10)100000 = 5 Show that you get the same answer by writing 100000 = 1000 xx 100 and then using the product rule. Verify the answer.

Is 7 xx 5 xx 3 xx 2 + 3 a composite number? Justify your answer.

Let f : R rarr R be defined by f(x) = cos (5x+2) . Is f invertible? Justify your answer.

Consider a closed loop C in a magnetic field as shown in figure. The flux passing through the loop is defined by choosing a surface whose edge coincides with the loop and using the formula phi=vecB_1 . dvecA_1 + vecB_2 . dvecA_2 +…. Now if we choose two different surfaces S_1 and S_2 having C as their edge, would we get the same answer for flux. Justify your answer.

Match the physical quantities given on column I with dimensions expressed in terms of mass (M) length (L) time (T), and charge (Q) given in column II and write the correct answer against the matched quantity in a tabular form in your answer book. {:("Column-I",,"Column-II"),("Angular momentum",,[ML^(2)T^(-2)]),("Latent heat",,[ML^(2)Q^(-2)]),("Torque",,[ML^(2)T^(-1)]),("Capacitance",,[ML^(3)T^(-1)Q^(-2)]),("Inductance",,[M^(-1)L^(-2)T^(2)Q^(2)]),("Resistivity",,[L^(2)T^(-2)]):}

Read the following information: ( 1 ) The resistivity of copper is lower than that of aluminium which in turn is lower than that of constantan. ( 2) Six wires labelled as A, B, C, D, E and F have been designed as per the following parameters: Answer the following questions using the above data: Arrange R_A , R_B and R_C in ascending order of their values. Justify your answer.

A cycle followed by an engine (made of one mole of perfect gas in a cylinder with a piston) is shown in figure. A to B: volume constant B to C: adiabatic C to D: volume constant D to A: adiabatic V_C=V_D=2V_A=2V_B (a) In which part of the cycle heat is supplied to the engine from outside ? (b) In which part of the cycle heat is being given to the surrounding by the engine ? (c) What is the work done by the engine in one cycle ? Write your answer in term of P_A,P_B,V_A (d) What is the efficiency of the engine ? ( gamma=5/3 for the gas , C_V=3/2R for one mole )

Differentiate (x^(2)-5x + 8) (x^(3) + 7x + 9) By using product rule

Let ** be the binary operation on the set {1,2,3,4,5} defined a"*" b = H.C.F of a and b Is the operation ** same as the operation ** defined in Exercise 4 above ? Justify your answer .