Now, in the above equation, we can see all the elements are zero in the second row of the matrix on the LHS. Therefore, A-1 does not exist. Note: Suppose A = IA, after applying the elementary transformation, if any row or column of a matrix on LHS is zero, then A-1 does not exist. […]

Directions (Q. No. 11 and 12) Choose the correct answer in the following questions: 11. If A, B are symmetric matrices of same order, then AB-BA is a (i) Skew-symmetric matrix (ii) Symmetric matrix (iii) Zero matrix (iv) Identity matrix Sol. Given, a and B are symmetric matrices → A’ = A and B’ = […]

Note: If two matrices have different orders then we can neither add nor subtract the matrices but we can multiply the matrices either the orders are same or number of columns of first matrix is equal to the number of rows of second matrix. By definition of equality of matrix as the given matrices are […]

Sol. (i) In the given matrix, the number of rows is 3 and the number of columns is 4. Therefore, the order of the matrix is 3 × 4. (ii) Since, the order of the matrix is 3 × 4, so there are 3 × 4 = 12 elements in it. 2. If the matrix […]

Q.1. Which of the following frequency/frequencies will be suitable for beyond the horizon communication using sky waves ? (a) 10 kHz (b) 10 MHz (c) 1 GHz (d) 1000 GHz Sol. Choice (b) is correct. This is because 10 kHz cannot be radiated due to large antenna size. 1 GHz and 1000 GHz will penetrate. […]

Q.1. In n- type which of the following statement is true: (a) Electrons are majority carriers and trivalent atoms are the dopants (b) Electrons are minority carriers and pentavalent atoms are the dopants (c) Holes are minority carriers and pentavalent atoms are the dopants (d) Holes are majority carries and trivalent atoms are the dopants […]

Q.1.(a) Two stable isotopes of 3Li6 and 3Li7 have respective abundances of 7.5  and 92.5 . These isotopes have masses 6.01512 u and 7.01600 u respectively. Find the atomic weight of lithium.(b) Boron has two stable isotopes 5B10. Their respective masses are 10.01294 u and 11.00931 u, and the atomic weight of boron is 10.811 […]

Q.1. Choose the current alternative from the clues given at the end of each statement : (a) The size of the atom in Thomson’s model is ……. The atomic size in Rutherford’s modal (much greater than/no different from/much less than) (b) IN the ground state of………., electrons are in stable equilibrium, while in …….. electrons […]

Q.1. find the (a) maximum frequency and (b) minimum wave-length of X- rays produced by 30 KV electrons. Given, h = 6.6310-34 Js. Q.2. the work function of caesium metal is 2.14 eV. When light of frequency 6⨯1014 Hz is incident on the metal surface, photoemission of electrons occurs. What is the (a) maximum kinetic […]

NCERT 12 Maths Inverse Trigonometric Functions – Chapter 2 (Ex.2.1), NCERT Class 12 maths chapter 2 solutions. Direction (Q. No. 1 to 10) Find the principal values of the following questions. Direction (Q. Nos. 11 to 14) Find the values of the following questions: Direction (Q. Nos. 11 to 14) Find the values of the […]

Q.1. Monochromatic light of wavelength 589 nm incident from air on a water surface. What are the wavelength frequency and speed of (a) reflected and (b) refracted light? of water is 1.33. Q.2. What is the shape of the wavefront in each of the following cases ? (a) light diverging from point source. (b) light […]

Q.1. A small candle 2.5 cm in size is placed 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance form the mirror should a screen be placed in order of receive a sharp image ? Describe the nature and size of the image. If the candle is […]

Q.1. shows a capacitor made of two circular plates each of radius 12 cm and separated by 5.0 mm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15 A. (a) Calculate the capacitance and the rate of change of potential difference […]

Q.1. A 100 Ω resistor is connected to a 220 V, 50 Hz ac supply.220 (a) What is the rms value of current in the circuit ? (b) What is the net power consumed over a full cycle ? Q.2. (a) The H inductor is connected to 220 V, 50 Hz a. c. supply. Determine […]

Q.1. Predict the direction of induced current in the situations described by the following (a) to (f). Sol. (a) South pole develops at q, current induced must be clockwise at q. In the coil, induced current is from p to q. (b) Coil p q in the would develop S – pole at q and […]

NCERT 12 Maths Solutions of Relations and Functions – Chapter 1 Ex 1.4 Q 1. Determine whether or not each of the definition of * given below gives a binary operation. In the event that * is not a binary operation, give justification for this. i. On Z+, defined * by a* b = a- […]

Q.1. A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field  at the centre of the coil? Q.2.A long straight wire carries a current of 35 A. What is the magnitude of the field at a point […]

Q.1. The storage battery of a car has an emf of 12 V. If the internal resistance of the battery is 0. 4 Ώ, What is the maximum current that can be drawn from the battery ? Q.2. A battery of emf 10 V and internal resistance 3 Ώ is connected to a resistor. If […]

Q.1. Two charges 5  10-8  C and -3  10-8 C are located 10  cm apart. At what points on the line joining the two charges is the electric potential zero ? Take the potential at infinity to be zero. Q.2. A regular hexagon of side 10 cm has a charge 5 μ C at each […]

Q.1. What is the force between two small charged spheres having charges of 2 × 10-7 C and 3 × 10-7 C placed 30 cm apart in air ? Q.2. The electrostatic force on a small sphere 0-4 μ C due to another small sphere of charge – 0.8μ C air is 0.2 N. (a) […]

Biology 12 Organism and Populations Chapter 13 – Exercise, Q 1. How is diapause different from hibernation? Ans 1. Hibernation is the phenomenon commonly depicted by ecothermal (cold-blooded) animals which escape cold by hiding them in shelters such as caves, burrows, cervices, hollow thee trunks, mud etc. revealing minimum physiological activity. This phenomenon is also […]

Q.1. Answer the following questions regarding earth’s magnetism. (a) A vector needs three quantities for its specification. Name the three independent quantities conventionally used to specify the earth’s magnetic field. (b) The angle of dip at a location in southern India is about 180. Would you expect a grater or lesser dip angle in Britain […]

NCERT Class 12 Maths Solutions of Relations and Functions – Chapter 1 Ex 3, Q 1. Let f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3} be given by f : {(1, 2), (3, 5), (4, 1) and g : {(1, 3), (2, 3), (5, 1)}. […]

Q 1. Crystals of Bt toxin produced by some bacteria do not kill the bacteria themselves because – Bacteria are resistant to the toxin Toxin is immature Toxin is inactive Bacteria encloses toxin in a special sac. Ans 1. Toxin is inactive. Q 2. What are transgenic bacteria? Illustrate using any one example. Ans 2. […]

Q 1. Show that the function f : R* → R* defined by f(x) = 1/x is one-one, where R* is the set of all non-zero real numbers. Is the result true, if the domain R* is replaced by N with co-domain being same as R*? Sol. It is given that f : R* → R* is defined by f(x) = […]

Q 1. Fill in the blanks: Plants are called as ______ because they fix carbon dioxide. In an ecosystem dominated by trees, the pyramid (of numbers) is ______ type. In aquatic ecosystems, the limiting factor for the productivity is ______. Common detritivores in our ecosystem are ______. The major reservoir of carbon on earth is […]

Q – 4.1. From the rate expressions for the following reactions, determine their order of reaction and the dimensions of the rate constants: 3 NO (g) ⟶ N2O (g) + NO2 (g) ; Rate = k [NO]2 H2O2 (aq) + 3 I- (aq) + H+ ⟶ 2 H2O (I) + I-3 ; Rate = k […]

Q – 5.1. Distinguish between the meaning of the terms adsorption and adsorption. Give one example of each. Ans. Adsorption – 1. It is a surface phenomenon, i.e., it occurs only at the surface of the adsorbent. 2. In this phenomenon, the concentration on the surface of adsorbent is different from that in the bulk. […]