Tick (✓) the correct answer:
Question: Tick (✓) the correct answer: The compound interest on Rs 5000 at 8% per annum for 2 years, compounded annually, is (a) Rs 800 (b) Rs 825 (c) Rs 832 (d) Rs 850 Solution: (c) Rs 832 $A=P \times\left(1+\frac{R}{100}\right)^{n}$ $=$ Rs. $5000 \times\left(1+\frac{8}{100}\right)^{2}$ $=$ Rs. $5000 \times\left(\frac{108}{100}\right)^{2}$ $=$ Rs. $5000 \times\left(\frac{27}{25}\right)^{2}$ $=$ Rs. $5000 \times\left(\frac{27}{25}\right) \times\left(\frac{27}{25}\right)$ $=$ Rs. $(8 \times 27 \t...
Read More →A magnetic compass needle is placed in a plane
Question: A magnetic compass needle is placed in a plane of paper near point A as shown in figure. In which plane should a straight current carrying conductor be placed so that it passes through A and there is no change in the deflection of the compass ? Under what condition is the deflection maximum and why? Solution: The straight current carrying conductor should be placed in the plane of the paper. The deflection of the compass is maximum when the conductor passes through A and perpendicular ...
Read More →Arun took a loan of Rs 390625 from Kuber Finance.
Question: Arun took a loan of Rs 390625 from Kuber Finance. If the company charges interest at 16% per annum, compounded quarterly, what amount will discharge his debt after one year? Solution: Let the principal amount be $P=$ Rs 390625 . Annual rate of interest, $R=16 \%$ Rate of interest for a quarter year $=\frac{16}{4} \%=4 \%$ Time, $n=1$ year $=4$ quarter years Then the amount with the compound interest is given by $A=$ Rs. $P \times\left(1+\frac{R}{100}\right)^{n}$ $=$ Rs. $390625 \times\...
Read More →The most important safety device method
Question: The most important safety device method used for protecting electrical appliances from short circuiting or overloading is (a)earthing (b)use of stabilizers (c)use of electric meter (d)use of fuse. Solution: (d).Explanation :Fuse melts and the circuit breaks as soon as the current in the circuit exceeds safe limit....
Read More →Sudershan deposited Rs 32000 in a bank, where the interest is credited quarterly.
Question: Sudershan deposited Rs 32000 in a bank, where the interest is credited quarterly. If the rate of interest be 5% per annum, what amount will he receive after 6 months? Solution: Let the principal amount be $P=$ Rs 32000 . Annual rate of interest, $R=5 \%$ Rate of interest for a quarter year $=\frac{5}{4} \%$ Time, $n=6$ months $=2$ quarter years Then the amount with the compound interest is given by $A=$ Rs. $P \times\left(1+\frac{R}{100}\right)^{n}$ $=$ Rs. $32000 \times\left(1+\frac{5...
Read More →To convert AC generator to DC generator
Question: To convert AC generator to DC generator (a)slip rings and brushes must be used (b)split ring type commutator must be used (c)rectangular wire loop is to be used (d)stronger magnetic field is to be used. Solution: (b)split ring type commutator must be used...
Read More →Neeraj lent Rs 65536 for 2 years at
Question: Neeraj lent Rs 65536 for 2 years at $12 \frac{1}{2} \%$ per annum, compounded annually. How much more could he earn if the interest were compounded half-yearly? Solution: Let the principal amount be $P=$ Rs. 65536 . Annual rate of interest, $R=\frac{25}{2} \%$ Rate of interest for a half year $=\frac{25}{4} \%$ Time, $n=2$ years $=4$ half year Then the amount with the compound interest is given by $A=P \times\left(1+\frac{R}{100}\right)^{n}$ $=$ Rs. $65536 \times\left(1+\frac{25}{100 \...
Read More →The strength of magnetic field inside
Question: The strength of magnetic field inside a long current carrying straight solenoid is (a)more at the ends than at the centre (b)minimum in the middle (c)same at all points (d)found to increase from one end to the other. Solution: (c).Explanation :Magnetic field inside a long current carrying straight solenoid is uniform....
Read More →A constant current flows in a horizontal
Question: A constant current flows in a horizontal wire in the plane of the paper from east to west as shown in figure. The direction of magnetic field at a point will be north to south. (a)directly below the wire (b)directly above the wire (c)at a point located in the plane of the paper, on the north side of the wire (d)at a point located in the plane of the paper, on the south side of the wire. Solution: (d).Explanation :Applying right hand thumb rule to know the direction of the magnetic fiel...
Read More →Using the principle of mathematical induction, prove each of the following
Question: Using the principle of mathematical induction, prove each of the following for all n ϵ N: $\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\ldots .+\frac{1}{(2 n-1)(2 n+1)}=\frac{n}{(2 n+1)}$ Solution: To Prove: $\frac{1}{1 \times 3}+\frac{1}{(3 \times 5)}+\ldots \ldots+\frac{1}{(2 n-1) \times(2 n+1)}=\frac{n}{(2 n+1)}$ Let us prove this question by principle of mathematical induction (PMI) Let $\mathrm{P}(\mathrm{n}): \frac{1}{1 \times 3}+\frac{1}{(3 \times 5)}+\ldots \ldots+\frac{1}{(2 n-1...
Read More →Choose the incorrect statement
Question: Choose the incorrect statement (a)Flemings right hand rule is a simple rule to know the direction of induced current. (b)The right-hand thumb rule is used to find the direction of magnetic fields due to current carrying conductors. (c)The difference between the direct and alternating currents is that the direct current always flows in one direction, whereas the alternating current reverses its direction periodically. (d)In India, the AC changes direction after every 1/60 seconds Soluti...
Read More →Sheela deposited Rs 20000 in a bank, where the interest is credited half-yearly.
Question: Sheela deposited Rs 20000 in a bank, where the interest is credited half-yearly. If the rate of interest paid by the bank is 6% per annum, what amount will she get after 1 year? Solution: Let the principal amount be $P=$ Rs. 20000 . Annual rate of interest, $R=6 \%$ Rate of interest for half year $=3 \%$ Time, $n=1$ year $=2$ half years Then the amount with the compound interest is given by $A=\mathrm{P} \times\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}$ $=$ Rs. $20000 \times\le...
Read More →Solve this
Question: Find $\frac{\mathrm{dy}}{\mathrm{dx}}$, when $y=x^{\sin x}+(\sin x)^{x}$ Solution: let $y=x^{\sin x}+(\sin x)^{x}$ $\Rightarrow y=a+b$ where $a=x^{\sin x} ; b=(\sin x)^{x}$ $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{da}}{\mathrm{dx}}+\frac{\mathrm{db}}{\mathrm{dx}}$ $\left\{\right.$ Using chain rule, $\frac{\mathrm{d}(\mathrm{u}+\mathrm{a})}{\mathrm{dx}}=\frac{\mathrm{du}}{\mathrm{dx}}+\frac{\mathrm{da}}{\mathrm{dx}}$ where a and $\mathrm{u}$ are any variables $\}$ $a=x^{\sin x}$ T...
Read More →Figure shows the arrangment of two coils
Question: Figure shows the arrangment of two coils wound on a non-conducting cylindrical rod. The plugh of the key is then inserted and later removed. (a)Deflection in the galvanometer remains zero throughout (b)There is momentary deflection in the galvanometer that dies out shortly and deflections in both the cases are in the same direction (c)There is momentary deflection in the galvanometer that dies out shortly and there is no effect when the key is removed (d)There are momentary deflections...
Read More →Mohd. Aslam purchased a house from Avas Vikas Parishad on credit.
Question: Mohd. Aslam purchased a house from Avas Vikas Parishad on credit. If the cost of the house is Rs 125000 and the Parishad charges interest at 12% per annum compounded half-yearly, find the interest paid by Aslam after a year and a half. Solution: Let the principal amount be $P=$ Rs. 125000 . Annual rate of interest, $R=12 \%$ Rate of interest for a half year $=6 \%$ Time, $n=1 \frac{1}{2}$ years $=3$ half years Then the amount with the compound interest is given by A $=\mathrm{P} \times...
Read More →Commercial electric motors do not use
Question: Commercial electric motors do not use (a)an electromagnet to rotate the armature (b)effectively large number of turns of conducting wire in the current carrying coil (c)a permanet magnet to rotate the armature id a soft iron on which the coil is wound. Solution: (c). Explanation :In commercial motor, armature rotates in the mag-netic field produced by an electromagnet. The strength of such magnetic field can be increased to the desired value. However, a permanent magnet provides a fixe...
Read More →A uniform magnetic field exists in
Question: A uniform magnetic field exists in the plane of paper pointing from left to right as shown in figure. In the field, an electron and a proton move as shown. The electron and proton experience (a)forces, both pointing into the plane of paper (b)forces, both pointing out of the plane of paper (c)forces, pointing into the plane of paper and out of the plane of paper respectively. (d)forces, pointing opposite and along the direction of the uniform magnetic field respectively. Solution: (a)....
Read More →Swati borrowed Rs 40960 from a bank to buy a piece of land.
Question: Swati borrowed Rs 40960 from a bank to buy a piece of land. If the bank charges $12 \frac{1}{2} \%$ per annum, compounded half-yearly, what amount will she have to pay after $1 \frac{1}{2}$ years? Also, find the interest paid by her. Solution: Principal, $P=$ Rs. 40960 Annual rate of interest, $R=\frac{25}{2} \%$ Rate of interest for half year $=\frac{25}{4} \%$ Time, $n=1 \frac{1}{2}$ years $=3$ half years Then the amount with the compound interest is given by $A=P \times\left(1+\frac...
Read More →Find the amount and the compound interest on Rs 160000 for 2 years
Question: Find the amount and the compound interest on Rs 160000 for 2 years at 10% per annum, compounded half-yearly. Solution: Principal, $P=$ Rs. 160000 Annual rate of interest, $R=10 \%$ Rate of interest for a half year $=\frac{10}{2} \%=5 \%$ Time, $n=2$ years $=4$ half years Then the amount with the compound interest is given by $A=P \times\left(1+\frac{R}{100}\right)^{n}$ $=160000 \times\left(1+\frac{5}{100}\right)^{4}$ $=160000 \times\left(\frac{100+5}{100}\right)^{4}$ $=160000 \times\le...
Read More →In a long straight solenoid,
Question: In a long straight solenoid, N-and S-poles are created at the two ends of the solenoid. Which of the following statements is incorrect ? (a)The field lines inside the solenoid are in the form of straight lines indicating that magnetic field is same at ail points inside the solenoid. (b)The pattern of the magnetic field associated with the solenoid is different from the pattern of the magnetic field around a bar magnet. (c)N-and S-poles exchange positions when the direction of the curre...
Read More →Find the amount and the compound interest on Rs 12800 for 1 year
Question: Find the amount and the compound interest on Rs 12800 for 1 year at $7 \frac{1}{2} \%$ per annum, compounded semi-annually. Solution: Principal, $P=$ Rs. 12800 Annual rate of interest, $R=\frac{15}{2} \%$ Rate of interest for a half year $=\frac{1}{2}\left(\frac{15}{2}\right) \%=\frac{15}{4} \%$ Time, $n=1$ year $=2$ half years Then the amount with the compound interest is given by $A=P \times\left(1+\frac{R}{100}\right)^{n}$ $=12800 \times\left(1+\frac{\frac{15}{4}}{100}\right)^{2}$ $...
Read More →Using the principle of mathematical induction, prove each of the following
Question: Using the principle of mathematical induction, prove each of the following for all n ϵ N: $\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+\ldots . .+\frac{1}{(3 n-2)(3 n+1)}=\frac{n}{(3 n+1)}$ Solution: To Prove: $\frac{1}{1 \times 4}+\frac{1}{(4 \times 7)}+\ldots \ldots+\frac{1}{(3 n-2) \times(3 n+1)}=\frac{n}{(3 n+1)}$ Let us prove this question by principle of mathematical induction (PMI) Let $P(n): \frac{1}{1 \times 4}+\frac{1}{(4 \times 7)}+\ldots \ldots+\frac{1}{(3 n-2) \times(3 n+1)...
Read More →A circular loop placed in a plane perpendicular
Question: A circular loop placed in a plane perpendicular to the plane of paper carries a current when the key is ON. The current is seen from points A and B (in the plane of the paper and on the axis of the coil) is anticlockwise and clockwise respectively. The magnetic field lines point from B to A. The N-pole of the resultant magnet is on the face close to (a)A (b)B (c)A if current is small, and B if current is large. (d)B if the current is small, and A if current is large. Solution: (a). Exp...
Read More →Find the amount and the compound interest on Rs 31250 for
Question: Find the amount and the compound interest on Rs 31250 for $1 \frac{1}{2}$ years at $8 \%$ per annum, compounded half-yearly. Solution: Principal, $P=$ Rs. 31250 Annual rate of interest, $R=8 \%$ Rate of interest for a half year $=\frac{1}{2} \times 8 \%=4 \%$ Time, $n=1 \frac{1}{2}$ years $=3$ half years Then the amount with the compound interest is given by A $=P \times\left(1+\frac{R}{100}\right)^{n}$ $=31250 \times\left(1+\frac{4}{100}\right)^{3}$ $=31250 \times\left(1+\frac{1}{25}\...
Read More →If the key in the arrangement shown
Question: If the key in the arrangement shown in figure is taken out (the circuit is made open) and magnetic field lines are drawn over the horizontal plane ABCD, the lines are (a)concentric circles (b)elliptical in shape (c)straight lines parallel to each other (d)concentric circles near the point O but of elliptical shapes as we go away from it Solution: Explanation :When no current flows through the wire, magnetic field lines over the plane ABCD will represent magnetic field of the earth. The...
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