Recent questions tagged mock-test-series-2015

If $A(-2,-1), B(a,0), C(4,b)$ and $D(91,2)$ are the vertices of a parallelogram, find the values of a and b.

asked Feb 19, 2015 by meena.p

1 answer

Find the coordinates of the circumcentre of the triangle whose vertices are $(8,6),(8.2)$ and $(2,-2)$. Also find its circum-radius

asked Feb 19, 2015 by meena.p

1 answer

$ABC$ is a right angled triangle , right angled at A. Find the area of the shaded region if $AB = 6cm, BC = 10cm$ and $I$ is the centre of the incircle of $\Delta ABC.$

asked Feb 19, 2015 by meena.p

1 answer

Sonia buys a shop for $Rs. 1,20,000$. She pays half the amount in cash and agrees to pay the balance in $12$ annual installments of $Rs. 5000$ each. If the rate of interest is $12 \%$ and she pays with the installment due on the unpaid amount, find the total cost of the shop.

asked Feb 19, 2015 by meena.p

0 answers

Ramesh has got $24000/$ - as Puja Bonus. He donated ` 5000/'- to temple. He gave $`12000/-$ to his wife, ` $2000/-$ to his servant and gave rest of the amount to his daughter. a. What is the probability of wife's share? b. Calculate the probability of servant's share? c. What is the probability of daughter's share? d. Which value are depicted by Ramesh from the way the amount is distributed?

asked Feb 19, 2015 by meena.p

1 answer

A fast train takes 3 hrs less than the a slow train for a journey of $600\;km$. If the speed of the slow train is 10km/hr less than that of the fast train, find the speeds of the two trains

asked Feb 19, 2015 by meena.p

1 answer

If two tangents are drawn to a circle from an external point, then prove that, a)They subtend equal angles at the centre b) They are equally inclined to the segment, joining the centre to that point.

asked Feb 19, 2015 by meena.p

0 answers

Two circles with centres A and B of radii $3\;cm$ and $4\;cm$ respectively intersect at two points C and D such that AC and BC are tangents to the two circles. Find the length of the common chord

asked Feb 19, 2015 by meena.p

1 answer

An aeroplane flying horizontally $1\;km$ above the ground is observed at an angle of elevation of $60^{\circ}$. After 10 seconds, its elevation is observed to be $30^{\circ}$. Find the speed of the aeroplane in km/hr

asked Feb 19, 2015 by meena.p

1 answer

If the angle of elevation of a cloud from a point h meteres above a lake is a and the angle of depression of its reflection in the lake be b, prove that the distance of the cloud from the point of observation is $\large\frac{2hsec \alpha}{tan \beta -tan \alpha}.$

asked Feb 19, 2015 by meena.p

1 answer

A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface of the remainer is $\large\frac{8}{9}$ of the curved surface of the whole cone, find the ratio of the line-segment into which the cone’s altitude is divided by the plane.

asked Feb 19, 2015 by meena.p

1 answer

Water flows at the rate of $10\;m$ per minute through a cylindrical pipe having its diameter as $5\;mm$. How much time will it take to fill a conical vessel whose diameter of base is $40\;cm$ and depth $24\;cm$?

asked Feb 19, 2015 by meena.p

1 answer

Draw a circle of radius $6\;cm$. From a point $10\;cm$ away from its centre, construct the pair of tangents to the circle and measure their lengths.

asked Feb 19, 2015 by meena.p

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How many numbers of two digits are divisible by 7?

asked Feb 19, 2015 by meena.p

1 answer

$O$ is the centre of the circle and $BCD$ is tangent to it at $C.$ Prove that $\angle BAC + \angle AC = 90^{\circ}$

asked Feb 19, 2015 by meena.p

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Find the value of ‘k’, if the points $A(8,1), B(3,-4)$ and $C(2,k)$ are collinear

asked Feb 19, 2015 by meena.p

1 answer

How many terms of the series $54,51,48…$ is taken so that their sum is $513?$ Explain the double answer.

asked Feb 19, 2015 by meena.p

1 answer

$O$ is the centre of the circle and $BCD$ is tangent to it at $C$. Prove that $\angle BAC + \angle ACD = 90^{\circ}$

asked Feb 19, 2015 by meena.p

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Solve by the method of completing the squares: $3x^2 + 2x-1=0$

asked Feb 19, 2015 by meena.p

1 answer

The sum of three numbers in an $A.P.$ is $-3,$ and their product is $8$. Find the numbers [ ans: -4,-1,2 or 2,-1,-4]

asked Feb 19, 2015 by meena.p

2 answers

From a thin metallic piece, in the shape of a trapezium $ABCD,$ in which $AB$ is parallel to $CD$ and $\angle BCD = 90^{\circ}$, a quarter circle $BEFC$ is removed. Given $AB = BC = 3.5\;cm$ and $DE = 2cm,$ calculate the area of the remaining piece of the metal sheet.

asked Feb 19, 2015 by meena.p

1 answer

The cost of painting the total outside surface of a closed cylindrical oil tank at $50\;paise$ per sqdm is $Rs. 275$. The height of the tank is $5$ times the radius of the base of the tank. Find its volume .

asked Feb 19, 2015 by meena.p

1 answer

How many lead shots each having diameter $3\;cm$ can be made from a cuboidal lead solid of dimensions $9cm \times 11cm \times 12cm$

asked Feb 19, 2015 by meena.p

1 answer

IF $\Delta ABC$ is isosceles with $AB =AC$ and centre $(O,r)$ is the incircle of the $∆ABC$ touching $BC$ at $L$. Prove that $L$ bisects $BC.$

asked Feb 19, 2015 by meena.p

0 answers

A circus tent is cylindrical upto a height of $3m$ and conical above it. I the diameter of the base is $105\;m$ and the slant height of the conical part is $53\;m$, find the total canvas used in making the tent.

asked Feb 19, 2015 by meena.p

1 answer

In a musical chair game, the person playing the music has been advised to stop playing the music at any time within $2$ minutes after she startys playing. What is the probability that the music will stop within half a minute after starting?

asked Feb 19, 2015 by meena.p

1 answer

Prove that the points $(a,b+c),(b,c+a),(c,a+b)$ are collinear.

asked Feb 18, 2015 by meena.p

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Determine the ratio of the volume of a cube to that of a sphere which will exactly fir inside the cube.

asked Feb 18, 2015 by meena.p

1 answer

If a circle is inscribed in a parallelogram, how will the parallelogram change?

asked Feb 18, 2015 by meena.p

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What is the value of ‘t’, if the points $(t,2t),(-2,6)$ and $(3,1)$ are collinear?

asked Feb 18, 2015 by meena.p

1 answer

What is the diameter of the semicircular protractor whose perimeter is $36\;cm$?

asked Feb 18, 2015 by meena.p

1 answer

What is the maximum volume of a cone that can be carved out of a solid hemisphere of radius ‘r’ ?

asked Feb 18, 2015 by meena.p

1 answer

From the letter “Mathematics” a letter is selected. What is the probability that the selected letter is a vowel?

asked Feb 18, 2015 by meena.p

1 answer

What is the angle of elevation of the sun when the length of the shadow of a vertical pole is equal to the height?

asked Feb 18, 2015 by meena.p

1 answer

Find the value of $a_{30} – a_{10}$ for the A.P. $4,9,14,19… $

asked Feb 18, 2015 by meena.p

1 answer

For what value of $p,$ does the equation has real roots, $2px^2 – 8x +p=0$

asked Feb 18, 2015 by meena.p

1 answer

a)A capacitor is used in the primary circuit of induction coil why? b)A power transmission line feeds input power at $2300\;V$ to a step down transformer with its primary windings having $4000$ turns. What should be the number of turns in the secondary in order to get the output power at $230\;V$? c)What is the peak value at $22V\; AC$?

asked Feb 11, 2015 by meena.p

0 answers

Derive an expression for the impedance of a series L-C-R circuit connected to an AC supply of variable frequency. Plot a graph showing the variation of current with the frequency of the applied voltage. Explain briefly how the phenomenon of resonance in the circuit can be used in the tuning mechanism of a radio or a TV set?

asked Feb 11, 2015 by meena.p

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An AC voltage of peak $20\;V$ is connected in series with a silicon diode and a load resistance of $500 \Omega$. The forward resistance of the diode is $10 \Omega$ and the barrier voltage is $0.7\;V$. Find the peak current through diode and the peak voltage across the load. What will happen to these values if the diode is assumed to be ideal?

asked Feb 11, 2015 by meena.p

1 answer

Why is Zener diode considered as a special purpose semiconductor diode? Draw the I-V characteristics of Zener diode and explain briefly how reverse current suddenly increase at the breakdown voltage? Describe briefly with the help of a circuit diagram how a Zener works to obtain a constant DC voltage from the unregulated DC output of a rectifier?

asked Feb 11, 2015 by meena.p

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a)Define the term decay constant and half life of a radio active sample. Derive the relation connecting the two. b)How many disintegration per second will occur in one gram of $_{92}U^{238},$ if its half life against alpha decay is $1.42 \times 10^{17}\;s$?

asked Feb 11, 2015 by meena.p

0 answers

Using Bohr’s postulates, derive the expression for the frequency of radiation emitted when electron in hydrogen atom undergoes transition from higher energy state quantum number $(ni)$ to the lower state $(nf)$. When electron in hydrogen atom jumps from energy state $ni = 4$ to $nf = 3,2,1,$ identify the spectral series to which the emission lines belong.

asked Feb 11, 2015 by meena.p

0 answers

Shwetha on entering her apartment switched on the tubelight, but only found it not to work. She called on an electrician. He inspected it and suggested to change the choke. On replacing it, she found it to work properly. 1. What is the function of the choke coil? 2. Identify the value exhibited here. 3. Why is a capacitor used in the primary circuit of an induction coil?

asked Feb 11, 2015 by meena.p

0 answers

A) An infinite line charge produces a field of $9 \times 10^4 N/C$ at a distance of $2\;cm$. Calculate the linear charge density b)An arbitrary surface encloses a dipole. What is the electric flux through this surface?

asked Feb 11, 2015 by meena.p

0 answers

Give reasons, (1).For ground wave transmission, size of the antenna $(l) $ should be comparable to wavelength of signal i.e; $l = \large\frac{\lambda}{4}$ (2). Audio signals, converted into an e.. wave, are not directly transmitted as such. 3. The amplitude of modulating signal is kept less than the amplitude of carrier wave.

asked Feb 11, 2015 by meena.p

0 answers

A resistor of resistance $4000 \Omega$ and a capacitor of resistance $200 \Omega$ are connected in series to a $220\;V\; 50\; Hz$ a.c. source. If the currents in the circuit is $0.49$ ampere, find the 1. Voltage across the resistor and capacitor. 2. Value of inductance required so that voltage and current are in phase.

asked Feb 11, 2015 by meena.p

0 answers

In a metre bridge experiment a student observed a balance point at the point J, where AJ = l. Draw the equivalent Wheatstone Bridge circuit diagram for this setup The values of R and X are both doubles and then interchanged. What would be the new position of the balance point? If in this set up, the galvanometer and battery are interchanged at the balance position, how will the balance point get affected?

asked Feb 11, 2015 by meena.p

1 answer

1.Name the type of biasing of a p-n type junction diode so that the junction offers a very high resistance. 2.Name two factors on which the electrical conductivity of a pure semiconductor at a given temperature depends. 3. Identify the logic gates marked x and y in the following figure. Write down the output as when A = 1 , B = 1 and A = 0 and B = 0

asked Feb 11, 2015 by meena.p

0 answers

A) Why photoelectric effect cannot be explained on the basis of wave nature of light? Give reasons. b) Write the basic features of photon picture of electromagnetic radiation on which Einsteins’s photoelectric equation is based.

asked Feb 10, 2015 by meena.p

1 answer

In Young’s double slit experiment, the two slits $0.15\;m$ apart are illuminated by monochromatic light of wavelength 450nm.$ The screen is $1.0\;m$ away from the slits. 1. Find the distance of the second a) bright fringe b) dark fringe from the central maximum. 2. How will the fringe pattern change, if the screen is moved away from the slits?

asked Feb 10, 2015 by meena.p

1 answer

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