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Recent questions and answers in Real Numbers

Questions >> Class 10 >> CBSE X Math >> Real Numbers

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 $\large\frac{2hsec \alpha}{tan \beta -tan \alpha}.$

answered Jan 15, 2019 by tkumawat035

1 answer

In the Figure $PQRS$ is a square laws with side $PQ= 42 meters$. Two circular flower beds are there on the sides $PS$ and $QR$ with center at $Q,$ the intersection of its diagonals. Find the total area of the two flower bed (shaded parts)

answered Jun 4, 2018 by phool0120

1 answer

Find the value of k so that the area of the triangle with verices $(1,-1) , (-4,2k)$ and $(-k,-5)$ is 24 sq.units

answered Nov 26, 2017 by praveendaral123

1 answer

A card is drawn at random from a well -shuffled deck of playing cards . Find the probability that the card drawn is (i) A card of spade or an ace (ii) a black king (iii) neither a jack nor a king (iv) either a king or a queen

answered Jan 30, 2017 by thounaxorvillexingha

1 answer

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

answered Aug 25, 2016 by kvcr37776

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]

answered Aug 25, 2016 by kvcr37776

2 answers

Find the value of k for which the points $A(k+1,2k) ,B(3k,2k+3) $ and $ c(5k-1,5k)$ are collinear .

answered Mar 18, 2015 by meena.p

1 answer

A truck covers a distance of $150 km$ at a certain average speed and then covers another 200 km at an average speed which is $20\;km/hr$ more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck?

answered Mar 18, 2015 by meena.p

1 answer

An arithmetic progression $5, 12,19....., $ has I st terms. Find its last term hence find the sum of its last 15 terms.

answered Mar 18, 2015 by meena.p

1 answer

A bag contains white, black and red balls only. A ball is drawn at random from the bag if the probability of getting a white balls is $\large\frac{3}{10} $ and that of black is $\large\frac{2}{5}$, then find the probability of getting a red balls. If the bag contains 20 black balls, then find the total number of balls in the bag.

answered Mar 18, 2015 by meena.p

1 answer

Find the coordinates of a point P on the line segment joining $A(1,2) $ and $B(6,7)$ Such that $AP= \large \frac{2}{5} $$AB$

answered Mar 18, 2015 by meena.p

1 answer

The 13th term of an A.P is four times its 3rd term . If its fifth term is 16, then find the sum of its first ten terms

answered Mar 18, 2015 by meena.p

1 answer

Solve the following quadratic equation for $x_i.\qquad x^2-2ax-(4b^2-a^2)=0$

answered Mar 18, 2015 by meena.p

1 answer

Find the relation between x and y if the points $A(x,y) ,B(-5,7)$ and $C(-4,5)$ are collinear .

answered Mar 18, 2015 by meena.p

1 answer

Find the value of 'k' so that the area of the triangle with vertices $(k+1,1)(4,-3)$ and $(7,-k)$ is $6 \;sq.units$

answered Mar 17, 2015 by meena.p

1 answer

If the 20th term of an AP is five times its third term . If its 10th term is 41, then find the sum of its first fifteen term

answered Mar 17, 2015 by meena.p

1 answer

Solve for $x : 2x^2+6 \sqrt 3 x -60 =0$

answered Mar 17, 2015 by meena.p

1 answer

All vertices of a rhombus be on a circle. Find the area of the rhombus , if the area of the circle is $1256\;cm^2$ $(\pi= 3.14)$

answered Mar 17, 2015 by meena.p

1 answer

If $A(4,3) ,B(-1,y) $ and $C(3,4) $ are the vertices of a right triangle $ABC$, right angled at A, then find the value of Y.

answered Mar 17, 2015 by meena.p

1 answer

From each end of solid metal was scooped out in hemispherical form of same diameter . The height of the cylinder is 10 cm and its base is of radius $4.2 \;cm$ . The rest of the cylinder is melted and covered into a cylindrical wire of $1.4\;cm$ thickness . Find the length of the wire $(\pi=\large\frac{22}{7})$

asked Mar 17, 2015 by meena.p

0 answers

At a Point A, 20 metres above the level of water in a lake , the angle of elevation of a cloud is $30^{\circ}$ . The angle of depression of the reflection of the cloud in the lake, at A ia $60^{\circ}$ . Find the distance of the cloud from A.

answered Mar 17, 2015 by meena.p

1 answer

Construct a $\Delta ABC$ in which $AB= 6\;cm, \angle A=30^{\circ}$ and $ \angle B=60^{\circ}$ construct another $ \Delta AB'C'$ similar to $\Delta ABC$ with base $AB'= 8 \;cm$

asked Mar 17, 2015 by meena.p

0 answers

Prove that the tangent drawn at the mid point of an arc of a circle is parallel to the chord joining the end points of the arc.

answered Mar 17, 2015 by meena.p

1 answer

Prove that the length of the tangents drawn from an external point to a circle are equal

answered Mar 17, 2015 by meena.p

1 answer

A train travels at a certain average speed for a distance of 54 km and then travels a distance of $63\;km$ at an average speed of $6\;km/h$ more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

answered Mar 17, 2015 by meena.p

1 answer

Find the 60th term of the AP $8,10,12....,$ if it has a total of 60 terms and hence find the sum of its last 10 terms .

answered Mar 17, 2015 by meena.p

1 answer

Find the 60th term of the AP $8,10,12....,$ if it has a total of 60 terms and hence find the sum of its last 10 terms .

asked Mar 17, 2015 by meena.p

0 answers

The diagonal of a rectangular field is 16 meters more than the shorter side. If the longer side is 14 meters more than the shorter side, then find the lengths of the sies of the field.

answered Mar 17, 2015 by meena.p

1 answer

The diagonal of a rectangular field is 16 meters more than the shorter side. If the longer side is 14 meters more than the shorter side, then find the lengths of the sies of the field.

asked Mar 17, 2015 by meena.p

0 answers

$504$ cones , each of diameter $3.5\;cm$ and height 3 cm, are melted and recast into a metallic sphere. find the diameter of the sphere and hence find its surface [use $\pi =\large\frac{22}{7}$ ]

answered Mar 17, 2015 by meena.p

1 answer

A cubical block of side 10 cm is surmounted by a hemisphere . What is the largest diameter that the hemisphere can have ? Find the cost of painting the total surface area of the solid so formed, at the rate of $5$ per $100 \;sq\;cm$ [Use $\pi = 3.14$]

answered Mar 17, 2015 by meena.p

1 answer

A hemispherical bowl of internal diameter $36\;cm$ contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm Find the height of the each bottle. If $10 \%$ liquid is wasted in this transfer .

answered Mar 17, 2015 by meena.p

1 answer

If the coordinates of points A and B are $(-2,-2)$ and $(2,-4)$respectively, find the coordinates of P such that $AP=\large\frac{3}{7} $$AB$, where P lies on the line segment AB.

answered Mar 17, 2015 by meena.p

1 answer

The angle of elevation of an aeroplane from a point A on the ground is $60^{\circ}$. After a flight of 15 seconds the angle of elevation changes to $30^{\circ}$. If the aeroplane is flying at a constant height of $1500 \sqrt 3\;m$ find the speed of the palne in km/hr

answered Mar 17, 2015 by meena.p

1 answer

Solve for x$ \sqrt 3 x^2 -2 \sqrt 2 x -2 \sqrt 3 =0$

answered Mar 17, 2015 by meena.p

1 answer

The 14th term of an AP is twice its 8th term . If its 6th term is $-8$ , then find the sum of its first 20 terms

answered Mar 17, 2015 by meena.p

1 answer

Find the ralation between x and y if the points $A(x,y), B(-5,7)$ and $C(-4,5)$ are collinear.

answered Mar 17, 2015 by meena.p

1 answer

The points $A(4,7),B(p,3)$ and $C(7,3)$ are the vertices of a right triangle , right angled at B. Find the value of P.

answered Mar 17, 2015 by meena.p

1 answer

In an AP, if $S_5+S_7=167$ and $S_{10} =235$ , then find the AP , where $S_n$ denotes the sum of its first n terms.

answered Mar 17, 2015 by meena.p

1 answer

Solve the following quadratic equation for x: $4x^2+4bx-(a^2-b^2) =0$

answered Mar 17, 2015 by meena.p

1 answer

A triangle ABC is drawn to circumscribe a circle of radius 3 cm. such that the segments $BD$ and $DC$ are respectively of length 6 cm and 9 cm. If the are $\Delta ABC$ is $54\;cm^2$, then find the lengths of sides $AB$ and $AC $

answered Mar 17, 2015 by meena.p

1 answer

Two tangents $RQ$ and $RP$ are drawn from an external point R to the circle with center $Q$. If $ \angle PRQ=120^{\circ}$ then prove that $OR=PR=RQ$

answered Mar 17, 2015 by meena.p

1 answer

In figure , $PQ$ is a chord of a circle with centre $O$ and $PT$ is a tangent . If $\angle QPT =60^{\circ}$, find $\angle PRQ$

answered Mar 17, 2015 by meena.p

1 answer

Two different dice are tossed together , Find the probability that the product of the two numbers on the top of the dice is 6.

answered Mar 17, 2015 by meena.p

1 answer

A tower AB is 20 m high and BC , its shadow on the ground is $ 20 \sqrt 3 \;m$ long. Find the Sun's altitude.

answered Mar 17, 2015 by meena.p

1 answer

If the quadratic $px^2- 2 \sqrt 5 px +15 =0$ has two equal roots, then find the value of p.

answered Mar 17, 2015 by meena.p

1 answer

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.

answered 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

answered 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 $\Delta ABC.$

answered 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

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