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The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3 If each of them manages to save Rs.2000 per month, find their monthly income.

A chord 10cm long is drawn in a circle whose radius is 5sqrt2 cm. Find the area of both the segments.

Determine a point which divides a line segment 6 cm long externally in the ratio 3:5.

The points P (4, 1) and Q (-2, 4) are reflected in line y = 3. Find the co-ordinates of P', the image of P and Q', the image of Q.

The mean of x_(1) andx_2is M_1 and that of x_1, x_2, x_3 ... x_4is M, then the mean of ax_1, ax_(2) , x_(3)//a is

A fast train takes 3 hours less than a slow train for ajourney of 600 km . If the speed of the slow train is 10 km/hr less than the fast train, find their speeds.

Name a single transformation that maps P' to P''.

List all the subsets of the following sets. (i) B={p,q} (ii) C={x,y,z} (iii) D={a,b,c,d} (iv) E=1,4,9,16} (v) F={10,100,1000}

Statements: 1. All flowers are trees. 2. No fruit is tree.Conclusions: 1. No fruit is flower. 2. Some trees are flowers.

Find acuteangles A and B when2 sin(A+ B)= sqrt3 and 2 cos (A-B)= sqrt3

A train travels a distance of 480 km at a uniform speed. If the speed had been 8km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

Smt. Desai sold shares of face value 100 when the market value was 50 and received 4988.20. She paid brokerage 0.2% and GST on brokerage 18%, then hhow many shares did she sell?

Two angles forming a linear pair of angles are equal. Find the measure of each angle.

When the polynomial 2x^(3)-kx^(2)+(5k-3)x-8 is divided by x-2 the remainder is 14. Find the value of 'k'.

If sec theta+tantheta=p,then find the value of sectheta-tantheta

The point on the x-axis which is equidistant from the points (5, 4) and (-2, 3) is

Two dice are thrown simultaneously. Find the probability that : both the dice show the same number.

Find the median for the following distribution :

Find the mode of following distribution. :

If ABCD is a parallelogram and A(-2,4), B-= (-3,5) and D(3, -2) Find the co-ordinates of C

Evaluate : (3 cos 55^(@))/(7 sin 35^(@)) - (4 cos 70^(@) cosec 20^(@))/(7 (tan 5^(@) tan 25^(@) tan 45^(@) tan 65^(@) tan 85^(@))) .

If2 x - 3y = 7 and (a + b )x - (a + b - 3) y = 4a + bhave an infinite number of solutions then

Smt. Desai shares of face value 100 when the market value was 60 and received 5978.76. She paid brokerage 0.3% and GST on brokerage 18%, then how shares did she sell?

What is the rank of P from the bottom in a class of 30 students? I. M is third from the top and there are five students between M and P. II. The rank of K is fourth from the bottom and there are 17 students between K and P.

Find the value of y for which the distance between the points P(2, -3) and Q(10, y) is 10 units.

The rain water from a 22 m xx 20 m roof drains into a cylindrical vessel of diameter 2 m and height 3.5m. If the the rain water the rainfall in centifall in

A survery was conducted by a group of student as a part of their envionment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house. Which methode did you use for finding the mean, and why ?

Smt. Mita Agrawal invested 10,200 when MV of the share is 100. She sold 60 shares when the MV was 125 and sold remaining share when the MV was 90. She paid 0.1% brokerage for each tranding. Find the whether she made profit or loss? and how much?

A survey regarding the heights (in cm) of 50 girls of class X of a school was conducted and the following data was obtained. Find the mean, median and mode.

Fill in the blanks : {:("Point","Transformation ","Image"),(.........., "Reflection in y - axis",(0,6)):}

How many triangles are there in the following figure?

How many triangles are there in the following figure ?

Find the value of k for which x=2 is a root (solution) of equation kx^(2)+2x-3=0.

Find perimeter of Rhombus with side=14cm.

Find the distance between the pair of points (a, b) and (-a, -b)

If eye is called hand, hand is called mouth, mouth is called ear, ear is called nose and nose is called tongue, with which of the following would a person hear?

Find the co-ordinates of the points fo trisection of the line joining the points (3,-2) and (-3, -4).

Statements: 1. Some books are pens. 2. Some pens are erasers.Conclusions: 1. All books are erasers. 2. Some erasers are books.

The polynomials 3x^(3)-ax^(2)+5x-13 and (a+1)x^(2)-7x+5 leaves the same remainder when divided by x-3. Find the value of 'a'.

PointsA (-1,y)and B (5, 7)lieon a circle with centreO (2, - 3) . Find the values of y . Hencefind the radius of the circle.

Check whether , -150 is a term fo the AP: 11,8,5,2,…..

A cone and a hemisphere have the same base and the same height. Find the ratio between their volumes.

A man travels 370km partky by train and partly by car. If he covers 250 km by train and the rest by car, it takes him 4 hours, but if he travels 130 km by train and the rest by car, it takes 18 minutes more. Find the speed of the train and that of the car.

A tent is in the form of a cylinder of diameter 4.2 m and height 8 m surmounted by a conc of equal base and heitght 6m, find the volume of air in the tent.

A card is drawn from a pack of 100 cards numbered 1 to 100. Find the probability of drawing a number which is a perfect square.

Find which of the following is a G.P. : 4,8,16 , . . . . . . . . . . . . .

Find the coordinates of centroid of the triangle with vertices: (1, -1), (0, 6) and (-3, 0)

A sum of 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is 20 less than its preceding prize, find the value of each of the prizes