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Find the mean from the following distribution table using short cut method :

Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob's age was seven times that of his son. What are their present ages?

Is it possible to design a rectangular park of perimeter 80 m and area 400 m^(2)? If so, find its length and breadth.

Find x and y if [{:(,3,-2),(,-1,4):}] [{:(,2x),(,1):}] +2 [{:(,-4),(,5):}] =4[{:(,2),(,y):}]

Find the mean and median of the following distribution :

If P=[{:(,1,2),(,2,-1):}] and Q=[{:(,1,0),(,2,1):}] then compute : (i) P^2-Q^2 (ii) (P+Q) (P-Q) Is (P+Q) (P-Q) =P^2-Q^2 true for matrix algebra?

A person savedRs. 500 in the first month and increased his saving by Rs. 50 every month. What is his savings at the end of 5 years?

Determine whether the following points are collinear or not: A(-4,4),K(-2,5/2),N(4,-2)

From a point P outside a circle, with centre O tangents PA and PB are drawn, prove that : (i) angleAOP=angleBOP (ii) OP is the perpendicular bisector of chord AB.

What number should be added to the polynomial x^2 + 7x - 35 so that 3 is the zero of the polynomial?

Find the 100th term of the sequence: sqrt3, 2sqrt3, 3sqrt3,…..

Three positive numbers form a GP. If the middle number is increased by 8, the three numbers form an AP. If the last number is also increased by 64 along with the previous increase in the middle number, the resulting numbers form a GP again.Then :-

A(-3, 0), B(10, -2) and C(12, 3) are the vertices of triangle ABC. Find the equation of a altitude through A.

A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 80 m, calculate the total area of canvas required. Also, find the total cost of canvas used at Rs 15 if the width is 1.5 m.

Thirty women were examined in a hospital by a doctor and their heart beats per minute were recorded and summarised as shown . Find the mean heart beats per minute for these women, choosing a suitable method.

One root of the equation x^2 +ax +7=0 is 1.Find the value of a.

Write the additive inverse of matrices A,B, and C where A=[6,-5], B=[{:(,-2,0),(,4,-1):}] and C=[{:(,-7),(,4):}]

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are lengths 6 cm and 8 cm respectively. Find the sides AB and AC.

trianglePQR~trianglePMN."In" trianglePQR,PQ= 4 cm , QR = 5 cm and PR = 6 cm. Construct trianglePQR and trianglePMN such that (PR)/(PN)=5/3

Duringthe medical check up of 35 students of a class, their weights were recorded as follows : Draw a less then type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.

If A and B are two sets such that A subset B then what is AcupB?

How many three digit numbers are divisible by 7 ?

Fill in the blanks in the following table, given that 'a' is the first term, d the common difference and a_n the n^(th) term of the A.P :

Statements: 1. No man is a donkey. 2. Rahul is a man. Conclusions: 1. Rahul is not a donkey. 2. All men are not Rahul.

If the pth term of an A.P. is (2p+3), find the A.P.

If in a certain language MYSTIFY is coded as NZTUJG, how is NEMESIS coded in that language?

A chemist has two solutions of hydrochloric acid in stock. One is 50% solution and the other is 80% solution. How much of each should be used to obtain 100ml of a 68% solution.

Solve each of the following equatins : 2^(2x)-3xx2^(x+2)+32=0

A hollow metal sphere of internal and external radii 2 cm and 4 cm respectively is melted into a solid cone of base radius 4 cm. Find the height and slant height of the cone.

Find x and y from the following equations: (i) [{:(,5,2),(,-1,y-1):}]-[{:(,1,x-1),(,2,-3):}] =[{:(,4,7),(,-3,2):}] (ii) [-8,x]+[y-2]=[-3,2]

A round table top has six equal designs as shown in the figure. If the radius of the table top is 14cm, find the cost of making the designs with paint at the rate of rs 5 per cm^(2) ( use sqrt(3)=1.732)

If the sum of n terms of A.P. is (1)/(2) (3n^(2) + 7n) , find its n^(th) term and write its 25th term.

Two types of boxes A, B are to be placed in a truck having capacity of 10 tone. When 150 boxes of type.A and 100 boxes of type B are loaded in the truck, it weighes 10 tone. But truck, it can still accommodate 40 boxes ot type B, so that it is fully loaded. Find the weight of each type of box.

If a -= b (mod m), then which of the following is not always true ?

How many zeros does q(x) have ?

Find a quadratic polynomial each with the given numbers as the sum and product of its zeros respectively. (i) -1/4, 1/4, (ii) sqrt(2), 1/3

Three identical coins are tossed together. What is the probability of obtaining : all heads ?

Divide 3x^2 - x^3 - 3x + 5 by x - 1 - x^2.

If A=[{:(,8,6),(,-2,4):}] and B=[{:(,-3,5),(,1,0):}] then solve for 2 xx 2 matrix X such that (i) A+X=B (ii) X-B=A

A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears a prime-number less than 23, is:

Ramu marked a dot in first square, 2 dots in second square, 3 dots in the third square and so on. Then the total number of squares required to mark a total of 55 dots is equal to:

The venn diagram representing State, Country and Blanket is:

In the given figure AB=BC,angleABC=68^(@) and DB are the tangents to the circle with centre O.Calculate the measure of: (a) angleACB (b)angleAOB (C )angleADB

Which term of the A.P. 3, 15, 27, 39,...........will be 132 more than its 54th term?

If the median of the distribution given below is 28.5, find the values of x and y.

Express each of the following numbers as a product of its prime factors. 3825

Find the next three terms of the series : (2)/(27),(2)/(9),(2)/(3), . . . . . . . . . . .