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If for two matrices M and N, N =[(3,2),(2,-1)]and product MxxN = [-1 4] , find matrix M.

ABC and BDE are two equilateral trainales, such that D is the mid-point of BC. Ratio of the area of triangles ABC and BDE is :

DeltaABC~DeltaPQR, AB=8 , BC=10, AC=9, PQ=12. Find PR and QR.

Divide a line segment AB in the ratio 3:7, What is the minimum number of points marked on a ray AX at equal distances?

Draw the graphs of the equations x-y+1=0 and 3x+2y-12=0. Determine the coordinate of the vertices of the triangle formed by these lines and the x -a xis and shade the triangular region.

Constract two circles of radii 2 cm and 4 cm, the distance of whose centres is 8 cm. Construct a direct common tangent to these two circle.

Drw a DeltaABC in which BC = 6 cm, CA = 5 cm and AB = 4 cm. Construct and triangle similar to it and of scale factor 3/5.

How many independent words can 'HEARTLESS' be divided into without changing the order of the letters and using each letter only once?

Which of the following sets are equal? A={x:x is a letter in the word FOLLOW}

Solve each of the following pairs of equations by reducing them to a pair of linear equations. 6x+3y=6xy and 2x+4y=5xy.

The ratio of the remainders when the expressionx^2 +bx +c is divided by (x - 3) and (x-2) respec-tively is 4: 5. Find b and c, if (x- 1) is a factor of the given expression.

Find the sum of i] 41, 36, 31, ....... upto 10 terms ii] -26, -24, -22, ..... upto 36 terms.

Draw a circle of radius 6cm. From a point 10cm away its centre, construct the pair of tangents to the circle .

Show that 1 + sqrt(2) is irrational.

Find the AtimesB, AtimesB, and BtimesA. A={m, n}: B=Phi.

Two poles of heights 7 m and 12 m stand on a plane ground. If the distance between their tops.

Evaluate : [{:(,cos 45^@, sin 30^@),(,sqrt2 cos 0^@, sin 0^@):}] [{:(,sin 45^@, cos 90^@),(,sin 90^@, cot 45^@):}]

Four carrom board pans are arranged as shown in figure . Radius of the pan is 3 cm each . Then find the areain between of them .

Differentiate the following with respect to x using first principle method. "cosec"(2x+3)

Find the zeros of the following polynomials and verify the relationship between the zeros and the coefficients of the polynomials. (i) 3x^(2) + 4x -4, (ii) 7y^(2) - 11/3 y -2/3, (iii) p^(2) -30 (iv) sqrt(3)x^(2) - 11x + 6sqrt(3), (v) a(x^(2) +1)-x(a^(2)+1), (vi) 6x^(2) +x-2

A metal pipe has a bore (inner diameter) of 5 cm. The pipe is 5 mm thick all round. Find the weight, in kilogram, of 2 metres of the pipe if 1 cm ^(3) of the metal weighs 7.7 g.

A tree is broken by wind, its upper part touches the ground at a point 10 m from the foot of the tree and makes an angle of 60° with the ground. The entire length of the tree is

In what ratio does the line x - y -2 =0divide the line segment joining the points (3,-1) and (8,9) ?

List the teeth under each of the following type Pre-molars

Evaluate each of the following in terms of x and y, if it is given that x = log_(2)3 and y = log_(2)5 log_(2)6750

Determine for which power of the variable x, the equation x-6sqrtx+2=0 is a quadratic equation.

ax^2 +bx +c=0 is a quadraticequation then

A(6, 1), B(8, 2) and C(9, 4) are three vertices of parallelogram ABCD. If E is the mid-point of DC, then find the area of DeltaADE.

In the following AP's find the missing terms in the boxes. (i) 2.__________,26 Let the missing term bex. (ii) ___________13, ___________,3. (iii) 5,_______,________,9(1)/(2) (iv) -4,_____,______,_______,_______,6. (v) ______,38,_____,_______,________-22.

A lot consists of 144 ball pens of which 20 are defective. A customer will buy a pen only if it is not defective. The shopkeeper draws one pen at random and gives it to the customer. What is the probability that:the customer will buy it?

0. 3 bar(2)when expressed in the form p/q(p ,\ q\are integers q\ !=0), is

If two radit of a circle are inclined to each other at an angle of 70^(@), then the tangents at the end points of those radii are inclined to each other at an angle of……..

Which of the following is a true statement?

Find the value of x sqrt(3) sin x = cos x

Find the value of k for which the lines(k+1) x + 3ky +15=0 and 5x + ky +5=0 are coincident.

If the angle of elevation of a cloud from a point h metres above the surface of a lake is alpha and the angle of depression of its reflexion in the lake is beta, prove that the height of the cloud is (h (tan beta + tan alpha))/(tan beta - tan alpha) metres.

Find the sum of first 24 terms of the list of numbers whose nth term is given by a_(n) = 3 + 2n

By investing 7500rs in a company paying 10 percent dividend, an annual income of 500rs is received. What price is paid for each of 100rs share ?

Find the area of the segments shaded in figure, if PQ=24cm, PR=7cm and QR is the diameter of the circle with centre O ( Take pi=(22)/(7))

P^^Q means (P+Q)/(Q-P)andPvvQ means (Q-P)/(Q+P) Answer the following questions: 8^^6xx10vv8

Spherical shaped marbles of diameter 1.4cm each, are dropped into a cylindrical beaker of diameter 7cm containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6cm.

Find the roots of the following quadratic equations by the method of completing the square : (i) x^(2)-10-24=0 (ii) 2x^(2)-7x-39=0 (iii) 5x^(2)+6x-8=0 (iv) sqrt3x^(2)+11x+6sqrt3=0

Construct an isosceles triangle whose base in 8 cm and altitude 4 cm and then another triangle whose sides are 1(1)/(2) times the corresponding sides of the isosceles triangle.

A man buys 400 twenty rupee shares at a discount of 20% and receives a return of 12% on his money. Calculate : (i) the amount invested by him (ii) the rate of dividend paid by the company

A self help group wants to manufacture joker's caps of 3 cm. radius and 4 cm height. If the available paper sheet is 1000 cm^2 , then how many caps can be manufactured from that paper sheet ?

Find x so that x, x+2,x+6 are consecutive terms of a geometric progression.

Construct Caley's table for Z_(7) under multiplication modulo 7.

If alpha and beta are the zeroes of the polynomial x^(2)+x+1, then (1)/(alpha)+(1)/(beta)=

In the following AP's find the missing terms in the boxes. (i) 2.____,26 Let the missing term bex. (ii) _13, ___,3. (iii) 5,_,____,9(1)/(2) (iv) -4,_,,_,_,6. (v) ,38,_,_,____-22.