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If the system of equations4x + y =3 and (2k-1) x + ( k-1) y =2k +1 is inconsistent, then find k.

Express the following statements using symbols. (i) The element 'x' does not belong to 'A'. (ii) d' is an element of the set 'B'. (iii) 'I' belongs to the set of Natural numbers. (iv) '8' does not belong to the set of prime numbers P.

A dice is thrown once. Find the probability of getting : a number greater than 4

In a certain code SIKKIM is written as THLIJL. How is TRAINING written in that code?

Factorise x^(3)+6x^(2)+11x+6 completely using factor theorem.

Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is800m^(2)? If so, find its length and breadth.

Draw the graphs of the equations 5x-y=5" and "3x-y=3. Determine the coordinates of the vertices of the triangle formed by these lines and y-axis.

For what value of n, are the nth terms of two AP’s : 15, 12, 9 ,........and -15, -13, -11.... equal?

From the word 'ASTOUNDER', how many independent words can be made without changing the order of the letters and using each letter once only?

The marks obtained in mathematics by 30 students of Class X of a certain scholl are given in table the below. Find the mean of the marks obtained by the students.

Bisect a triangle by a striaght line drawn parallel to the base.

Find the value of k if the following two quadratic equations have real and equal roots :

Find the sum of 8 terms of the G.P. : 3+6+12+24+ . . . . .. . . . . .

Two candidates attempt to solve a quadratic equation of the form ax^2 + bx +c=0. One starts with a wrong value of b and find the roots to be 2 and 6. The other starts with the wrong values of c and find the roots to be +2,-9. The correct roots of the equation are

If the 3rd and 9th terms of an A.P. Are 4 and -8 respectively, which term of this A.P. Is zero?

What is the amount of divident received per share of face value 10 dividend declared is 50%

If the common difference of an AP is 3, then find the value of a_(17) - a_(12)

The probability of getting a rotten eggs in a lot of 400 eggs is 0.035. The number of rotten eggs in the lot is:

Find the area of the trianglevertices are (2, 3) (-1, 0), (2, -4)

Numbers in each series follow some rule. Find the missing term. 2, 4, 6, 10, 12, 22, 34, 36, ?

If z_1,z_2 are complex numbers such that, |(z_1-3z_2)/(3-z_1.bar z_2)|=1 and |z_2|ne 1 then find |z_1|

Check whether the following equations are consistent or inconsistent. Solve them graphically. 2x-2y-2=0 and 4x-4y-5=0.

The sum of the fourth and eighth terms of an arithmetic progression is 24 and the sum of the sixth and tenth terms is 44. Find the first three terms of the Arithmetic progression.

Is -150 a term of 11, 8, 5, 2…………

If A=[{:(,2,5),(,1,3):}], B=[{:(,4,-2),(,-1,3):}] and I is the identify matric of the same order and A^(t) is the transpose of matrix A, find A^(t) B+BI.

Draw the graphs of the following equations on the same graph paper :3x - 2y = 9, 4y - 6x + 12 = 0Find the area of trapezium formed by these two lines and the axes.

Find the unknown values is each of the following figures. All lengths given in centimetres. (Measures are not in scale) (a) (C)

Draw the two tangents from a point which is 5 cm away from the centre of a circle of diameter 6 cm. Also, measure the lengths of the tangents.

Express the complex number in the form r(cos theta+isin theta)(ii)1-sin alpha +icos alpha

Polynomial x^3-ax^2+bx-6 leaves remainder -8 when divided by x-1 and x-2 is a factor of it. Find the values of 'a' and 'b'.

ABC is a triangle with vertices A(-8, 3), B(4, 5), C(-6,1). Find the vertices of a parallelogram in this DeltaABC sharing vertex B and having half the area of Delta ABC. Find the area ot the paralelogram so formed.

Write the following rationals in decimal form using 15/16

A right circular of volume 1386 cm^(3) is cut from a right circular cylinder of radius 4 cm and height 49 cm, such that a hollow cylinder of uniform thickness, with a height of 49 cm and an outer raidus of 4 cm is left behind. Find the thickness of the hollow cylinder left behind.

IfA(2,2), B(-2, -2) , C(-2sqrt(3), 2sqrt(3)) and D(-4-2sqrt(3), 4+2sqrt(3)) are the co-ordinates of 4 points. What can be said about these four points ?

Write the following sets in roster form (i) B= {x:x is a natural number smaller than 6} C= {x:x is a two-digit natural number such that the sum of its digits is 8). (iii) D= {x : x is a prime mimber which is a divisor of 60}. E= {x:x is an alphabet in BETTER}.

A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.

P is any point on the circle with centre at O. Draw a tangent to that circle at P and cut off the part PQ equal to the radius of the circle from that tangent. From the point Q, draw another tangent QR to that circle and find the value of angle(PQR).

Find the sum of the geometric series : 1,(1)/(2),(1)/(4),(1)/(8), . . . .. . . . . . upto 12 terms.

Find the roots of the quadratic equations given in Q. 1 above by applying the quadratic formula. (i) 2x^(2)-7x+3=0 (ii)2x^(2)+x-4=0 (iii) 4x^(2)+4sqrt(3)x+3=0 (iv) 2x^(2)+x+4=0

Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m^(2)? If so, find its length and breadth.

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

If A(3, 4) and C (1, -1) are two opposite angular points of square ABCD, find the coordinates of other two vertices.

Solve : (i) 2x^(2)-7x=39 (ii) x^(2)=5x (iii) x^(2)=16

For the following APs, write the first term and the common difference: (i) 3,1,-1,-3,…. (ii) -5,-1,3,7,…….. (iii) 1/3, 5/3, 9/3, 13/3,……… (iv) 0.6, 1.7 , 2.8, 3.9,………

Which term of the series : 21, 18, 15, is -81 ? Can any term this series be zero ? If yes, find the number of terms.