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Draw an isosceles triangle ABC in which AB=AC= 6 cm and BC=5 cm. Construction a triangle POR similar to DeltaABC in which PQ=8 cm. Also justify the construction.

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

Draw Delta PQR such that PQ=6.8 cm, vertical angle is 50^(@) and the bisector of the vertical angle meets the base at D where PD=5.2 cm.

Rijwana's monthly salary is Rs.25,000. She contributes Rs.600 per month towards GPF and pays Rs.7000 towards annual LIC premium. Find the amount of income tax she has to pay for the last month if she paid Rs. 4000 per month towards income tax for 11 months.

Let the function f and g be defined by the graphs in the accompanying diagram. What is the value of f(g(3))?

A survey conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members in a household. Find the mode of this data.

Statements: 1. All men are girls. 2. Some girls are students. Conclusions: 1. All girls are men. 2. Some girls are not students.

Consumption of coal by an engine varies as the square of its speed. When the speed is 50 km per hour the consumption of coal is 100 kg per hour . If the cost of 1 kg of coal be 25 P and other expenses per hour be rs 4 , find the minimum expenses when the engine runs 300 km .

Find the roots of the following quadraticequations by factorisation :100x^(2) -20x+1=0

Find the value of the expression [ (cot (20^(@) - theta) + tan (70^(@) + theta))/(sin (70^(@) + theta)) ]sin (20^(@) - theta)

From a wooden cube of side a cm, a right circular cylinder of maximum volume is cut. Then, the volume of the cylinder is ......... cm.

Salman invests a sum of money in 50rs shares paying 15% dividend quoted at 20% premium. If his annual dividend is600rs, calculate (i) the number of shares he bought (ii) his total investment (iii) the rate of return on his investment

Find the values of 'm', if the roots of the following quadratic equation are equal, (4+m)x^(2)+(m+1)x+1=0.

IF a=5^(1//3)+5^(-1//3)andb=5^(1//3)-5^(-1//3) then (a^3-3a)/(b^3+3b)=........

A man sees the top of a tower in a mirror which is at a distance of 87.6mfrom the tower.The mirror is on the ground facing upwards.The man is 0.4m away from the mirror and his height is 1.5m.How tall is the tower?

An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45^(@). What is the height of the chemney ?

For the A.P. 7,15,23,31,……., write the first term, common difference and next two terms.

If the ratio of the compound interest in 3 years and the simple interest in 2 years of a certain principal be 13:4 then what will be the rate of interest?

A dealer X in Hapur (UP) supplies goods/services, worth Rs. 50,000 to some other dealer Y in the same city. Now the dealer Y supplies the same goods/services to dealer Z in Calcutta at a profit of Rs. 20,000. Find : output and input taxes for the dealer Y. [The rate of GST at each stage is 28%].

A dealer X in Hapur (UP) supplies goods/services, worth Rs. 50,000 to some other dealer Y in the same city. Now the dealer Y supplies the same goods/services to dealer Z in Calcutta at a profit of Rs. 20,000. Find : net GST payable by dealer Y. [The rate of GST at each stage is 28%].

If P(E )=0.75, what is the probability of 'not E'?

Express the following decimals in the form of p/ q , and write the prime factors of q. What do you observe? 43.bar(12)

Express the following decimals in the form of p/ q , and write the prime factors of q. What do you observe? 4.123

Which term of the AP: 3,8,13,18,……. Is 78?

Express the following decimals in the form of p/ q , and write the prime factors of q. What do you observe? 0.1201201

IFsec theta sin(36^(@) + theta) =1 . Find the value ofthetaso thattheta and 36^(@) + thetaare acute angles.

Point A (4,-1) is reflected as A' in the y - axis . Point B on reflection in the x - axis is mapped as B' (-2,5). Write the co- ordinates of A' and B.

For which values of a and b , the zeroes of q(x)=x^(3)+2x^(2)+a are also the zeroes of the polynomial p(x)=x^(5)-x^(4)-4x^(3)+3x^(2)+3x+b? Which zeroes of p(x) are not the zeroes of q(x)?

If sin A =cos B ,then prove that A+B =90 ^(@)

Find the slope of the line passing through the given two point (2a, 3b) and (a, -b)

The point which divides the line segment joining the points (7,-6) and (3,4) in ratio1:2internally lies in the

A straight line AB is 8 cm long. Draw and describe the locus of a point which is : always 4 cm from the line AB. Mark the two points X and Y, which are 4 cm from AB and equidistant from A and B. Describe the figure AXBY.

Fill in the blanks : {:("Point","Transformation ","Image"),((5, -7),.....................,(-5, 7)):}

Find the quadratic polynomial whose zeroes are 2 and (-1)/(3)

If A=[{:(,0,2),(,5,-2):}], B=[{:(,1,-1),(,3,2):}]and is a unit matrix of order 2 xx 2 find : (i) AB (ii) BA (iii) AI (Iv) A^2 (v) B^2A

Statements: 1. Some dogs are goats. 2. All goats are cows. Conclusions: 1. All cows are goats. 2. Some dogs are cows.

The perimeter of circle with center 'O'is 24cm, the angle formed by an are of the cirlce at its centre is 30^(@). Find thelength of the are AB.

A cone of equal height and equal base is cut off from a cylinder of height 24 cm and base radius 7 cm .Find the total surface and volume of remaining solid.

The radius of a solid right circular cylinder decreases by 20% and its height increases by 10%. Find the percentage change in its : curved surface area

The radius of a solid right circular cylinder decreases by 20% and its height increases by 10%. Find the percentage change in its : volume

Saritha's annual salary is Rs. 160,000. She contributes Rs. 6000 towards GPF and pays an LIC annual premium of Rs. 5000. Calculate the income tax she will have to pay in the year.

If cos A =(12)/( 13), then find sin A and tan A ( A lt 90 ^(@))

find the equation of circle in each of the following cases (b) touches both the coordinate axes insecond quadrant and having radius 2

Find the solution of x+2y=10 and 2x+4y=8 graphically.

Find thecoordinates of the circumcentre of the triangle whose vertices are (3,\ 0),\ (-1,\ -6)and (4,\ -1). Also,find its circumradius.

An A.P. consists of 60 terms. If the first and the last terms 7 and 125 respectively, find the 31st term.

If the lines 5x+12y=3 and10x+ 24y-58=0 are tangents to a circle, then find the radius of the circle.

The total surface area of a right circular cone of slant height 13 cm is 90picm^(2). Calculate its radius in cm.

Write down the decimal expansionsof those rational numbers m Question 1 above which have terminating decimalexpansions.

Find the value of 'k' for which x=3 is a solution of the quadratic equation, (k+2)x^(2)-kx+6=0 Hence, find the other root of the equation.