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If α, β, γ and Δ are the roots of the polynominal equation (x^{2}  3x + 4)(x^{2} + 2x + 5)= 0, then the quardratic equation whose roots are α + β + γ + Δ and αβγΔ is
α + β = 3, α.β = 4
γ + Δ = 2, γ.Δ = 5
α + β + γ + Δ = 3  2 = 1
α.β.γ.Δ = 4 × 5 = 20
Required quadratic equation is
x^{2}  (α + β + γ + Δ)x + (αβγΔ) = 0
x^{2}  x + 20 = 0
Diameter of two circular plates are respectively 18cm and 80 cm. The diameter of the plate which has an area equal to the combined area of two given plates is
Combined area of two plates = π (9)^{2} + π (40)^{2}
= π (81 + 1600)
= 1681 π cm^{2}.
Let R be the Radius of plate, whose area is combined area of two plates.
Area of plate = πR^{2} = 1681 π
⇒ R^{2} = 1681
⇒ R = 41 cm.
Diameter = 2 x 41 = 82 cm
The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4?
Let the cricket player makes x runs in his next innings
∴ 32 × 10 + x = 11 × 36
∴ x = 396  320 = 76
OABC is a rhombus whose vertices A, B and C lie on a circle with centre at O. If radius of circle is 10cm. The area of the rhombus
If A, B, and C lie on the circle, O is the center of the circle, and the radius is 10 cm, then OA, OB, OC, AB, and BC must all measure 10 cm because OA, OB, and OC are all radii, and AB and BC are congruent because of congruent sides of a rhombus.
Hence, the area of the rhombus is twice the area of an equilateral triangle with sides that measure 10 cm.
Diagonals of a rhombus are in the ratio 3:4 and its area is 2400 cm^{2}. Side of the rhombus is
Let the diagonals of a rhombus are 3K and 4K. Then
Area of rhombus = 1/2 x product of diagonals
2400 = 1/2 x 3K x 4K
or 400 = K^{2}
or K = 200
∴ The Diagonals are 60 cm and 80 cm
we know that, if a be side of the rhombus and AC and BD be its diagonals then
(AC)^{2} + (BD)^{2} = 4 × a^{2}
or (60)^{2} + (80)^{2} = 4 × a^{2}
or 3600 + 6400 = 4 × a^{2}
or 10000 = 4a^{2}
or 2500 = a^{2}
or a = 50 cm
The equation x² + Kxy + y²  5x  7y + 6 = 0 represents a pair of st. lines, then K is
Find Compound Interest on Rs 15625 for 9 months at 16% p.a compounded quarterly.
A shopkeeper marks his goods 20% above the cost price but allows 30% discount for cash. His net loss is
Let C.P. of goods = Rs. 100
∴ Marked price = 100 + 20
= Rs 120
∴ Selling price after allowing 30% discount for cash
If the magnitude of angle θ is three times that of the angle φ in the given figure, then ∠φ is equal to
The angle of elevation of the top of an incomplete tower at a point 40 m from its base is 45°,If the elevation of the completed tower at the same point is 60°,then the height through which the tower has been raised is
2 pipes A and B can fill a cistern in 20 minutes and 25 minutes respectively, Both are opened together but at the end of 5 minutes B is turned off. Total time taken to fill the cisten is
In ΔABC , if a , b , c , are in A.P . , then tan A/2 tan C/2 =
If x sin³α+y cos³α=sinα cosα and x sinαy cosα=0, then x²+y²=
A solid cylindrical block of radius 12 cm and height 18 cm is mounted with a conical block of radius 12 cm and height 5 cm. The total lateral surface of the solid thus formed is :
Lateral surface of the solid = Curved surface of cone + Curved surface of cylinder + Surface area of bottom
= πrl + 2πrh + πr^{2}, where h is the height of the cylinder
The edges of a cuboid are in the ratio 1:2:3 and its surface area is 88 cm². The volume of the cuboid is :
Study the graph given below to answer these questions.
Q. In which year, were the gross sales proceeds the highest?
Sales proceeds in the year
1992 = 180 × 210 = Rs 37800 million
Sales proceed in the year
1993 = 160 × 207 = Rs 33120 million
Sales proceeds in the year
1994 = 150 × 210 = Rs 31500 million
Sales in the year
1995 = 195 × 210 = Rs 40950 million
It is highest in the year 1995
Study the graph given below to answer these questions.
Q. Which year was the least profitable from the fiscal point of veiw ?
Study the graph given below to answer these questions.
Q. In which year the number of cars sold was the lowest but financial turnover , the maximum ?
The year 1996 the number of cars sold is least and financial turnover maximum
Study the graph given below to answer these questions.
Q. In which year, the maximum profit was generated visavis in ?
In the 1991 profit generated is the maximum
These questions refer to the following circle graph showing the expenditure distribution of a certain family.
If the family spends Rs.6,500 per month, how much are its annual taxes ?
These questions refer to the following circle graph showing the expenditure distribution of a certain family.
Q. How many degrees should there be in the central angle showing clothing , taxes and transportation combined ?
Required angle
= 360/100 × 35 = 126°
These questions refer to the following circle graph showing the expenditure distribution of a certain family.
Q. How much more money per month is spent by the family on food as compared to the rent ?
These questions refer to the following circle graph showing the expenditure distribution of a certain family.
Q. If the expenditure budget of the family is raised to Rs.8,000 per month and distribution on various items remain the same , then the monthly expenses on both , the entertainment and the transport, will be
Expenses on entertainment and transport
= 8000 × 18%
= Rs 1440
The pie chart given below shows the funding arrangements for National Highways Development Projects: phase I. Study the chart carefully to answer these questions.
Q. Near about 25% of the funding arrangement is through :
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