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If \(S_n \) denotes the sum of the first \(n \) terms in an AP and \(S_1:S_4=1:10 \) then the ratio of first term to fourth term is
Two people agree to meet on January 9, 2021 between 6 : 00 PM to 7 : 00 PM with the understanding that each will wait no longer than 20 minutes for the other. What is the probability that they will meet?
\(ABCD \) is a trapezium such that \(AB, DC\) are parallel and \(BC\) is perpendicular to them. If \(\angle DAB =45^o,BC=2\ cm \) and \(CD=3\ cm \) then \(AB= \)
If the ratio of the roots of the equation \(x^22ax+b=0 \) is equal to that of the roots \(x^22cx+d=0 \) then
There are two buildings one on each bank of a river opposite to each other. From the top of one building \(60\ m \) high, the angle of depression of the top and foot of the other building are \(30^o \) and \(60^o \) respectively. What is the height of the other building?
\(35.7\left(3+\dfrac{1}{3+\dfrac{1}{3}}\right)\left(2\dfrac{1}{2+\dfrac{1}{2}}\right)c \)
If one zero of the polynomial \(4x^28kx9 \) is the negative \(1:3 \) the other, The value of \(k \)
If zeroes of the polynomial \(x^28x+k=0 \) are the HCF of \((6,12) \), the value of \(k \) is
Find the number of solid spheres each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm
A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to its base. The ratio of the volume of the smaller cone to the whole cone
A right circular cone of radius 3 cm has a CSA of \(47.1\ cm^2 \). The volume of the cone is
Find the mean of 32 numbers, such that if the mean of 10 of them is 15 and the mean of 20 of them is 11. The last two numbers are 10.
The daily minimum steps climbed by a man during a week were. Mon – 35, Tue – 30, Wed – 27, Thur – 32, Fri – 23, Sat – 28. Find the mean
If the mean of 4 numbers 2, 6, 7, a is 15 and also mean of 5 numbers 6, 18, 1, a, b is 50. The value of b is
If the median of a distribution is 28.5, the value of \(x \) and \(y \) is
A bag has 5 white marbles, 8 red marbles and 4 purple marbles. If we take a marble randomly than what is the probability of not getting purple marble?
A fish tank has 5 male fish and 8 female fish. The probability of fish taken out is a male fish is
A metallic sphere of internal and external diameters 4 cm and 8 cm respectively is melted and recast into the form of a cone with a base diameter 8 cm. The height of the cone is
A solid piece of iron in the form of a cuboid of dimension \(49\ cm\times33\ cm\times24\ cm \) is moulded to form a solid sphere. The radius of the sphere is
A solid cylinder of radius \(r \) and height \(h \) is placed over other cylinder of same height and radius. The total surface area of the shape so formed is
A sum of Rs. 2000 is invested at 4% SI per year. If the total interest at the end of each year forms an AP then the interest at the end of 30 year is
By increasing the list price of an article by Rs. 10, a person can buy 10 articles less for Rs. 1200. The original price of article is
The first, second and last terms of an AP are respectively 4, 7, 31. How many terms are there in the given AP?
If 5th term of an AP is zero, then 26th term is the 12th term.
If \(\dfrac{x+3}{x+2}=\dfrac{3x7}{2x3} \), the value of \(x \) is
A man 6 ft tall casts a shadow 4 ft long at the same time when a flag pole casts a shadow 50 ft long. The height of the flag pole is
If two positive integers \( a\) and \(b \) are written as \(a=p^3q \) and \(b=pq^3 \), \( p\) and \(q \) are prime numbers, HCF of \((a,b)= \)
If the HCF of 65 and 117 is expressible in the form of 65m – 117 the value of m is
\(\dfrac{987}{10500} \) will have
A rational number in its decimal expansion is 327.7081. What would be the prime factors of \(q \), when the number is expressed in the form of \(\dfrac{p}{q} \) form?