The length of the diameter of the circle which touches the xaxis at the point (1, 0) and passes through the point (2, 3) is
Let the equation of the circle is
(x1)^{2 }+ (yk)^{2 } = k^{2}
It passes through (2, 3)
⇒ (21)^{2} + (3k)^{2} = k^{2}
⇒ 1+9+k^{2}6k = k^{2}
⇒ 106k=0
⇒ k=10/6
⇒ k = 5/3
⇒ diameter = 10/3
The value of ii is :
Let A=i^{i}
⇒ log A = i log i
∵ e^{i θ} = cos θ + i sin θ
∴ e^{iπ/2} = i
∴ i . π/2 = log i
∴ log A = i · i π/ 2 =  π / 2
⇒ A = e^{π/2}
If two vertices of a triangle are (5, 1), (2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex is
Let the third vertex C be (x_{1} , y_{1}) since O(0, 0) is the orthocenter
m_{CO} × m_{AB} = – 1
⇒ y 1  0 x 1  0 · 3   1  2  5 =  1
⇒ y 1 x 1 · 4 7 = 1
⇒ 7 x 1 = 4 y 1
Also mBO × mAC = – 1
⇒ 3  2 × y 1 + 1 x 1  5 =  1
⇒ 3 y 1 + 3 = 2 x 1  1 0
⇒ 3 × 7 4 x 1 + 3 = 2 x 1  1 0
⇒ x_{1} = – 4
y_{1} = – 7
Hence, the third vertex is (– 4, – 7)
If a < 0, the function f(x) = eax + e ax is a monotonically decreasing function for values of x
given by :
f(x) = eax + e ax
But a < 0
∴ e ax  e  ax > 0
⇒ e ax > e  ax
⇒ ax >  ax ⇒ 2 ax > 0
∴ ax > 0, then x < 0 (∴ a < 0)
How many threedigit numbers can be formed without using the digits 0, 2, 3, 4, 5 and 6 ?
Threedigit numbers are to be formed by using the digits 1, 7, 8 and 9.
To form a number of three digits, we are to fill up three places : the hundred's, the ten's and the unit's. The hundreds place can be filled in 4 different ways because anyone of 1, 7, 8 and 9 can fill up this place.
Similarly, ten's and unit's places can also be filled in 4 different ways each.
Accordingly, by FPC, the no. of threedigit numbers = 4 × 4 × 4 = 6 4
For what value of 'a' is the area bounded by the curve y=a^{2} x 2+ax+1 and
the straight line y = 0, x = 0 & x = 1 the least ?
How many five digit numbers can be formed by using the digits 1,2,3,4,5 without repetition of digits?
1,2,3,4,5
Number of given digits (=5) Number of Digits number
to be formed (=5) Number of such numbers
A particle is moving in a circular motion of radius R. Its tangential retardation at any time is equal to the centripetal acceleration. If it starts with speed v0, then the speed after one revolution is
Hence, speed after one revolution
A particle starts moving with velocity from origin, where k is a constant. The general equation for its path is
Comparing vx = ky^{2}
vy = kx
and slope
A stationary body of mass 3 kg explodes in to three pieces of equal mass. Two of the piece fly off along xaxis and yaxis with equal speed 2 m/s and time of explosion is 10–3 s, then average force on the third piece
By conservation of angular momentum
and average force on third particle
Two particles of equal mass are moving along xaxis and yaxis respectively, if initial velocity of 1st particle is zero but acceleration is constant whereas 2nd particle acceleration is zero, then path of centre of mass
x ∝ y^{2}, path is parabolic.
Find the P – O bonds are present in P_{4}O_{6}?
When hydrogen peroxide is added to acidified potassium dichromate, a blue colour is produced due to the formation of
If B.O.D. of a river is high, it means that the river is
Which of the following has unstable enol form?
Red, Yellow and _________ form a primary colour scheme
Any of a group of colours from which all other colours can be obtained by mixing.Red, Yellow and Blue form a primary colour scheme
Identify the structure
The Rashtrapati Bhavan is the official home of the President of India located at the Western end of Rajpath in New Delhi, India.
What is the finish of sanitary fittings
The following sanitary fittings are commonly used in buildings, for efficient collection and removal to the house drain: 1. Wash basins 2. Sinks 3. Bath tubs 4. Water closets 5. Urinals 6. Flashing cisterns
A 3D problem figure is given below. Identify the correct front view from the options
A 3D problem figure is given below. Identify the correct top view from the options
Identify the structure
The Statue of Liberty is a colossal neoclassical sculpture on Liberty Island in New York Harbor in New York, in the United States. The copper statue, a gift from the people of France to the people of the United States, was designed by French sculptor Frédéric Auguste Bartholdi and its metal framework was built by Gustave Eiffel. The statue was dedicated on October 28, 1886.
If a colour is made darker by adding black, the result is called a __________.
If a colour is made darker by adding black, the result is called a Shade
Complete the series of the problem figures by choosing the correct answer from the options given below
CN Tower is also known as
Its name "CN" originally referred to Canadian National, the railway company that built the tower. Following the railway's decision to divest noncore freight railway assets prior to the company's privatization in 1995, it transferred the tower to the Canada Lands Company, a federal Crown corporation responsible for real estate development.
Higher the purity of a colour, higher the ______.
Chroma: the quality of a color's purity, intensity or saturation. For example: A gray color is a neutral  an extreme low chroma. Fireengine red may be a hi chroma red.
Identify the building
LIC Building is a 15storied building in Chennai, India, serving as the southern regional headquarters of the Life Insurance Corporation of India
Find the correct 3D figure from the options, which has the same front view as given in the problem figure, looking in the direction of the arrow
A.
B.
C.
D.
Identify the building
The Petronas Towers, also known as the Petronas Twin Towers, are twin skyscrapers. According to the Council on Tall Buildings and Urban Habitat (CTBUH)'s official definition and ranking, they were the tallest buildings in the world from 1998 to 2004 and remain the tallest twin towers in the world.
In the given problem figure, find out the total number of surfaces of objects
TEOTIHUACAN is famous for ___________
TEOTIHUACAN is an ancient Mesoamerican city located in a subvalley of the Valley of Mexico, located in the State of Mexico 40 kilometres (25 mi) northeast of modernday Mexico City, known today as the site of many of the most architecturally significant Mesoamerican pyramids built in the preColumbian Americas.
A sheet of paper is folded & cut in the given steps. Select the correct answer from the options given below which resembles the pattern paper acquires when it is unfolded
Why India Gate was built ?
This monument is regarded as the heritage of India and is located on RajPath in New Delhi. India Gate was designed by Sir Edwin Lutyens and was built in 1931 and initially named as 'All India War Memorial'. ... India Gate was built to honor these soldiers.
Identify the structure
The Louvre Pyramid is a large glass and metal pyramid designed by ChineseAmerican architect I. M. Pei, surrounded by three smaller pyramids, in the main courtyard ) of the Louvre Palace in Paris
Why was Statue Of Liberty Built?
1865  1886. In 1865, a French political intellectual and antislavery activist named Edouard de Laboulaye proposed that a statue representing liberty be built for the United States. This monument would honor the United States' centennial of independence and the friendship with France.
Which of the following dices is identical to the unfolded figure shown below
Why is Statue Of Liberty green in colour ?
When the Statue was unveiled in 1886, it was a shiny brown color, like a penny. By 1906, the color had changed to green. The reason the Statue of Liberty changed colors is that the outer surface is covered with hundreds of thin copper sheets. Copper reacts with the air to form a patina or verdigris.
Understand the relationship between a & b. Choose the missing figure from the options given such that a similar relationship is established between c & d
In the given problem figure, find out the total number of surfaces of objects
Identify the structure
The Taj Mahal meaning "Crown of the Palaces" is an ivorywhite marble mausoleum on the south bank of the Yamuna river in the Indian city of Agra
____________ is a tint of red.
Identify the material
The material in the image is Glass.
A sheet of paper is folded & cut in the given steps. Select the correct answer from the options given below which resembles the pattern paper acquires when it is unfolded
Understand the relationship between a & b. Choose the missing figure from the options given such that a similar relationship is established between c & d
If Orange : Juice, then Mango : ________
Mango pulp is the inner fleshy yellow, sweet part of the mango. Pulp of mango can be easily extracted by peeling any variety of mango and then crushing it. In order to extract mango pulp, crush using your hands or put the pieces in a mixer or food processor and blend to a pulp.
Understand the relationship between a & b. Choose the missing figure from the options given such that a similar relationship is established between c & d
Violet, indigo, blue, green, yellow, orange, red form the ____________.
There are seven wavelength ranges within the visible spectrum that each correspond to a different color. The colors fall in an order commonly referred to with the acronym ROYGBIV. ROYGBIV can aid in remembering the order of the colors: red, orange, yellow, green, blue, indigo, and violet.
Assuming the question figure to be a transparent sheet with a given pattern. Find out the
correct figure from the options which would appear when the problem figure is
folded along the dotted line
A 3D problem figure is given below. Identify the correct front view from the options.
In the given problem figure, find out the total number of surfaces of objects
Complete the series of the problem figures by choosing the correct answer from the options given below
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