The distance between two vertical poles is 60 m. The height of one of the poles is double the height of the other. The angles of elevation of the top of the poles from the middle point of the line segment joining their feet are complementary to each other. The heights of the poles are

Solution
BE = DE = 30 metres
∠AEB = θ ∴ ∠CED = 90°  θ
[∵ angles of elevation are complementary to each other.]
From ,ΔABE,
⇒tanθ = ^{AB}⁄_{BE}⇔tanθ = ^{h}⁄_{30}
⇒h = 30 tanθ... (i)
From ,ΔCDE, tan (90°  θ) = ^{2h}⁄_{30}
cotθ = 15 ⇒ h = 15cotθ... (ii)
By multiplying both equations,
h^{2} = 30 × 15 × tan θ. cot θ
⇒h^{2} = 30 × 15 [ ∴ tans. cotθ = 1]
⇒h = 15.\(\sqrt{2}\) metre = AB
⇒2h = 30.\(\sqrt{2}\) metre = CD
A dishonest fruit vendor sells his goods at cost price but he uses a weight of 900 gm for the kg weight. His gain per cent is

Solution
Gain per cent =\(\frac{1000 900}{900}\times 100\)
\(=\frac{100}{900}\times 100\)
\(=\frac{100}{900}=11\frac{1}{9}%\)
The numerical value of \(\frac{5}{sec^{2}θ}+\frac{2}{1+cot^{2}θ}+3sin^{2}θ\) is

Solution
Expression
\(\frac{5}{sec^{2}θ}+\frac{2}{1+cot^{2}θ}+3sin^{2}θ\)
\(=5cos^{2}θ+\frac{2}{cosec^{2}}+3sin^{2}θ\)
= 5 cos^{2}θ + 2 sin^{2}θ + 3 sin^{2}θ
\(\left [ 1 + cot^{2}\theta = cosec^{2}\theta; \frac{1}{sec\theta} = cos\theta; \frac{1}{cosec \theta} = sin \theta \right ]\)
Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is

Solution
Let the length of each train be x metres.
Relative speed
= (46  36 =) 10 kmph=\(\frac{10×5}{18}\) 18 metres/ second
=\(\frac{25}{9}\) 59 metre / second
Now, according to the question,
\(\frac{2x}{\frac{25}{9}}=36 \Rightarrow 2x =\frac{36\times 25}{9}=100\)
⇒x = 50 metres
The LCM of two positive integers is twice the larger number. The difference of the smaller number and the GCD of the two numbers is 4, The smaller number is

Solution
Let the numbers be xH and yH where H is the HCF and yH > xH.
∴ LCM = xyH
∴ xyH= 2yH ⇒x = 2
Again, xH  H = 4
⇒2H  H = 4 ⇒H = 4
∴ smaller number = xH = 8
Which of the following is not a secondary storage unit?

Solution
RAM is not a secondary storage device. Storage consists of storage devices and their media not directly accessible by the Central Processing Unit (CPU). Secondary storage is all data storage that is not currently in a computer's primary storage or memory
A wire carrying current is
The enormous amount of energy released in an explosion of an atmoic bomb is due to the

Solution
display device containing cathoderay tube (CRT)that generates an electron beam that is used to produce visible patterns or graphs on a phosphorescent screen. A sonometer is an apparatus made of hollow box having two holes. A string is attached to it by which the transverse vibrations of strings can be studied.
The concept of Sovreign Parliament originated in
The maximum biological damage is produced by
Human Development Index was developed by
The Minimum Wages Act was first passed in India in the year
The food stocks that are built up during the years of bumper vest are called
Agricultural Commodities are graded with
The Accounting Year of Reserve Bank of India runs from
Mohini went to movies nine days ago. She goes to the movies only on Thursday. What day of the week is today ?
If BEAUTIFUL is written as CDOGHJKMN, how LEAF can be written in that code ?
From the given alternative words, select the word which cannot be formed using the letters of the given word
SUPERIORITY
Ramesh drives his car 4 km to east, then takes left turn and drives 6 km. He again turns to his left hand side and travels 4 km. How many km is Ramesh away from his starting place ?
The age of a father is twice that of his son’s at present age. After 5 years the sum of their ages will be 85. How old are they now ?