Find the principal value :
\(Cot^{-1}(\frac{-1}{√3})\)
([1, H. F¨urstenberg]) Consider \(\mathbb{N}\) with the arithmetic progression topology. Verify the following:
(1) For a prime number p, the basis element {np : n ≥ 1} is closed.
(2) There are infinitely prime numbers.
The British Governor-General who introduced the Postal system in India was (1) Lord Dalhousie (2) Lord Wellesley (3) Lord Auckland (4) Lord Bentinck
हरियाणा में पहली बार राष्ट्रपति शासन लगाया गया?
(a) 20 मार्च 1965
(b) 21 नवम्बर 1967
(c) 10 अप्रेल 1969
(d) 12 दिसम्बर 1970
हरियाणा राज्य का वन क्षेत्र कितना हैं ?
(a) 1050 वर्ग किमी.
(b) 1560 वर्ग किमी.
(c) 1780 वर्ग किमी.
(d) 800 वर्ग किमी.
एक व्यक्ति के पास 100 किग्रा. चीनी थी जिसका कुछ भाग उसने 7% लाभ पर तथा बाकी 17% लाभ बेचा ऐसा करने से उसे सम्पूर्ण पर 10% लाभ हुआ 7% लाभ पर उसने कितनी चीनी बेचीं?
(a) 65 किग्रा
(b) 35 किग्रा
(c) 30 किग्रा
(d) 70 किग्रा
Frequencies emitted by a straight instrument can be studied by_____?
Give five of your favourite non-open subsets of \(\mathbb{R^2}\) .
When was Mahatma Gandhi arrested during the ‘Quit India Movement’ of 1942? (1) 7th August 1942 (2) 30th April 1942 (3) 9th August 1942 (4) 5th July 1942
Which of the following princely states did not accede to the Indian Union after independence?
(1) Hyderabad (2) Junagarh (3) Kashmir (4) Jodhpur
‘Dyarchy’ was introduced in the Government of India Act of (1) 1909 (2)1919 (3) 1935 (4)None of these
LCM and HCF of two numbers are 48 and 8 respectively. If one of the numbers is 16, the second number is
Paralympic Games 2015 will be held in –
Consider this famous question on real analysis. The function \(f(x)=x\sin(\pi/x)\) for \(x>0\) satisfying Rolle’s theorem for any interval \((1/n,1/(n+1)),n \in \mathbb{N}\). The discussion leads to finding the solutions \(\pm x_1, \pm x_2 , \cdots\) of the equation \(\tan(/pi/x)=\pi/x\) where \(\frac{1}{k+1/2}<x<\frac{1}{k}\) . Show that this equation has no other solution in the complex plane. Hence find the sum of the series \(\sum_{k=1}^\infty z_k^{-2}\) .
The differential equation \(y''+2x(y')^2=0\), satisfying the condition y(1) = 0, y'(1) = 1
(a) has no solution
(b) has a unique solution
(c) has two distinct solutions
(d) has an infinite number of solutions
Who revived the Theosophical Society ? (1) Mother Teresa (2) Annie Besant (3) Florence Nightingale (4) Sarojini Naidu
Ajanta Ellora Caves are situated near which of the following cities?
(1) Mount Abu (2) Aurangabad (3) Bijapur (4) Madurai
What is Gandhi’s definition of Rama Raj? (1) The rule as it was during the time of Rama (2) Sovereignty of the people based on the pure moral authority
(3) The greatest good of all
(4) The absolute power concentrated in the hands of a king
All Questions
Physics
Chemistry
Mathematics
English
Organic Chemistry
Inorganic Chemistry
Physical Chemistry
Algebra
Geometry
Who, among the following, has been known as the ‘Frontier Gandhi’?
(1) Khan Abdul Ghaffar Khan (2) Khan Saheb (3) Chaudhary Shaukatullah (4) Liaquat Ali Khan
Which among the following fort was known as the ‘Key of Deccan’? (1) Kalinjar (2) Ajaygarh (3) Asirgarh (4) Gulbarga
The name of India's first indigenous anti-radiation missile is -
1) Tandav
2) Trinetra
3) Saksham
4) Rudram
The great silk route to the Indians was opened by :
(1) Kanishka (2) Ashoka (3) Harsha (4) Fa-Hien
Any interval \((x,y)\) in a simply ordered set is convex: If \(a,b \in (x,y)\) then \(x<a<b<y\) and hence \((a,b) \subseteq (x,y)\).
Which of the following was the early capital of the Rashtrakutas? (1) Sopara (2) Ellora (3) Vatapi (4) Ajanta
Show that any ring with 6 elements is commutative.
Determine the splitting field \(E\) for each of the following polynomials over \(\mathbb{Q}\) . Also determine \([E: \mathbb{Q}]\) in each case.
(i) \(x^4 -2\) (ii) \(x^4 -6x^2 -7\) (iii) \(x^5 -3x^3 + x^2 -3\) .
The pointer data type address of _____ operator is used.