Latest Questions

Use the Intermediate Value Theorem to show that 2 has a positive
square root.

Let \(G\) be a finite group. Show that the only homomorphism from \(G\) to \((\mathbb{Z} ,+)(\) or to \((\mathbb{Q} ,+)\) or to \((\mathbb{R} ,+) )\) is the zero homomorphism.

The Greek viewed “politics” on the basis of :
(1) Both ethical and legalistic terms
(2) Ethical terms
(3) Terms of power
(4) Legalistic terms

The communication satellites are invariably -

1) revolving at their own speed

2) stationary

3) geostationary

4) changing their track and speed

नोजवान भारत सभा, भिवानी की स्थापना किसने की?

 (a) राधाकृष्ण वर्मा

 (b) राधाकृष्ण सिंह

 (c) भगवानदास

 (d) राधाकृष्ण शर्मा

नदी में एक व्यक्ति किसी निश्चित बिंदु से धारा के विपरीत d किमी. दुरी तय करके वापिस उसी बिंदु तक 5 घंटे 15 मिनट में पहुच जाता है वह धारा के विपरीत 2d किमी. की दुरी 7 घंटे में तैर सकता है यदि 2d किमी. दुरी धारा की दिशा में तय करने में उसे कितना समय लगेगा?

 (a) 3 घंटे 30 मिनट

 (b) 2 घंटे 20 मिनट

 (c) 1 घंटा 12 मिनट

 (d) इनमे से कोई नही

The terminal velocity for a skydiver with an unopened parachute is about?

Japanese folk tradition and ritual, with no founder or single sacred scripture, is popularly known as
(1) Taoism
(2) Zoroastrianism
(3) Shintoism
(4) Paganism

The largest interval on which the solution of the initial value problem \(\frac{dx}{dt}=x^3\) , x(0) = 1 is defined as

(a) \(t>\frac{1}{2}\)      (b) \(t<\frac{1}{2}\)       (c) \(\frac{-1}{2}<t<\frac{1}{2}\)           (d) −1 < t < 0

Alberuni came to India with
(1) Mahmud of Ghazni
(2) Alexander
(3) Babur

(4) Timur

In which year Salt Satyagraha took place?
(1) 1929                (2) 1930
(3) 1931                (4) 1932

Prove that

L{\(Sin{at} \)} =\(\frac{a} {(s^{2}+a^{2})},s>0\)

Who among the following is not a moderate ?
(1) Pherozeshah Mehta
(2) Surendranath Banerjee
(3) Womesh Chandra Bonnerjee
(4) Bal Gangadhar Tilak

The number of prime numbers between 0 and 50 is

Which two countries were involved in a Hundred Years War ?
(1) Turkey and Austria
(2) England and France
(3) Palestine and Israel
(4) Germany and Russia

If a group \(G \neq \{e\}\) has no nontrivial subgroups, show that \(G\) must be a finite group of prime order.

During the Second World War,  which one of the following countries was not one of the three Axis Powers, which fought against the Allied Powers?
(1) Germany            (2) Italy
(3) China                   (4) Japan

If a group of order \(p^n\) , where \(p\) is a prime, contains exactly one subgroup each of orders \(p,p^2, \cdots ,p^{n-1}\) , prove that it is cyclic.