Latest Questions

0.08% of 120% of 50000 is equal to_____?

Who was the greatest Bhakti poet of Maharasthra ?
(1) Ramdas                           (2) Tukaram
(3) Namdeva                         (4) Eknath

The first telegraph line between Calcutta and Agra was opened in
(1) 1852                                      (2) 1853
(3) 1854                                      (4) 1855

राज्य के किस नगर में चिकित्सा के लिए विदेशी लोग अधिक मात्रा में आते है?

 (a) रोहतक

 (b) करनाल

 (c) गुडगाँव

 (d) फरीदाबाद

किस चोहान शासक ने तोमरो का अंत किया?

 (a) पृथ्वीराज III

 (b) विग्रहराज II

 (c) पृथ्वीराज I

 (d) इनमे से कोई नही

एक समचतुर्भुज की एक भुजा 5 सेमी तथा एक विकर्ण 8 सेमी है इसका क्षेत्रफल क्या होगा?

 (a) 20 वर्ग सेमी

 (b) 24 वर्ग सेमी

 (c) 26 वर्ग सेमी

 (d) 40 वर्ग सेमी

Consider the initial value problem (IVP) \(\frac{dy}{dx}=xy^{\frac{1}{2}},y(0)=0,(x,y)\in \mathbb{R} \times \mathbb{R}\) . Then, which of the following are correct?

(a) The function f(x, y) = \(xy^{\frac{1}{3}}\) does not satisfy a Lipschitz condition with respect to y in any neighborhood of y = 0.

(b) There exists a unique solution for the IVP.

(c) There exists no solution for the IVP.

(d) There exists more than one solution of the IVP.

The attribution of human form or qualities to things such as machines or computers is called?

Who were the first kings to issue gold coins in India?

(1) Mauryas                        (2) Indo-Greeks
(3) Guptas                          (4) Kushans

Write the strum sequence and find the eigen values of following matrix:

    \(\left[ \begin{array}{cc} 1&-1&0&0&0&0 \\ 1&1&-1&0&0&0 \\ 0&1&1&-1&0&0 \\ 0&0&1&1&-1&0 \\0&0&0&1&1&-1 \\ 0&0&0&0&1&1\end{array} \right]\)

What was the name of the Newspaper edited by Gandhiji till 1933?
(1) Sarvodaya
(2) Arya
(3) Times of India
(4) Young India

Which of the following was published by Gandhiji during his stay in South Africa?
(1) Young India
(2) Indian Opinion
(3) Nav Jivan
(4) None of these

Which great Indian leader was called Desh Nayak by Gurudev Rabindranath Tagore?

What was the immediate cause of the Mutiny of 1857?
(1) The discontentment of the soldiers
(2) The use of greased cartridges in the new Enfield Rifle
(3) The social conditions of India
(4) The introduction of railways and telegraphs

Let \(R\) be a commutative ring. Show that the set \(N=\{ a\in R |a^m =0\) for some positive integer m\(\}\) is an ideal of \(R\) which is contained in every prime ideal of \(R\). Further show that \(R/N\) is a ring with no non-zero nilpotent elements. \((N\) is called the nilradical of \(R)\).

The official court language of the Guptas was
(1) Pali                (2) Prakrit
(3) Hindi              (4) Sanskrit

The policy of ‘imperial preferences’ adopted by Britain in its colonies in 1932 is also known as the
(1) Hong Kong Agreement
(2) London Agreement
(3) Ottawa Agreement
(4) Paris Agreement

An element \(m\) of the \(R\)-module \(M\) is called a torsion element if \(rm=0\) for some non-zero element \(r \in R\) .

(i) Prove that if \(R\) is an integral domain then \(T\) or \((M)\) , the set of torsion elements of \(M\) , is a submodule of \(M\) (called the torsion submodule of \(M\)).

(ii) Give an example of a ring \(R\) and an \(R\)-module \(M\) such that \(T\) or\((M)\) is not an \(R\)-submodule.

(iii) If \(R\) has zero-divisors, show that every non-zero \(R\)-module has non-zero torsion elements.