Latest Questions

_____ bit is also called as the most significant bit or sign bit.

(a) Show that the center of a group \(G\) is a characteristic subgroup of \(G\).

(b) Prove that characteristic subgroups are normal. Give an example of a normal subgroup which is not characteristic.

(c) Show that if \(H\) is the only subgroup of order \(n\) in \(G\), or if \(H\) is the only subgroup of index \(k\) in \(G\), then \(H\) is characteristic in \(G\).

‘There are no politics devoid of religion’ is stated by
(1) Nehru
(2) Gandhi
(3) Vinoba Bhave
(4) Jaya Prakash Narayan

सिखों का प्रमुख त्यौहार कौन-सा है ?

4 1/2% स्टॉक में रु 9600 निवेश करने पर 360 वार्षिक आय हो, तो रु 100 के स्टॉक का मूल्य कितना होगा?

 (a) 115

 (b) 120

 (c) 100

 (d) 125

In which Rock Edict Ashoka mentions the casualties of the Kalinga War and declares the renunciation of war?

(1) Maski Edict
(2) Rock Edict \(\mathrm{XIII}\)
(3) Rock Edict \(\mathrm{XI}\)
(4) Rock Edict \(\mathrm{X}\)

Mahatma Gandhi started his Dandi March from
(1) Dandi
(2) Porbandar
(3) Ahmedabad
(4) Sabarmati Ashram

What is Aditya-L1 that is often mentioned in news?

1) Rover sent to Mars by Indian Space Research Organisation (ISRO)

2) Half-humanoid developed by ISRO for mission Gaganyaan.

3) ISRO's first scientific expedition to study the Sun.

4) ISRO's first telescope to study the outer atmosphere of Sun.

Ajanta Caves were built during period of
(1) Gupta                  (2) Kushana
(3) Maurya                (4) Chalukya

Who was the founder of Kolkata’s first “Atmiya Sabha” (philosophical discussion circle) held in 1815?
(1) Ram Mohan Roy
(2) Lala Lajpat Rai
(3) Rabindranath Tagore
(4) Jawahar Lal Nehru

Let \(X\) be a first countable space and let \(A\) be a subset of \(X\). Then the following are true:

(1) (Sequence Lemma) \(A\) point \(x \in \overline{A}\) if and only if there is a sequence of points of A converging to \(x\).

(2) (Continuity Versus Sequential Continuity) Let \(f: X \rightarrow Y\) . Then \(f\) is continuous if and only if \(f\) is sequentially continuous.

“Earth provides enough to satisfy everyman’s need but not everyman’s greed”. Who said this?

(1) Guru Nanak Dev
(2) Mahatma Gandhi
(3) Pope Paul \(\mathrm{VI}\)
(4) Smt. Indira Gandhi

The great silk route to the Indians was opened by :

(1) Kanishka           (2) Ashoka
(3) Harsha              (4) Fa-Hien

Give five of your favourite metrics on \(\mathbb{R^2}\).

Who among the following introduced the Mansabdari system?

(1) Shah Jashan                              (2) Sher Shah
(3) Akbar                                          (4) Jahangir

Which monument is known as the “Dream in Stones’?
(1) Char Minar
(2) Ajanta Caves
(3) Sanchi Stupa
(4) Panch Mahal

__________was the first Muslim ruler of Delhi.
(1) Akbar
(2) Shahjahan
(3) Qutub-ud-din-Aibak
(4) Ala-ud-din Khilji