List of top Questions asked in CUET (PG)

In the context of the mathematical identities found in Siddhantic trigonometry, choose the correct set of definitions:
A. \(\frac{\text{Trijya} \times \text{Kotijya}}{\text{Bhujajya}} = \text{Kotisparsharekha} \) (Cotangent)
B. \(\text{Bhujajya} - \text{Trijya} = \text{Natamshajya} \)
C. \(\frac{\text{Trijya} \times \text{Kanchha}}{\text{Tri}} = \text{Vijya} \)
D. \(\text{Tri} - \text{Bhujajya} = \text{Padujya} \)
E. \(\frac{\text{Bhujajya} \times \text{Jizjya}}{\text{Trijya}} = \text{Kranjya} \) (Sine of Declination)

Identify the correct definitions for celestial coordinate circles and parameters used in 'Goladhyaya' (Spherical Astronomy):
A. The arc of the ecliptic between the equator and the planet is called 'Kranti' (Declination).
B. The circle passing through the celestial poles and the planet's position is the 'Ahoratravritta' (Diurnal Circle).
C. The angular distance between the North Pole and the Zenith is the 'Sthanaksha' (Co-latitude).
D. The arc of the meridian between the Zenith and the celestial North Pole is called 'Lambansha'.
E. The vertical distance of a planet above the horizon is called 'Lagnansha'.

According to the decimal place-value system (Dashagunanika) used in Indian mathematics, identify the correct numerical equivalents for the following terms:
A. Sahasram = 1,000
B. Abjam = 100,000
C. Laksham = 100,000
D. Prayutam = 1,000,000
E. Koti = 1,000,000

Identify the correct structural definitions from the 'Samhita' and 'Siddhanta' literature regarding the division of time and cycles:
A. Brihat Samhita states that exactly 100 Deva-years constitute a Mahayuga.
B. Exactly 60 Ghatikas constitute one complete Savana day (60 Ghatis = 1 Day).
C. Exactly 4 Yugas (Krita, Treta, Dvapara, Kali) together form one 'Mahayuga'.
D. A standard lunar month consists of exactly 30 lunar days (Tithis).
E. One 'Kritayuga' consists of 432,000 human years.

Identify the correct definitions for various time-measures (Manas) related to the Sun and Devas:
A. One complete solar year for humans is equal to one 'Deva-day' (day and night).
B. The duration between two consecutive sunrises on Earth is a 'Savana' day.
C. One complete solar year is equal to one 'Pitra-day'.
D. The time taken for the Sun to move between two successive conjunctions is a 'Saura' month.
E. One 'Savana' month consists exactly of 30 lunar days (tithis).

Identify the correct statements regarding the classification of Time (Kaala) in Indian Astronomy from the following:
A. Lokanama-antakrit-kalah: Time is the ultimate destroyer of all worlds and beings.
B. Pranadi-kathito murtakalah: Time measured from 'Prana' onwards is called 'Murta' (manifest).
C. Trutyadyo-amurtakalah: Time measured from 'Truti' onwards is called 'Amurta' (unmanifest/abstract).
D. Nadi-shashtya tu nakshatrakalah: Exactly sixty Nadis constitute one sidereal day (Nakshatra-ahoratra).
E. Sthulakalah murtakalo bhavati: Gross time (calculable by humans) is equivalent to Murta time.

Categorize the following astronomical works into their correct traditional genres (Karana, Arsha, Tantra, etc.):
A. Grahalaghava: Karanagrantha
B. Suryasiddhanta: Arshagrantha (Divine Revelation)
C. Aryabhatiya: Tantragrantha
D. Siddhantashiromani: Tantragrantha
E. Ketaki Grahaganita: Tantragrantha

Based on the provided chronological data for astronomers, which of the following sets of dates are correctly associated with their respective authors?
A. Nilakantha: 1556 CE
B. Ramadaivajna: 1565 CE
C. Narayana: 1571 CE
D. Munishvara: 1225 CE
E. Divakara: 1265 CE

Identify the correct trigonometric identities used in Indian mathematical astronomy from the following list:
A. Jya(A + B) = (Jya A \(\cdot\) Kotijya B + Kotijya A \(\cdot\) Jya B) R
B. Jya(A - B) = (Jya A \(\cdot\) Kotijya B - Kotijya A \(\cdot\) Jya B) R
C. Kotijya(A + B) = (Kotijya A \(\cdot\) Kotijya B - Jya A \(\cdot\) Jya B) R
D. Kotijya(A - B) = (Kotijya A \(\cdot\) Kotijya B + Jya A \(\cdot\) Jya B) R
E. Jya(A + B) = 2 \(\cdot\) Jya A \(\cdot\) Kotijya B

According to the properties of the Sine (Jya) and Cosine (Kotijya) in the four quadrants of the celestial circle, identify the correct statements from the following:
A. In the first quadrant, Jya (Sine) is positive.
B. In the second quadrant, Jya is negative.
C. In the third quadrant, Jya is positive.
D. In the fourth quadrant, Jya is negative.
E. In the fourth quadrant, Kotijya (Cosine) is positive.

Identify the correct geometric definitions related to quadrilaterals and triangles from the following statements:
A. A figure with four equal angles and equal opposite sides is an 'Ayata' (Rectangle).
B. The sum of three angles of a triangle is less than two right angles.
C. A triangle with one angle equal to 90 degrees is a 'Sama-konam' (Right triangle).
D. A figure with all four sides equal and all four angles equal is a 'Samachatur-bhuja' (Square).
E. A triangle is defined as having exactly 5 primary components.

Arrange the following steps of 'Spashta-graha-sadhana' (calculating true planetary position) in their correct mathematical sequence:
A. Mean Planet +/- Half Sheeghra Correction
B. First Manda Correction
C. Second (Final) Sheeghra Correction
D. Manda-spashta Planet
E. Anomaly (Sheeghra-kendra) Calculation

In the calculation of the Sun's longitude using the Ahargana (cumulative day count) method in 'Grahalaghava', arrange the following computational steps in their correct functional sequence:
A. Ahargana 150 = Phalam (result in minutes)
B. Finding the total Ahargana (Day count)
C. Ahargana 70 = Phalam
D. Summation of results to find the Sun's position
E. Ahargana 70 = Phalam (result in degrees)

Arrange the following astronomical texts in chronological order based on their period of composition:
A. Brahmasphutasiddhanta
B. Trishatika
C. Panchasiddhantika
D. Aryabhatiya
E. Khandakhadyaka

Arrange the following planets in increasing order of their 'Asta-kalasha' (Arc of visibility/setting degrees):
A. Neechasthah Shukrah (Venus at perigee)
B. Guruh (Jupiter)
C. Shanih (Saturn)
D. Mangalah (Mars)
E. Margi Budhah (Direct Mercury)

In Aryabhata's alphabetical notation system, arrange the following syllables in increasing order of the decimal place values they represent:
A. Ri
B. Ki
C. Ra
D. Yu
E. Ku

Arrange the following celestial elements in the correct logical sequence of their study/definition while learning spherical astronomy:
A. Yamya-uttaravrittam (Meridian)
B. Khamadhyam (Zenith)
C. Shanku (Gnomon)
D. Drigvrittam (Vertical Circle)
E. Kshitijavrittam (Horizon)

Arrange the following phases of a total solar eclipse in their correct chronological sequence:
A. Mokshah (Release)
B. Sparshah (First Contact)
C. Sammilanam (Total Immersion)
D. Unmilanam (Emergence)
E. Madhyam (Maximum Phase)

Arrange the following Nakshatras in their correct reverse order (Vyutkramah) relative to their standard sequence:
A. Ashlesha
B. Swati
C. Purva Phalguni
D. Anuradha
E. Hasta

According to the Surya Siddhanta, what is the correct downward sequence of the planetary orbits starting from the orbit of Saturn?

Arrange the following day-measures (Dina-manas) in increasing order of their duration (Vriddhy-anusaram):
A. Savana-dinam (Terrestrial Day)
B. Paitra-dinam (Lunar Month)
C. Nakshatra-dinam (Sidereal Day)
D. Brahma-dinam (Kalpa)
E. Divya-dinam (Solar Year)

In the 'Pitra-day' (time-measure for the Manes), what is the correct chronological sequence of lunar tithis from the moment of their sunrise to midnight?

Arrange the following Ritus (Seasons) in their correct sequential order starting from the month of Chaitra (the beginning of the lunar year):
A. Grishma (Summer)
B. Sharad (Autumn)
C. Vasanta (Spring)
D. Hemanta (Pre-winter)
E. Varsha (Monsoon)

Assertion (A): If the first number \( k = 5 \) and the second number \( kh = 10 \), then the square of their sum is 225.
Reason (R): This is derived from the algebraic identity: \( (k + kh)^2 = k^2 + 2k \cdot kh + kh^2 \).

Assertion (A): The center of the Ecliptic (Kranti-vritta) and the North Pole of the Ecliptic (Kadamba) are essential reference points in celestial geometry.
Reason (R): This is because the distance between the pole of a circle and every point on that circle is exactly ninety degrees (90\(^\circ\)).