List of top Questions asked in CUET (PG)

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.
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)
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.
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
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
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 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)
Arrange the following astronomical texts in chronological order based on their period of composition:
A. Brahmasphutasiddhanta
B. Trishatika
C. Panchasiddhantika
D. Aryabhatiya
E. Khandakhadyaka
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
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\(^\circ\)).
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)
According to the Surya Siddhanta, what is the correct downward sequence of the planetary orbits starting from the orbit of Saturn?
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)
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?
Assertion (A): The formula for the Lambajya (Cosine of Latitude) can be expressed as: \( \text{Lambajya} = \frac{\text{Palabha} \times \text{Trijya}}{\text{Palakarna}} \).
Reason (R): This is because all 'Aksha-kshetras' (latitude triangles) in a sphere are similar triangles (Sajatiya Kshetras).
Assertion (A): The phenomenon of eclipses arises from the periodic conjunction (Amavasya) and opposition (Purnima) of the Sun and the Moon.
Reason (R): This celestial geometry is mathematically derived from the remnants (Shesha) of the solar and lunar months and the calculation of intercalary months (Adhimasa).
Assertion (A): The calculation of Ahargana (cumulative day count) is performed primarily to determine the mean positions of planets (Madhyama-sadhana).
Reason (R): This is because the mathematical relationship between time and planetary revolutions leads to the manifestation of their visible celestial motion.
Assertion (A): The concept of 'Vidhoma' and 'Paitra' lunar cycles refers to the specific month-types defined in Vedic time-keeping.
Reason (R): This is based on the standard rule that exactly thirty lunar days (Tithis) constitute a lunar month (Chandra Maasa).
Assertion (A): In the standard sine-table derivation, the difference $3538 - 3534 = 4$ represents the value of the first Utkramajya (Versine).
Reason (R): This value is geometrically derived from the relationship between the radius (Vyasardha) and the standard sines of a quadrant.
Assertion (A): The specific differences in longitudes between signs, such as the pair (21, 29), are crucial for determining local planetary times.
Reason (R): This is because the local time of rising (Udaya-Maana) for signs varies based on the latitude of the observer.
What is the name for the difference between the true longitude (Spashta) and mean longitude (Madhyama) of a planet?
What is the technical name given to the difference (elongation) between the longitudes of the Sun and the Moon?