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CUET PG MCA Progressions PYQ

CUET PG MCA PYQ
The a, b, c and d are in GP and are in ascending order such that a+d = 112 and b+c 48. If the GP is continued with a as the first term, then the sum of the first six terms is:





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CUET PG MCA Previous Year PYQ CUET PG MCA CUET 2022 PYQ

Solution

CUET PG MCA PYQ
Match the list
LIST 1 LIST 2
A. If 4th term of a G.P. is square of its second term, and its first term is 3, then common ratio is _______ I. 5
B. The first term of an AP is 5 and the last term is 45 and the sum of the terms is 400. The number of terms is_____ II. -5/2
 C. The sum of three numbers which are in AP is 27 and sum of their squares is 293. Then the common difference is ______ III. 16
D. The fourth and 54th terms of an AP are, respectively, 64 and -61. The common difference is ______ IV. 3
choose the correct answer from the options given below:





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Solution

CUET PG MCA PYQ
If a, b and c are in Geometric Progression and $a^{\frac{1}{x}}=b^{\frac{1}{y}}=c^{\frac{1}{z}}$ then, x, y, z are in
1. Arithmetic Progression
2. Geometric Progression
3. $\frac{2}{y}=\frac{1}{x}+\frac{1}{z}$
4. $x=y+z$






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Solution

We are given:

\(a^{\tfrac{1}{x}} = b^{\tfrac{1}{y}} = c^{\tfrac{1}{z}} = k\)

\(\Rightarrow a = k^x,\; b = k^y,\; c = k^z\)

Since \(a, b, c\) are in G.P.:

\(b^2 = ac\)

\(\Rightarrow (k^y)^2 = (k^x)(k^z)\)

\(\Rightarrow k^{2y} = k^{x+z}\)

\(\Rightarrow 2y = x+z\)

This implies \(y\) is the arithmetic mean of \(x\) and \(z\).

\(\therefore\; x, y, z \text{ are in Arithmetic Progression.}\)

Correct Answer: (1) Arithmetic Progression

CUET PG MCA PYQ
The arithmetic means of two observations is 125 and their geometric mean is 60. Find the harmonic mean of the two observations.





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CUET PG MCA PYQ
The terms $1,\, \log _y(x),\, \log _z(y)\, and\, 15\log _x(z)$ are in AP.

Based on this information answer the following questions. 
The Common difference of AP is 





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CUET PG MCA PYQ
The terms $1,\, \log _y(x),\, \log _z(y)\, and\, 15\log _x(z)$ are in AP.

Based on this information answer the following questions. 
The value of xy is:  





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Solution

CUET PG MCA PYQ
The terms $1,\, \log _y(x),\, \log _z(y)\, and\, 15\log _x(z)$ are in AP.

Based on this information answer the following questions. 
yz is equal to : 





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Solution

CUET PG MCA PYQ
Math List I with List II:
 LIST I LIST 2
 A. In a GP, the third term is 24 and 6th term is 192. The common ratio is _____ I. 78
 B. Let Sn denotes the sum of first n terms of an AP. If S2n=3Sn, then S3n/Sn equals to _______ II. 6
 C. The sum of 3 terms of a GP is 13/12 and their product is -1. The first term is ______ III. -1
 D. The least value of n for which the sum 3+6+9+...+n is greater than 1000 is  IV. 2
Choose the correct answer from the options given below :





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