TS Polycet (Polytechnic) 2015 Previous Question Paper with Answers And Model Papers With Complete Analysis

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Q). The probability of guessing the correct answer to a certain test question is x/12. he probability of not guessing the correct answer to this question is 2/3, then x =
A) 2
B) 3
C) 4
D) 6

View Answer

C) 4
Explanation: P(A)= x/12, P( $\overline A$

)
∴P(A)= P( $\overline A$

) = 1
x/12 +2/3 = 1
⇒ x/12 = 1-2/3 ⇒ x/12=1/3 ⇒ x=12/3 = 4

Q). The width of the rectangle in a histogram represents
A) mid-values
B) frequency
C) number of classes
D) class interval

View Answer

D) class interval
Explanation: Class interval

Q). Which of the following cannot be determined graphically?
A) Mean
B) Median
C) Mode
D) None

View Answer

A) Mean
Explanation: Mean

Q). The mean of x and 1/x is M, then the mean of x³ and 1/x³ is
A) M³
B) M³+3
C) M(4M²-3)
D) $\frac{(4M^2\;\;-\;3)}2M$

View Answer

C) M(4M²-3)
Explanation: $\overline x$

= Mean ⇒ $\frac{x+{\displaystyle\frac1x}}2$

=M⇒x+1/x = 2M
Mean = $\frac{x^3+{\displaystyle\frac1{x^3}}}2$

= $\frac12\lbrack(x+\frac1x)^3-3x\frac1x(x+\frac1x)\rbrack$

= $\frac12\lbrack(2M)^3-3(2M)\rbrack$

= $\frac12(8M^3-6M)$

= 4M³ – 3M = M(4M²-3)

Q). From the following distribution, find the number of pupils who scored less than 40 marks:

Class interval	0-9	10-19	20-29	30-39	40-49	50-59
Frequency	6	5	7	9	8	4

A) 18
B) 11
C) 28
D) 27

View Answer

D) 27
Explanation: The number of pupils who scored less than 40 marks = 6 + 5 + 7 + 9 = 27

Q). From the following table, what is AM?

X	1	2	3	4	…….	n
y	1	2	3	4	…….	n

A) 2n+1
B) $\frac{2n+1}2$

C) $\frac{2n+1}3$

D) $\frac{n(n+1)}2$

View Answer

C) $\frac{2n+1}3$

Explanation: AM = $\frac{\Sigma fx}{\Sigma f}$

= $\frac{1.1\;+\;2.2\;+\;3.3\;+\;4.4\;+...................+\;n.n}{1+2+3+4+\;.........+n}$

= $\frac{12\;\;+22-+32\;\;+\;42\;+...........+n^2}{1+2+3+4+\;.........+n}$

= $\frac{\displaystyle\frac{ri(n+1)(2n+1)}6}{\displaystyle\frac{n(n+1)}2}$

= 2n+1/3

Q). If HCF (26,169) = 13, then LCM (26, 169) =
A) 26
B) 52
C) 338
D) 13

View Answer

C) 338
Explanation: L.C.M x H.C.F = a x b
L.C.M.,x 13 = 26 x 169
L.C.M. = 26×169/13
L.C.M. = 2×169 = 338

Q). If log ₁₀ 2 = 0.3010, then the number of digits in 4²⁰¹³ is
A) 1211
B) 1212
C) 1210
D) None

View Answer

B) 1212
Explanation: log ₁₀ 2 = 0.3010
4²⁰¹³= (2²)²⁰¹³ = 2⁴⁰²⁶
log ₂ 4026 = 4026(log 2)
= 4026 (0.3010)
= 1211.826 = 1212
Number of digits in 4²⁰¹³ = 1212.

Q). $\sqrt[4]{81\;} - 8\sqrt[3]{216\;} +15\sqrt[5]{32\;} + \sqrt{225}$ =
A) 0
B) -1
C) 2
D) 7