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Question 1
A
{2, 3} 
B
{2, 3, 4} 
C
{3, 4, 6} 
D
{2} 
Explanation.

T = {evenn numbers from 1 to 12}
N = {common factors of 6,8 and 12}
Find T ∩ N
T = {2, 4, 6, 8, 10, 12}
N = {2}
T ∩ N = {2} i.e value common to T & N


Correct Option:
D

Question 2
A

\(\frac{1}{3}\)

 
B

\(\frac{2}{8}\)

 
C

\(\frac{3}{7}\)

 
D

\(\frac{1}{8}\)

 
Explanation.
2, 1, \(\frac{1}{2}\), \(\frac{1}{4}\).....

There are 4 terms in the series
Therefore the next number will be the 5th term

Tn = ar\(^{n - 1}\) (formular for geometric series)

a = first term = 2

r = common rate = \(\frac{\text{next term}}{\text{previous term}}\) = \(\frac{1}{2}\)

n = number of terms

T5 = 5th term = ?

T5 = ar\(^{5 - 1}\)

= ar\(^4\)

= 2 \(\times\) (ar\(^{n - 1}\))4

= 2 \(\times\) \(\frac{1}{16}\)

= \(\frac{1}{8}\)

Correct Option:
D

Question 3
A
\(\frac{3}{4}\) 
B
\(\frac{3}{10}\) 
C
\(\frac{1}{4}\) 
D
\(\frac{1}{20}\) 
Explanation.
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

E1 = {3, 6, 9, 12, 15, 18}

E2 = {4, 8, 12, 16, 20}

Probability of E2 = \(\frac{5}{20}\) i.e \(\frac{\text{Total number in}E_2}{\text{Entire number in set}}\)

Probability of set E2 = 1 ? \(\frac{5}{20}\)

= \(\frac{15}{20}\)

= \(\frac{3}{4}\)

Correct Option:
A

Question 4
A

2.6cm

 
B

3.5cm

 
C

3.6cm

 
D

7.0cm

 
Explanation.
Curved surface area of cylinder = 2πrh

110 = 2 \(\times\) \(\frac{22}{7}\) \(\times\) r \(\times\) 5

r = \(\frac{110 \times 7}{44 \times 5}\)

= 3.5cm

Correct Option:
B

Question 5
A

q - \(\frac{8}{7}\)

 
B

7 - \(\frac{q}{4}\)

 
C

8 - \(\frac{q}{2}\)

 
D

7 + \(\frac{q}{8}\)

 
Explanation.
Y = Px2 + q

Y = 2x2 - 1

Px2 + q = 2x2 - 1

Px2 = 2x2 - 1 - q

p = \(\frac{2x^2 - 1 - q}{x^2}\)

at x = 2

P = \(\frac{2(2)^2 - 1 - q}{2^2}\)

= \(\frac{2(4) - 1 -q}{4}\)

= \(\frac{8 - 1 - q}{4}\)

P = \(\frac{7 - q}{4}\)

Correct Option:
B

Question 6
A

\(\frac{\sqrt{3}}{2\sqrt{2}}\)

 
B

-3 - \(\frac{1}{2}\)

 
C

\(\frac{1}{2}\)-2

 
D

1 + \(\frac{\sqrt{2}}{2}\)

 
Explanation.
hypotenuse
sin = \(\frac{1}{2}\)

\(\sin45 = \frac{1}{\sqrt{2}}\)

= \(\frac{2}{2}\)

= (sin45 + sin30)

= \(\frac{1}{\sqrt{2}} + \frac{1}{2}\)

= \(\frac{\sqrt{2}}{2}\) + \(\frac{1}{2}\)

= \(\frac{\sqrt{2} + 1}{2}\)

= \(\frac{1 + \sqrt{2}}{2}\)

Correct Option:
D

Question 7
A
\(\frac{- \pi}{2}\) 
B
-1 
C
D
\(\frac{ \pi}{2}\) 
Explanation.
y = xsinx

\(\frac{dy}{dx}\) = \(1 \sin x + x \cos x\)

= \(\sin x + x \cos x\)

At x = \(\frac{\pi}{2}\)

= sin\(\frac{\pi}{r}\) + \(\frac{\pi}{2} \cos {\frac{\pi}{2}}\)

= 1 + \(\frac{\pi}{2}\) \(\times\) 10

= 1

Correct Option:
C

Question 8
A

24oC

 
B

20oC

 
C

34oC

 
D

30oC

 
Explanation.
t α h, t = 20, h

t = ? h = 60

t = kh where k is constant

20 = 50k

k = \(\frac{20}{50}\)

k = \(\frac{2}{5}\)

when h = 60, t = ?

t = \(\frac{2}{5}\) \(\times\) 60

t = 24oC

Correct Option:
A

Question 9
A
B
C
2\(\frac{2}{3}\) 
D
3\(\frac{2}{3}\) 
Explanation.

No official Explanation yet!

Correct Option:
D

Question 10
A
\(\frac{\text{NSL}}{M}\) 
B
\(\frac{N^2SL}{M^2}\) 
C
\(\frac{N^2SL}{M}\) 
D
\(\frac{NSL}{M^2}\) 
Explanation.
M = \(\frac{\sqrt{SL}}{T}\),

make T subject of formula square both sides

M2 = \(\frac{N^2SL}{T}\)

TM2 = N2SL

T = \(\frac{N^2SL}{M^2}\)

Correct Option:
B

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