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Question 21
A
B
C
D
Explanation.
Share Answer \(\begin{vmatrix} 5 & 3 \\ x & 2 \end{vmatrix}\) = \(\begin{vmatrix} 3 & 5 \\ 4 & 5 \end{vmatrix}\)

10 - 3x = 15 - 20

-3x = 15 - 20 - 10

-3x = -15

x = 5

Correct Option:
C

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Question 22
A
-1 
B
C
D
Explanation.
Share Answer Recall that a unit matrice is a diagonal matrix in which the elements in the leading diagonal is unity. Therefore,

I3 = \(\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}\)

I3 = \(+1\begin{vmatrix} 1 & 0 \\ 0 & 1 \end{vmatrix} - 0\begin{vmatrix} 0 & 0 \\ 0 & 1 \end{vmatrix} + 0 \begin{vmatrix} 0 & 1 \\ 0 & 0 \end{vmatrix} \)

I3 = +1(1 - 0) - 0(0 - 0) + 0(0 - 0)

= 1(1)

= 1

Correct Option:
C



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Question 25
A
line parallel to 7x + 13y + 8 = 0 
B
circle 
C
semicircle 
D
bisector of the line 7x + 13y + 8 = 0 
Explanation.
Share Answer

No official Explanation yet!


Correct Option:
A

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Question 26
A
\(\frac{1}{2}\) 
B
\(\frac{2}{5}\) 
C
\(-\frac{4}{7}\) 
D
\(-\frac{2}{3}\) 
Explanation.
Share Answer PQ = \(\frac{y_1 - y_0}{x_1 - x_0}\) = \(\frac{-3 - (-7)}{-2 - 5}\) = \(\frac{-3 + 7}{-2 - 5}\) = \(\frac{4}{-7}\)

Correct Option:
C

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Question 27
A
\(\sqrt{13}\) 
B
\(3\sqrt{2}\) 
C
\(\sqrt{26}\) 
D
\(10\sqrt{5}\) 
Explanation.
Share Answer P1 (4, 3), P2 (x, y)

y = 2x + 4 .....(1)

y = 7 - x .....(2)

Substitute (2) in (1)

7 - x = 2x + 4

7 - 4 = 2x + x

3 = 3x

x = 1

Substitute in eqn (2)

y = 7 - x

y = 7 - 1

y = 6

P2 (1, 6)

Distance between 2 points is given as

D = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

D = \(\sqrt{(1 - 4)^2 + (6 - 3)^2}\)

D = \(\sqrt{(-3)^2 + (3)^2}\)

D = \(\sqrt{9 + 9}\)

D = \(\sqrt{18}\)

D = \(\sqrt{9 \times 2}\)

D = \(3\sqrt{2}\)

Correct Option:
B

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Question 28
A
y = 2x - 3 
B
y = 2x + 5 
C
y = 3x - 2 
D
y = 2x + 1 
Explanation.
Share Answer \(\frac{y - y_1}{x + x_1}\) = \(\frac{y_2 - y_1}{x - x_1}\)

\(\frac{y - 1}{x + 2}\) = \(\frac{4 - 1}{-\frac{1}{2} + 2}\)

= \(\frac{y - 1}{x + 2}\) = \(\frac{3}{\frac{3}{2}}\)

y = 2x + 5

Correct Option:
B

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Question 29
A
\(\frac{1}{2}\) 
B
\(\frac{\sqrt{2}}{2}\) 
C
\(-\frac{\sqrt{2}}{2}\) 
D
\(-\frac{1}{2}\) 
Explanation.
Share Answer

\(\theta\) = 135o

Cos 135o = Cos(90 + 45)o

= cos90ocos45o - sin90osin45o

= 0cos45o - (1 x \(\frac{\sqrt{2}}{2}\))

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


Correct Option:
C

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Question 30
A
2x - \(\frac{1}{x^2}\) 
B
2x + x2 
C
2x - x2 
D
2x + \(\frac{1}{x^2}\) 
Explanation.
Share Answer y = x2 - \(\frac{1}{x}\)

y = x2 - x-1

\(\frac{\delta y}{\delta x}\) = 2x + x-2


\(\frac{\delta y}{\delta x}\) = 2x + \(\frac{1}{x^2}\)

Correct Option:
D

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