Q1
mcq
1 mark
If $\{(a, 8), (6, b)\}$ represents an identity function, then the value of $a$ and $b$ are respectively:
- A. $(8, 6)$
- B. $(8, 8)$
- C. $(6, 8)$
- D. $(6, 6)$
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Q2
mcq
1 mark
$f(x)=\dfrac{x^{11}}{3}-(x-1)^3$ represents a function which is:
- A. linear
- B. cubic
- C. reciprocal
- D. quadratic
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Q3
mcq
1 mark
If the H.C.F. of 65 and 117 is expressible in the form of $65m-117$, then the value of $m$ is:
- A. 4
- B. 2
- C. 1
- D. 3
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Q4
mcq
1 mark
The value of $(1^3+12^3+13^3+\cdots+115^3)-(11+21+31+\cdots+115)$ is:
- A. 14400
- B. 14200
- C. 14280
- D. 14520
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Q5
mcq
1 mark
The solution of the system $x+y-3z=-6$, $-7y+17z=7$, $3z=9$ is:
- A. $x=1, y=2, z=3$
- B. $x=-1, y=2, z=3$
- C. $x=-1, y=-2, z=3$
- D. $x=1, y=-2, z=3$
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Q6
mcq
1 mark
For the given matrix $A=\begin{pmatrix}1&3&5&7\\2&4&6&8\\9&11&13&15\end{pmatrix}$, the order of the matrix $A^T$ is:
- A. $2\times 3$
- B. $3\times 2$
- C. $3\times 4$
- D. $4\times 3$
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Q7
mcq
1 mark
Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, what is the distance between their tops?
- A. 13 m
- B. 14 m
- C. 15 m
- D. 12.8 m
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Q8
mcq
1 mark
The point of intersection of the straight lines $3x-y=4$ and $x+y=8$ is:
- A. $(5, 3)$
- B. $(2, 4)$
- C. $(3, 5)$
- D. $(4, 4)$
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Q9
mcq
1 mark
The straight line given by the equation $x=11$ is:
- A. Parallel to X axis
- B. Parallel to Y axis
- C. Passing through the origin
- D. Passing through the point $(0, 11)$
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Q10
mcq
1 mark
If $\tan\theta\cdot\cot\theta=2$, then $\tan^2\theta\cdot\cot^2\theta$ is equal to:
- A. 2
- B. 4
- C. 2
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Q11
mcq
1 mark
A solid sphere of radius $x$ cm is melted and cast into a shape of a solid cone of same radius. The height of the cone is:
- A. $3x$ cm
- B. $x$ cm
- C. $4x$ cm
- D. $2x$ cm
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Q12
mcq
1 mark
A spherical ball of radius $r_1$ units is melted to make 8 new identical balls each of radius $r_2$ units. Then $r_1:r_2$ is:
- A. 2 : 1
- B. 1 : 2
- C. 4 : 1
- D. 1 : 4
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Q13
mcq
1 mark
For a collection of data, $\Sigma x^2=140$, $\Sigma x=28$ and $n=7$, the standard deviation is:
- A. 4
- B. 2
- C. 16
- D. 8
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Q14
mcq
1 mark
The probability of a red marble selected at random from a jar containing $p$ red, $q$ blue and $r$ green marbles is:
- A. \(\dfrac{q}{p+q+r}\)
- B. \(\dfrac{p}{p+q+r}\)
- C. \(\dfrac{p+q}{p+q+r}\)
- D. \(\dfrac{p+r}{p+q+r}\)
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