Q1
5 marksComplex Numbers ArithmeticLocating Points in the Complex Plane (Quadrant/Axis)View
The point corresponding to the complex number $\frac { 2 - \mathrm { i } } { 1 - 3 \mathrm { i } }$ in the complex plane is located in which quadrant? A. First quadrant B. Second quadrant C. Third quadrant D. Fourth quadrant
Let $U = \{ 1,2,3,4,5,6 \} , A = \{ 1,3,6 \} , B = \{ 2,3,4 \}$. Then $A \cap \left( \complement_U B \right) =$ A. $\{ 3 \}$ B. $\{ 1,6 \}$ C. $\{ 5,6 \}$ D. $\{ 1,3 \}$
Q3
5 marksConic sectionsFocal Distance and Point-on-Conic Metric ComputationView
The parabola $y ^ { 2 } = 2 p x ( p > 0 )$ has its focus at a distance of $\sqrt { 2 }$ from the line $y = x + 1$. Then $p =$ A. 1 B. 2 C. $2 \sqrt { 2 }$ D. 4
Q6
5 marksNormal DistributionMultiple-Choice Conceptual Question on Normal Distribution PropertiesView
The measurement result of a certain physical quantity follows a normal distribution $N \left( 10 , \sigma ^ { 2 } \right)$. Which of the following conclusions is incorrect? A. The smaller $\sigma$ is, the greater the probability that the physical quantity falls in $( 9.9,10.1 )$ in a single measurement. B. The smaller $\sigma$ is, the probability that the physical quantity is greater than 10 in a single measurement is 0.5. C. The smaller $\sigma$ is, the probability that the physical quantity is less than 9.99 equals the probability that it is greater than 10.01 in a single measurement. D. The smaller $\sigma$ is, the probability that the physical quantity falls in $( 9.9,10.2 )$ equals the probability that it falls in $( 10,10.3 )$ in a single measurement.
Q7
5 marksLaws of LogarithmsCompare or Order Logarithmic ValuesView
Given $a = \log _ { 5 } 2 , b = \log _ { 8 } 3 , c = \frac { 1 } { 2 }$, which of the following judgments is correct? A. $c < b < a$ B. $b < a < c$ C. $a < c < b$ D. $a < b < c$
Q8
5 marksComposite & Inverse FunctionsSymmetry, Periodicity, and Parity from Composition ConditionsView
Given that the domain of function $f ( x )$ is $\mathbb { R }$, $f ( x + 2 )$ is an even function, and $f ( 2 x + 1 )$ is an odd function, then A. $f \left( - \frac { 1 } { 2 } \right) = 0$ B. $f ( - 1 ) = 0$ C. $f ( 2 ) = 0$ D. $f ( 4 ) = 0$
Which of the following statistics can measure the dispersion of the sample $x _ { 1 } , x _ { 2 } , \cdots , x _ { n }$? A. The standard deviation of the sample $x _ { 1 } , x _ { 2 } , \cdots , x _ { n }$ B. The median of the sample $x _ { 1 } , x _ { 2 } , \cdots , x _ { n }$ C. The range of the sample $x _ { 1 } , x _ { 2 } , \cdots , x _ { n }$ D. (option D not fully provided in source)