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  MATH SAMPLE QUESTION PAPER Class X Session 2023-24 MATHEMATICS STANDARD (Code No.041) Question 4 The nature of roots of the quadratic equation 9x2 – 6x – 2 = 0 is: (a)  No real roots (b)  2 equal real roots (c)  2 distinct real roots (d)  More than 2 real roots   Explanation :  To determine the nature of the roots of the quadratic equation  9x^2 - 6x - 2 = 0 , we need to calculate the discriminant   b^2 - 4ac  where a = 9 , b = -6 and c= -2 when we compare with  a x^2 + bx +c = 0 Discriminant =  b^2 - 4ac = (-6) ^2 - 4 x (9) x (-2) => 36 -(-72) = 36+ 72 => 108 Since the discriminant is positive (108>0), the quadratic equation has two distinct real roots . So, the correct option is: ? Guess the Option and comment below   👇

  MATH SAMPLE QUESTION PAPER Class X Session 2023-24 MATHEMATICS STANDARD (Code No.041) Question 3 The lines representing the given pair of linear equations are non-intersecting. Which of the following statements is true?   \begin{flalign} (a)\;\;& \frac{a1}{a2} =\frac{b1}{b2} =\frac{c1}{c2}&\\ (b)\;\;& \frac{a1}{a2} =\frac{b1}{b2} \neq\frac{c1}{c2}&\\ (c)\;\;& \frac{a1}{a2} \neq\frac{b1}{b2} =\frac{c1}{c2}&\\ (d)\;\;& \frac{a1}{a2} \neq\frac{b1}{b2} \neq\frac{c1}{c2}&\\ \end{flalign} Explanation :  Let us examine each choice and determine the right response. \[(a) \  \  \frac{a1}{a2}  = \frac{b1}{b2} = \frac{c1}{c2} \] This option suggests that the ratios of the coefficients for x and y and the constant terms in the two equations are all equal . In terms of slopes, it implies that the slopes of the two lines are equal. Additionally, it suggests that the lines pass through the same point on the y-axis. This option is no...

                                                                  MATH SAMPLE QUESTION PAPER Class X Session 2023-24 MATHEMATICS STANDARD (Code No.041) Question 2 The given linear polynomial y = f(x) has  (a) 2 zeros  (b) 1 zero and the zero is ‘3’  (c) 1 zero and the zero is ‘4’  (d) No zero   Explanation : A linear polynomial has the form y=mx+c, where m is the slope and c is the y-intercept. Since it's a linear polynomial, it represents a straight line. The number of zeros of a linear polynomial is the number of points where it intersects the x-axis .    If the slope ( m ) is not zero, the line will intersect the x-axis at exactly one point, unless it is parallel to the x-axis, in which case it will never intersect the x-axis. If the...

   MATH  SAMPLE QUESTION PAPER   Class X Session 2023-24    MATHEMATICS STANDARD (Code No.041) Question 1 If two positive integers a and b are written as   \[ a = \ x^3y^2 \ and \ b =\ xy^3 \]  , where x, y are prime numbers, then the result obtained by dividing the product of the positive integers by the LCM (a, b) is : (a) xy (b) xy2 (c) x3y3 (d) x2y2 Explanation:  First, understand the Prime number  A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself Example of prime Numbers 2, 3 , 5,7,11  , Let's take the number 5 for example. It is only divisible by 1 and itself. Similarly, 11 is also only divisible by 1 and itself.    Let's understand LCM (Least Common Multiple) of two numbers as an example Let's find the LCM of 12 and 15.  To find the LCM, we need to find the smallest multiple that both numbers share how can you write the Prime factorizati...

Machine learning (ML) can be used in momentum trading to analyse historical market data and identify patterns or trends that may not be apparent through traditional methods. ML algorithms can predict future price movements, generate trading signals, and optimise trading strategies based on the identified patterns. ML approaches offer several advantages in momentum trading, including the ability to analyse large datasets quickly, identify complex patterns, and adapt to changing market conditions. The ML approach for momentum trading utilises various types of data inputs, including historical price data, trading volumes, technical indicators (e.g., moving averages, RSI), etc. These inputs help ML algorithms in identifying patterns and making predictions. Key Points : XGBoost model to predict momentum and create a time-series momentum strategy. Improve the accuracy model using cross-validation and hyperparameter tuning. By using the prediction from multiple ML models such as Logistic Regr...

Mypy is a  Python type checker that can help decrease errors and enhance the quality of code. These tools detect problems and provide warnings for possible errors by examining code flow and type annotations.  Mypy  : Using Mypy can be done from the command line, as a stand-alone application, or as a component of an integrated linter in an editor or IDE. It is directly compatible because it is integrated into many editors and IDEs, including the Python extension for Visual Studio Code. When Mypy is run, it produces reports that emphasize consistency in the code by using the type information that is supplied. Most of Mypy's code checks will not be performed if type annotations are absent from the code. This way, if you are gradually annotating a codebase, Mypy will not waste time checking code that you are not attempting to type-check. On the other hand, Mypy can be used to manually flag unannotated code in different levels of strictness to meet specific needs. The "strict...

 CBSE MATHEMATICS (IX-X):