Advanced Math MCQ Quiz in हिन्दी - Objective Question with Answer for Advanced Math - मुफ्त [PDF] डाउनलोड करें

To simplify , combine the coefficients of the like terms, . This gives us . Therefore, option 4 is the correct answer. Option 1 incorrectly adds the exponents. Option 2 incorrectly combines coefficients. Option 3 incorrectly calculates the result.

The function halves in value for each increase in by . Therefore, the function can be expressed as . Given , we can substitute for to find . Hence, represents the function correctly. Option 1 correctly uses the initial condition at . Option 2 and Option 3 misrepresent the decay process, while Option 4 uses incorrect scaling.

The function decreases by with every unit increase in . This indicates an exponential decay model . Given , . Therefore, . Option 1 is correct. Option 2 suggests growth rather than decay. Option 3 incorrectly models the decay rate, and Option 4 misrepresents the exponential factor.

To find , substitute into the function: . First, calculate . Then . Add : . Thus, . Option 3 is correct, as it reflects the correct computation of the investment value.

Profit is calculated as sales minus expenses. Therefore, the expression for profit is . Simplifying this, we have: for the terms, and for the constants. Thus, the profit expression is , making option 1 the correct answer.

The quadratic requires the discriminant to be positive for two distinct real solutions. Here, and . Calculating, 0\) simplifies to 0\), or 3600\). Solving gives 60\) or . Therefore, the value satisfies 60\), ensuring two distinct real solutions. Thus, is the correct option.

To find the value of where the line intersects the parabola at one point, equate the equations: . Rearrange to form a quadratic: . For the quadratic to have exactly one solution, the discriminant must be zero. The discriminant is . Simplifying gives , solving for gives . Therefore, the value of is .

Start with the point : , so , which simplifies to . Substitute into the second point : , which simplifies to . Therefore, (since is positive). Now, calculate . The correct option is 3. Each step involves solving the exponential and linear equations that describe the behavior of nonlinear functions. The problem tests understanding of substitution and solving quadratics in the context of exponential growth. The final solution confirms that multiplication of these constants yields the correct value of .

The profit function is a downward-opening parabola, indicating a maximum profit at the vertex. Using , where and , we find . Substituting into the function gives . Therefore, the maximum profit is \$48, making option 2 correct.

The function is in the form with , indicating the parabola opens downwards, and the vertex is the maximum point. The time is where the projectile reaches its maximum height, as it is the vertex. The other times do not correspond to the vertex, hence they are incorrect.