Advanced Math MCQ Quiz in मराठी - Objective Question with Answer for Advanced Math - मोफत PDF डाउनलोड करा

To find the number of gadgets that minimizes the production cost, we look for the vertex of the quadratic function . The vertex -coordinate is found using , where and . Thus, . Therefore, the production cost is minimized at , or gadgets. Option is the correct choice. Options , , and do not yield the minimum cost as they do not correspond to the vertex of the parabola.

The height of the ball when it reaches the ground is 0. Therefore, we set and solve for . This is a quadratic equation in standard form, , where , , and . Solving this using the quadratic formula , we have: . Simplifying, . The positive solution is approximately . Therefore, the correct option is 3. Option 1 (1.5) and Option 2 (3.5) are too early for the ball to reach the ground, and Option 4 (4.5) is slightly beyond the correct time.

A quadratic function has only one real root when its discriminant is zero. For , the discriminant is . Set the discriminant to zero for one real root: . Solving for , we have and . Therefore, the value of is 9.

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 .