Nonlinear Equations in One Variable MCQ Quiz in தமிழ் - Objective Question with Answer for Nonlinear Equations in One Variable - இலவச PDF ஐப் பதிவிறக்கவும்

To solve the equation , we first divide both sides by to isolate the term: . Taking the square root of both sides, we get . The negative value of is . Therefore, the correct answer is , which corresponds to option 2. Options 1 and 3 provide positive values, and option 4 is incorrect as it does not satisfy the original equation.

Start by dividing both sides of the equation by , resulting in . Solving for , we take the square root of both sides: . The negative solution for is , thus the correct answer is option 3. The other options do not provide the correct negative solution as option 1 and 4 provide positive values, and option 2 provides an incorrect negative value.

To express in terms of and , start with . Add to both sides to obtain . Next, divide both sides by to isolate : . To solve for , take the square root of both sides: . Thus, option 2 is correct. Option 1 is identical, but option 3 misrepresents the squared relationship, and option 4 is not derived from the given formula.

Start from the equation . To solve for , subtract from both sides: . Then, divide both sides by to isolate : . This results in option 4 as the correct choice. Option 1 erroneously suggests subtracting without division. Option 2 incorrectly adds to . Option 3 reverses the subtraction order.

The maximum value of a downward opening parabola is at the vertex. The x-coordinate of the vertex is given by , where and . Thus, . Substitute into the function to find the maximum value: . Therefore, the maximum value of is 11.

The maximum height of a projectile is at the vertex of the parabola represented by the quadratic equation . The time at which the maximum height is reached can be found using . Here, and , so seconds. Substitute into the height equation to find the maximum height: meters. Thus, the maximum height reached is 35 meters.

The axis of symmetry for a quadratic function is given by the formula . For the function , substitute and : . Therefore, the axis of symmetry is . This is the vertical line that passes through the vertex of the parabola.

To find where the parabola touches the x-axis, we need to find the roots of the equation by setting . Solve by factoring: . This gives . Thus, the point where the parabola touches the x-axis is . Since the squared term indicates a double root, the parabola touches the x-axis at this point only.

The vertex form of a quadratic equation is given by , where is the vertex. To find the vertex for the equation , we first complete the square. Start by factoring out the from the and terms: . Next, complete the square inside the parentheses. Take half of , which is , and square it to get . Add and subtract inside the parentheses: . Simplify to get . Therefore, the vertex is .

The given absolute value equation can be rewritten as two separate equations: and . Solving the first equation, , we subtract 5 from both sides to get . Dividing by 3, we find . For the second equation, , subtracting 5 from both sides gives . Dividing by 3, we get , which is not needed for the positive value. Thus, the positive value of is . Hence, the correct answer is 10.