Optional Mathematics Question Paper SET D (Model Question)

What is the vertex of the parabola having equation ?

If and be the functions, then which one of the following is the notation for the composite function defined from ?

Which one of the following is the true value of ?

Which one of the following is equal trigonometric expression to ?

If and are angles of a , which one of the following is equal to ?

If a circle touches Y-axis with centre at , what is the diameter of the circle?

What is the figure called if a plane surface cuts the cone parallel to the generator of the cone?

The transformation which turns an object about a fixed point through a certain angle is called ........

If and be two vectors perpendicular to each other, then which one of the following relations is true?

Which one of the following set of numbers represents a continuous domain?

Which of the following is the appropriate formula to calculate the third quartile?

Write the condition for to be a factor of .

Use the rational root theorem to determine the possible roots of polynomial .

Find the composite function .

Write in the vertex form .

Explain the combined transformation involved to transform the function into .

Find .

Find .

Show the feasible region on graph of the constraints , , and .

How can the identity be converted in the form of ?

If , prove that:

Draw a labelled diagram showing the height of the house, ladder and angle of elevation.

Find the height of the house.

Write in terms of sum or difference.

If , and , verify the given identity.

State any one reason why the given identity cannot be verified for , and .

Write the matrix that transform the point into the point .

Find the angle between the line and the straight line .

Write the equation of the circle with centre and radius 'r'.

Find the centre and radius of the given circle.

If any point on the circumference of the circle is , find the equation of the diameter of the circle.

If R denotes reflection on X-axis and T denotes translation by vector , then find the image points of the given points P and Q under the combined transformation ToR.

Show the line PQ and its image line P'Q' on the same graph.

Write the position vector of E in terms of position vectors of A and C.

Find the position vector of F in terms of .

Prove by vector method:

From the box plots given above battery of which car has higher life in terms of median?

Find the coefficient of quartile deviation of the life of battery of car A when car B has 0.29.

For the family tour for a long distance to choose any one of two cars A or B from the above information, which car would you suggest to the family? Why?

Define the continuity of the functions.

Find the limiting value of the function when approaches to 2.

Find the value of .

Find whether the function is continuous or not at . How can you justify your answer?

Find the vertices of Image of under transformation by the matrix M.

Find the slope of the altitude of drawn from the point A to the line BC.

Is M a singular matrix? If not how can you make it singular?

Rama claims, "The transformation by the matrix M and its transpose matrix are same." Do you agree with Rama's statement? Justify your answer with example.

Write the relationship between a line segment joining P and Q and the third side BC.

Manamaya measured the sides PQ and CB and got CB = 2PQ. Prove this relationship by vector method.

Explain with reason whether Manamaya's statement would still be true if P and Q are any points in between AC and AB.

If A(2, 2), B(2, 8) and C(6, 2) are the vertices of , verify that .

Prove that:

The angle of the top of the tower is such that , based on this find the value of slope ().

Using inverse function , find the horizontal distance covered by him if the height of the tower is 200 m.

Rajesh says, "If the angle made by a line in a positive direction of X-axis is halved, then the slope of the line also becomes half." Using any value of and , justify his statement.