Short Quiz

Question 1 of 5

NCERT Exemplar

The two curves \(x^3-3 x y^2+2=0\) and \(3 x^2 y-y^3=2\)

A touch each other B cut at right angle C cut at an angle \(\frac{\pi}{3}\) D cut at an angle \(\frac{\pi}{4}\)

Select one option. Answers are shown after the test.

Question 2 of 5

NCERT Exemplar

The curve \(y=x^{\frac{1}{5}}\) has at \((0,0)\)

A a vertical tangent (parallel to \(y\)-axis) B a horizontal tangent (parallel to \(x\)-axis) C an oblique tangent D no tangent

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Question 3 of 5

NCERT Exemplar

The function \(f(x)=x^{\wedge} 3\) has \(f^{\prime}(0)=0\). What is true about the point \(x=0\) ?

A It is a local maximum. B It is a local minimum. C It is a point of inflection. D It is a point of discontinuity.

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Question 4 of 5

NCERT Exemplar

The radius of a spherical balloon is increasing. The rate of change of its volume is fastest when:

A The radius is smallest. B The rate of change of the radius is slowest. C The radius is largest. D The balloon is fully inflated.

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Question 5 of 5

NCERT Exemplar

If the curve a \(y+x^2=7\) and \(x^3=y\), cut orthogonally at ( 1, 1), then the value of \(a\) is:

A 1 B 0 C -6 D 6

Select one option. Answers are shown after the test.

Class 6