English Medium कक्षा १० - CBSE Question Bank Solutions

There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are 30° and 60° respectively. Find the width of the river and height of the other pole.

If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`

Check whether g(x) is a factor of p(x) by dividing polynomial p(x) by polynomial g(x),
where p(x) = x⁵ − 4x³ + x² + 3x +1, g(x) = x³ − 3x + 1

If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1.

Zeroes of a polynomial can be determined graphically. No. of zeroes of a polynomial is equal to no. of points where the graph of polynomial ______.

If p(x) = axr + bx + c, then –`"b"/"a"` is equal to ______.

The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is ______.

If tan θ = 3, then `(4 sin theta - cos theta)/(4 sin theta + cos theta)` is equal to ______.

If 2sin²β − cos²β = 2, then β is ______.

If 4 tanβ = 3, then `(4sinbeta-3cosbeta)/(4sinbeta+3cosbeta)=` ______.

If tan α + cot α = 2, then tan²⁰α + cot²⁰α = ______.

If 1 + sin²α = 3 sinα cosα, then values of cot α are ______.

If 2 and `1/2` are the zeros of px² + 5x + r, then ______.

Case Study -1

The figure given alongside shows the path of a diver, when she takes a jump from the diving board. Clearly it is a parabola.

Annie was standing on a diving board, 48 feet above the water level. She took a dive into the pool. Her height (in feet) above the water level at any time ‘t’ in seconds is given by the polynomial h(t) such that h(t) = -16t² + 8t + k.

The zeroes of the polynomial r(t) = -12t² + (k - 3)t + 48 are negative of each other. Then k is ______.

The value of tan A + sin A = M and tan A - sin A = N.

The value of `("M"^2 - "N"^2) /("MN")^0.5`

The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.

If the sum of the roots is –p and the product of the roots is `-1/"p"`, then the quadratic polynomial is:

An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related to representation of quadratic polynomial.

The zeroes of the quadratic polynomial `4sqrt3"x"^2 + 5"x" - 2sqrt3` are:

Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.

What will be the expression of the polynomial?

If one of the zeroes of the quadratic polynomial (k – 1)x² + k x + 1 is –3, then the value of k is ______.

A quadratic polynomial, whose zeroes are –3 and 4, is ______.