English Medium Class 10 - CBSE Question Bank Solutions

A tent is in the shape of a cylinder surmounted by a conical top. If the height and radius of the cylindrical part are 3 m and 14 m respectively, and the total height of the tent is 13.5 m, find the area of the canvas required for making the tent, keeping a provision of 26 m² of canvas for stitching and wastage. Also, find the cost of the canvas to be purchased at the rate of ₹ 500 per m².

If the discriminant of the quadratic equation 3x² - 2x + c = 0 is 16, then the value of c is ______.

The ratio of total surface area of a solid hemisphere to the square of its radius is ______.

Tamper-proof tetra-packed milk guarantees both freshness and security. This milk ensures uncompromised quality, preserving the nutritional values within and making it a reliable choice for health-conscious individuals.

500 ml milk is packed in a cuboidal container of dimensions 15 cm × 8 cm × 5 cm. These milk packets are then packed in cuboidal cartons of dimensions 30 cm × 32 cm × 15 cm.

Based on the above-given information, answer the following questions:

i. Find the volume of the cuboidal carton. (1)

ii. a. Find the total surface area of the milk packet. (2)

OR

b. How many milk packets can be filled in a carton? (2)

iii. How much milk can the cup (as shown in the figure) hold? (1)

Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So, he started to sketch his own rocket designs on the graph sheet. One such design is given below :

Based on the above, answer the following questions:

i. Find the mid-point of the segment joining F and G.    (1) 

ii. a. What is the distance between the points A and C?   (2)

OR

b. Find the coordinates of the points which divides the line segment joining the points A and B in the ratio 1 : 3 internally.    (2)

iii. What are the coordinates of the point D?    (1)

Assertion (A): Mid-point of a line segment divides the line segment in the ratio 1 : 1

Reason (R): The ratio in which the point (−3, k) divides the line segment joining the points (− 5, 4) and (− 2, 3) is 1 : 2.

If A(4, 3), B(-1, y) and C(3, 4) are the vertices of a right triangle ABC, right-angled at A, then find the value of y.

If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b, a + b). Prove that bx = ay.

The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) and R(–3, 6), find the coordinates of P.

If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.

If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p. Also, find the length of AB.

If the point P(2, 2) is equidistant from the points A(−2, k) and B(−2k, −3), find k. Also find the length of AP.

Consider the number 12ⁿ where n is a natural number. Check whether there is any value of n ∈ N for which 12ⁿ ends with the digital zero.

Consider the number 6ⁿ where n is a natural number. Check whether there is any value of n ∈ N for which 6ⁿ is divisible by 7.

Find the distance between two points

(i) P(–6, 7) and Q(–1, –5)

(ii) R(a + b, a – b) and S(a – b, –a – b)

(iii) `A(at_1^2,2at_1)" and " B(at_2^2,2at_2)`

If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay.

Find the value of x, if the distance between the points (x, – 1) and (3, 2) is 5.

Show that the points (a, a), (–a, –a) and (– √3 a, √3 a) are the vertices of an equilateral triangle. Also find its area.

Show that the points (1, – 1), (5, 2) and (9, 5) are collinear.

Show that four points (0, – 1), (6, 7), (–2, 3) and (8, 3) are the vertices of a rectangle. Also, find its area