List of top Mathematics Questions asked in CBSE Class X

A person on tour has ₹ 5,400 for his expenses. If he extends his tour by 5 days, he has to cut down his daily expenses by ₹ 180. Find the original duration of the tour and daily expense.

If \(a_n\) represents \(n^{\text{th}}\) term of the A.P. \(-\frac{15}{4}, -\frac{10}{4}, -\frac{5}{4}, \dots\) then value of \(a_{16} - a_{12}\) is

If the distance between the points (4, p) and (1, 0) is 5, then p is equal to :

In an A.P., \(15^{th}\) term exceeds the \(8^{th}\) term by 21. If sum of first 10 terms is 55, then form the A.P.

Represent the following pair of linear equations graphically and hence comment on the condition of consistency of this pair : \( x - 5y = 6; 2x - 10y = 12 \)

If \(\sin x = p\), then prove that : (i) \(\cot x = \frac{\sqrt{1 - p^2}}{p}\) (ii) \(\frac{1 + \tan^2 x}{1 + \cot^2 x} = \frac{p^2}{1 - p^2}\)

The sum of squares of two positive numbers is 100. If one number exceeds the other by 2, find the numbers.

If \(\cot \theta = \frac{7}{8}\), then find the value of \(\frac{(1+\sin \theta)(1-\sin \theta)}{(1+\cos \theta)(1-\cos \theta)}\).

In the given figure, a circle is centred at \((1, 2)\). The diameter of the circle is

The pair of linear equations \( \frac{3x}{2} + \frac{5y}{3} = 7 \) and \( 9x + 10y = 14 \), is :

In the given figure, \(XY \parallel QR\), \(\frac{PQ}{XQ} = \frac{7}{3}\) and \(PR = 6.3 \text{ cm}\). Find the length of \(YR\).

Evaluate: \(\frac{5 \cos^2 60^\circ + 4 \sec^2 30^\circ - \tan^2 45^\circ}{\sin^2 30^\circ + \cos^2 30^\circ}\)

Prove that: \(1 + \frac{\cot^2 \alpha}{1 + \csc \alpha} = \csc \alpha\)

In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic.

Find the area of the segment AYB shown in the figure, if the radius of the circle is 21 cm and \(\angle AOB = 120^\circ\). [Use \(\pi = 22/7\)]

Find the value of p, for which one zero of the quadratic polynomial \(px^2 - 14x + 8\) is 6 times the other.

Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

If the points \(A(4, 5)\), \(B(m, 6)\), \(C(4, 3)\) and \(D(1, n)\) taken in this order are the vertices of a parallelogram \(ABCD\), then find the values of \(m\) and \(n\).

If \(\frac{\sec \alpha}{\csc \beta} = p\) and \(\frac{\tan \alpha}{\csc \beta} = q\), then prove that \((p^2 - q^2) \sec^2 \alpha = p^2\).

If a regular hexagon ABCDEF circumscribes a circle, then prove that AB + CD + EF = BC + DE + FA.

In a flight of 600 km, an aircraft slowed down its speed due to bad weather. Its average speed for the trip reduced by 200 km/h from its usual speed and time of flight increased by 30 minutes. Find the scheduled duration of the flight.

Two pipes are used to fill a swimming pool. If the pipe of the larger diameter is used for 4 hours and the pipe of the smaller diameter for 9 hours, only half of the pool can be filled. Find how long it would take for each pipe to fill the pool, separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool.

If 2 sin A = 1, then the value of tan A + cot A is :

Which of the following sequence is not an A.P. ?

The area of a semicircle of diameter 'd' is :