List of top Questions asked in CBSE Class X

In the given figure, AB \(||\) DE and BD \(||\) EF. Prove that \(DC^2 = CF \times AC\).
AB || DE and BD || EF. Prove that DC2 = CF ×AC
Three friends plan to go for a morning walk. They step off together and their steps measures 48 cm, 52 cm and 56 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps ten times?
Prove that \(\left(1 + \frac{1}{\tan^2 \theta}\right) \left(1 + \frac{1}{\cot^2 \theta}\right) = \frac{1}{\sin^2 \theta - \sin^4 \theta}\).
If \(\alpha, \beta\) are zeroes of the polynomial \(8x^2 - 5x - 1\), then form a quadratic polynomial in x whose zeroes are \(\frac{2}{\alpha}\) and \(\frac{2}{\beta}\).
Find the zeroes of the polynomial \(p(x) = 3x^2 + x - 10\) and verify the relationship between zeroes and its coefficients.
The sum of a number and its reciprocal is \(\frac{13}{6}\). Find the number.
Two poles of equal heights are standing opposite each other on either side of the road which is 85 m wide. From a point between them on the road, the angles of elevation of the top of the poles are \(60^\circ\) and \(30^\circ\) respectively. Find the height of the poles and the distances of the point from the poles. (Use \(\sqrt{3} = 1.73\))
Solve the following pair of linear equations by graphical method : \(2x + y = 9\) and \(x - 2y = 2\).
Nidhi received simple interest of ₹1,200 when she invested ₹x at 6% per annum and ₹y at 5% per annum for 1 year. Had she invested ₹x at 3% per annum and ₹y at 8% per annum for that year, she would have received simple interest of ₹1,260.Find the values of x and y.
The given figure shows a circle with centre O and radius 4 cm circumscribed by \(\triangle ABC\). BC touches the circle at D such that BD = 6 cm, DC = 10 cm. Find the length of AE.
BC touches the circle at D such that BD = 6 cm
PA and PB are tangents drawn to a circle with centre O. If \(\angle AOB = 120^\circ\) and OA = 10 cm, then
PA and PB are tangents drawn to a circle with centre O

(i) Find \(\angle OPA\).
(ii) Find the perimeter of \(\triangle OAP\).
(iii) Find the length of chord AB.
The system of equations \(x+5=0\) and \(2x-1=0\) has
In a right-angled triangle ABC at A, if \(\sin B = \frac{1}{4}\), then the value of \(\sec B\) is:
The distance of point \((a, -b)\) from the \(x\)-axis is

In the adjoining figure, \(PQ \parallel XY \parallel BC\), \(AP=2\ \text{cm}, PX=1.5\ \text{cm}, BX=4\ \text{cm}\). If \(QY=0.75\ \text{cm}\), then \(AQ+CY =\)

If \(x = \cos 30^\circ - \sin 30^\circ\) and \(y = \tan 60^\circ - \cot 60^\circ\), then
If the mode of some observations is 10 and sum of mean and median is 25, then the mean and median respectively are
If the maximum number of students has obtained 52 marks out of 80, then
Assertion (A) : For two prime numbers \(x\) and \(y\) (\(x<y\)), HCF\((x, y) = x\) and LCM\((x, y) = y\). Reason (R): HCF\((x, y) \leq \) LCM\((x, y)\), where \(x, y\) are any two natural numbers.
In an experiment of throwing a die, Assertion (A): Event \(E_1\): getting a number less than 3 and Event \(E_2\): getting a number greater than 3 are complementary events. Reason (R): If two events E and F are complementary events, then \(P(E) + P(F) = 1\).

In the adjoining figure, if \(\dfrac{AD}{BD} = \dfrac{AE}{EC}\) and \(\angle BDE = \angle CED\), prove that \(\triangle ABC\) is an isosceles triangle.

A bag contains cards numbered from 5 to 100 such that each card bears a different number. A card is drawn at random. Find the probability that the number on the card is:
  • [(i)] a perfect square
  • [(ii)] a 2-digit number
Prove that: \[ \frac{\cos \theta - 2 \cos^3 \theta}{\sin \theta - 2 \sin^3 \theta} + \cot \theta = 0 \]
Find the zeroes of the polynomial: \[ q(x) = 8x^2 - 2x - 3 \] Hence, find a polynomial whose zeroes are 2 less than the zeroes of \(q(x)\)

The following data shows the number of family members living in different bungalows of a locality:
 

Number of Members0−22−44−66−88−10Total
Number of Bungalows10p60q5120


If the median number of members is found to be 5, find the values of p and q.