List of practice Questions

Assertion (A) : The probability that a leap year has 53 Mondays is \(\frac{2}{7}\).
Reason (R) : The probability that a non-leap year has 53 Mondays is \(\frac{5}{7}\).

Do the points \(P (1, 0)\), \(Q (- 5, 0)\) and \(R (- 2, 5)\) form a triangle ? If so, name the type of triangle formed.

If \(\tan \theta = \frac{24}{7}\), then find the value of \(\sin \theta + \cos \theta\).

Two concentric circles are of radii 5 cm and 4 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Find a quadratic polynomial whose zeroes are \((5 - 2\sqrt{3})\) and \((5 + 2\sqrt{3})\).

In \(\Delta ABC\), \(DE \parallel BC\). If \(AD = x\), \(DB = x - 2\), \(AE = x + 2\) and \(EC = x - 1\), then find the value of \(x\).

In the figure given, \(\Delta ABC \sim \Delta XYZ\), then find the values of \(x\) and \(y\). (Given: \(AB=4, BC=6, AC=y, XY=x, YZ=7.2, XZ=6\))

If \(x = h + a\cos\theta, y = k + b\sin\theta\), then prove that : \(\left(\frac{x-h}{a}\right)^2 + \left(\frac{y-k}{b}\right)^2 = 1\).

Prove that : \(\frac{\tan A}{1 + \sec A} - \frac{\tan A}{1 - \sec A} = 2\csc A\).

In the given figure, \(\Delta ABC\) is a right triangle in which \(\angle B = 90^\circ\), \(AB = 4\) cm and \(BC = 3\) cm. Find the radius of the circle inscribed in the triangle \(ABC\).

In the given figure, if a circle touches the side \(QR\) of \(\Delta PQR\) at \(S\) and extended sides \(PQ\) and \(PR\) at \(M\) and \(N\) respectively, then prove that : \(PM = \frac{1}{2}(PQ + QR + PR)\).

A right circular cylinder and a right circular cone have equal bases and equal heights. If their curved surface areas are in the ratio \(8 : 5\), then find the ratio between the radius of their bases to their height.

Two different coins are tossed simultaneously. What is the probability of getting :
(i) at least one head ?
(ii) at most one tail ?
(iii) a head and a tail ?

Prove that \(\sqrt{3}\) is an irrational number.

Find the ratio in which the \(x\)-axis divides the line segment joining the points \((6, 5)\) and \((-4, -1)\). Also find the point of intersection.

State and prove Basic Proportionality Theorem.

In the given figure, CM and RN are respectively the medians of $\Delta ABC$ and $\Delta PQR$. If $\Delta ABC \sim \Delta PQR$, then prove that : (i) $\Delta AMC \sim \Delta PNR$, (ii) $\Delta CMB \sim \Delta RNQ$.

The marks obtained by 80 students of class X in a mock test of Mathematics are given below in the table. Find median and the mode of the data :

Compare CSV, Spreadsheets, and SQL as data storage formats. Which one is best for handling massive, interrelated datasets?

Define and explain the following types of Biases: Recall Bias, Survivor Bias

Explain the four steps of the Statistical Problem-Solving Process in detail.

What is Data Merging? Mention one scenario where it is required.

Explain the concept of the Central Limit Theorem and its significance in data analysis.

Why is the Median considered a more robust measure of central tendency than the Mean when outliers are present?

Differentiate between Structured and Unstructured data with one example each.