List of practice Questions

The 6th term of the AP \( \sqrt{27}, \sqrt{75}, \sqrt{147}, \ldots \) is:
The value of \( k \) for which the pair of linear equations
\( (k+1)x + 2y = 15, \quad 4y = 3x - 8 \) has no solution, is:

If the given figure shows the graph of polynomial \( y = ax^2 + bx + c \), then:

In the given figure, a circle inscribed in \( \triangle ABC \) touches \( AB, BC, \) and \( CA \) at \( X, Z, \) and \( Y \) respectively.
\begin{center} \includegraphics[width=0.6\textwidth]{03.png} \end{center} If \( AB = 12 \, \text{cm}, AY = 8 \, \text{cm}, \) and \( CY = 6 \, \text{cm} \), then the length of \( BC \) is:
Cards numbered 10, 11, 12, ..., 30 are kept in a box and shuffled thoroughly. Rahit draws a card at random from the box. The probability that the number on the card is a multiple of 6 or 5 is:
Raina is 1.5 m tall. At an instant, his shadow is 1.8 m long. At the same instant, the shadow of a pole is 9 m long. How tall is the pole?
If \( x = p \cos^3 \alpha \) and \( y = q \sin^3 \alpha \), then the value of
\( \left( \frac{x}{p} \right)^{2/3} + \left( \frac{y}{q} \right)^{2/3} \text{ is:} \)
M is a point on y-axis at a distance of 4 units from x-axis and it lies below the x-axis. The distance of point M from point Q(3, 1) is:
In the given figure, \( PQ \) and \( PR \) are tangents to the circle such that \( PQ = 7 \, \text{cm} \) and \( \angle RPQ = 60^\circ \).
\begin{center} \includegraphics[width=0.6\textwidth]{02.png} \end{center} The length of chord QR is:
The total number of factors of the square of a prime number is:
Under which major headings and sub-headings (if any) will the following items be presented in the Balance Sheet of a company as per Schedule III, Part I of the Companies Act, 2013 ?

ABC Ltd. was registered with authorised capital of \(₹1,00,00,000\) divided into 10,00,000 equity shares of \(₹10\) each. On 1stApril, 2024, the company offered to the public for subscription, 1,00,000 shares. Applications for 99,000 shares were received and allotment was made in full to all the applicants. A shareholder holding 9,000 shares failed to pay the final call of \(₹3\) per share. 
Answer the following questions : 
(i) The authorised capital of the company is :
(ii) The issued capital of ABC Ltd. is:
(iii) The amount of calls-in-arrears will be:
(iv) The ’subscribed and fully paid up capital’ of ABC Ltd. will be:
(v) Subscribed but not fully paid up capital of ABC Ltd. will be:
(vi) The amount of ’Share Capital’ presented in the Balance Sheet of ABC Ltd. will be:

Draw a ray diagram to show image formation by a concave mirror when the object is placed between focus and center of curvature.

Rearrange the following parts to form a meaningful and grammatically correct sentence: 
P. a healthy diet and regular exercise 
Q. are important habits 
R. that help maintain good physical and mental health 
S. especially in today's busy world

As shown in the diagram, an electron enters perpendicularly into a magnetic field. Using Fleming’s Left-Hand Rule, determine the direction of the force experienced by the electron. 

"Sex of a newborn baby in humans depends on the father, not the mother." Confirm this statement with the help of a flow chart.
Identify the part of speech of the underlined word: She quickly finished her homework.
Write a four-step aquatic food chain. Among them, which group of organisms is most important and why?
निम्नलिखित काव्यांश को ध्यानपूर्वक पढ़कर उस पर आधारित दिए गए प्रश्नों के उत्तर लिखिए:

यह हार एक विराम है
जीवन महासंग्राम है
तिल-तिल बिंधूँगा पर दया की भीख मैं लूँगा नहीं
वरदान माँगूँगा नहीं।

स्मृति सुखद प्रहरों के लिए
अपने खंडहरों के लिए
यह जान लो मैं विश्व की संपत्ति चाहूँगा नहीं
वरदान माँगूँगा नहीं।

क्या हार में क्या जीत में
किंचित नहीं भयभीत मैं
संघर्ष पथ पर जो मिले यह भी सही वह भी सही
वरदान माँगूँगा नहीं।

लघुता न अब मेरी छुओ
तुम हो महान बने रहो
अपने हृदय की वेदना मैं त्यागूँगा नहीं
वरदान माँगूँगा नहीं।

चाहे हृदय को ताप दो
चाहे मुझे अभिशाप दो
कुछ भी करो कर्तव्य पथ से किंतु भागूँगा नहीं
वरदान माँगूँगा नहीं।
Population of Town A and B was 20,000 in 1985. In 1989, the population of Town A was 25,000, and Town B had 28,000. What will be the difference in population between the two towns in 1993?
लेख/आलेख विशेष रिपोर्ट से भिन्न कैसे हैं? (शब्द सीमा लगभग 40 शब्द)
एंकर बाइट किसे कहते हैं? टेलीविज़न पत्रकारिता में इसका क्या महत्त्व है? (शब्द सीमा लगभग 20 शब्द)
पत्रकारीय साक्षात्कार और सामान्य बातचीत में क्या अंतर है? (शब्द सीमा लगभग 40 शब्द)
रियालिटी शो : प्रतिभा की पहचान का मंच — इस पर लगभग 100 शब्दों में रचनात्मक लेख लिखिए।
मोबाइल टॉवरों का फैलता जाल — इस पर लगभग 100 शब्दों में रचनात्मक लेख लिखिए।