List of practice Questions

D is the mid-point of side BC of \(\triangle ABC\). CE and BF intersect at O, a point on AD. AD is produced to G such that \(OD = DG\). Prove that OBGC is a parallelogram.
In the same figure as 32(a), prove that \(EF \parallel BC\).
In the same figure as 32(a), prove that \(\triangle AEF \sim \triangle ABC\).
Using the conditions from 32(b), prove that \(AP = 2PQ\).
Using the conditions from 32(b), prove that \(PR = 2AP\).
The mean of the following distribution is 53. Find the missing frequency p.
Hence, find mode of the distribution.}
Compute median of the following data :

कडक शिस्त आणि संवेदनशीलता यांचा संगम म्हणजे 'लेफ्टनंट स्वाती महाडिक' हे विधान स्पष्ट करा.

'स्वसामर्थ्यावर विश्वास ठेवा' या अर्थाच्या कवितेतील ओळी स्पष्ट करा.

वस्तूंचे मानवीकरण कसे केले आहे, ते सांगा.

अरुणिमाच्या जिद्दीतून तुम्हाला मिळालेली प्रेरणा तुमच्या शब्दांत लिहा.

'वाट पाहणे' या प्रक्रियेतील दुःख आणि आनंद यांबाबत तुमचे विचार लिहा.

Two water taps together can fill a tank in \(8\frac{8}{9}\) hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

आजी - कुटुंबाचे आगळ' या शीर्षकाची समर्पकता स्पष्ट करा.

Write an original short story beginning with the words: It was midnight and the doorbell rang...
If the pair of linear equations : \( a_1x + b_1y + c_1 = 0 \) and \( a_2x + b_2y + c_2 = 0 \) is consistent and dependent, then

Which of the following sequence is \(\textit{not }\)an A.P. ?
 

In triangles ABC and PQR, \( \angle A = \angle Q \) and \( \angle B = \angle R \), then \( AB : AC \) is equal to :
If \( \cos A = \frac{4}{5} \), then the value of \( \tan A \) is :
Area of a segment of a circle of radius 'r' and central angle \( 60^\circ \) is :
The mean and median of a frequency distribution are 43 and 43.4 respectively. The mode of the distribution is :
The probability for a randomly selected number out of 1, 2, 3, 4, ..., 25 to be a composite number is :
Assertion (A) : The surface area of the cuboid formed by joining two cubes of sides 4 cm each, end-to-end, is \( 160 \text{ cm}^2 \).
Reason (R) : The surface area of a cuboid of dimensions \( l \times b \times h \) is \( (lb + bh + hl) \).
If \( \alpha, \beta \) are the zeroes of the quadratic polynomial \( px^2 + qx + r \), then find the value of \( \alpha^3\beta + \beta^3\alpha \).
In the given figure, \( \triangle AHK \sim \triangle ABC \). If \( AK = 10 \text{ cm} \), \( BC = 3.5 \text{ cm} \) and \( HK = 7 \text{ cm} \), find the length of \( AC \).