List of practice Questions

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 \( AC \).
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 \( \tan \theta + \frac{1}{\tan \theta} = 2 \), find the value of \( \tan^2 \theta + \frac{1}{\tan^2 \theta} \).
Prove that : \( \sqrt{\frac{1 - \sin \theta}{1 + \sin \theta}} = \sec \theta - \tan \theta \)
Prove that \( \sqrt{5} \) is an irrational number.
Find the coordinates of the points of trisection of the line segment joining the points \( A(-1, 4) \) and \( B(-3, -2) \).
Prove that : \( \frac{\sec^3 \theta}{\sec^2 \theta - 1} + \frac{\text{cosec}^3 \theta}{\text{cosec}^2 \theta - 1} = \sec \theta \cdot \text{cosec} \theta (\sec \theta + \text{cosec} \theta) \)
If \( \frac{\sec \alpha}{\text{cosec} \beta} = p \) and \( \frac{\tan \alpha}{\text{cosec} \beta} = q \), then prove that \( (p^2 - q^2) \sec^2 \alpha = p^2 \).
Prove that the lengths of tangents drawn from an external point to a circle are equal.
Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that \( \angle PTQ = 2 \angle OPQ \).