List of top Questions asked in Maharashtra Class X Board

\( ABCD \) is a trapezium, \( AB \parallel CD \), and the diagonals of the trapezium intersect at point \( P \). Write the answers to the following questions:
[(a)] Draw the figure using the given information.
[(b)] Write any one pair of alternate angles and opposite angles.
[(c)] Write the names of similar triangles with a test of similarity.
\( AB \) is a chord of a circle with center \( O \), \( AOC \) is the diameter of the circle, and \( AT \) is a tangent at \( A \). Write the answers to the following questions:
[(a)] Draw the figure using the given information.
[(b)] Find the measures of \( \angle CAT \) and \( \angle ABC \) with reasons.
[(c)] Determine whether \( \angle CAT \) and \( \angle ABC \) are congruent. Justify your answer.
Determine whether the points \( A(1, -3), B(2, -5), C(-4, 7) \) are collinear.
\( \triangle ABC \sim \triangle LMN \). In \( \triangle ABC \), \( AB = 5.5 \, \text{cm} \), \( BC = 6 \, \text{cm} \), \( CA = 4.5 \, \text{cm} \). Construct \( \triangle ABC \) and \( \triangle LMN \) such that \( \frac{BC}{MN} = \frac{5}{4} \).
Segment \( PM \) is a median of \( \triangle PQR \), \( PM = 9 \), and \( PQ^2 + PR^2 = 290 \). Find \( QR \).
Prove that, "If a line parallel to a side of a triangle intersects the remaining sides in two distinct points, then the line divides the sides in the same proportion."
\( \frac{1}{\sin^2 \theta} - \frac{1}{\cos^2 \theta} - \frac{1}{\tan^2 \theta} - \frac{1}{\cot^2 \theta} - \frac{1}{\sec^2 \theta} - \frac{1}{\csc^2 \theta} = -3 \), then find the value of \( \theta \).
A cylinder of radius \( 12 \, \text{cm} \) contains water up to the height \( 20 \, \text{cm} \). A spherical iron ball is dropped into the cylinder, and thus the water level is raised by \( 6.75 \, \text{cm} \). What is the radius of the iron ball?
Draw a circle with centre \( O \) having radius \( 3 \, \text{cm} \). Draw tangent segments \( PA \) and \( PB \) through the point \( P \) outside the circle such that \( \angle APB = 70^\circ \).
Radius of a sector of a circle is \( 3.5 \, \text{cm} \) and length of its arc is \( 2.2 \, \text{cm} \). Find the area of the sector.
Find the length of the hypotenuse of a right-angled triangle if the remaining sides are \( 9 \, \text{cm} \) and \( 12 \, \text{cm} \).
Find the slope of the line passing through the points \( A(2, 3) \) and \( B(4, 7) \).
Find the surface area of a sphere of radius \( 7 \, \text{cm} \).
A circle having radius \( 3 \, \text{cm} \), then the length of its largest chord is:
Two circles of radii \( 5 \, \text{cm} \) and \( 3 \, \text{cm} \) touch each other externally. Find the distance between their centres.
Find the side of a square whose diagonal is \( 10\sqrt{2} \, \text{cm} \):
A line makes an angle of \( 45^\circ \) with the positive direction of the X-axis. Find the slope of the line.
Out of the dates given below, which date constitutes a Pythagorean triplet?
Find the value of \( \sin 0 \times \csc 0 \):
What is the slope of the X-axis?

'खालील प्रश्न सोडवा :चूक की बरोबर ते लिहा : खवटपणा ही ऑक्सिडीकरण प्रक्रिया आहे.

'काचेचा हवेच्या संदर्भात असलेला अपवर्तनांक $\frac{3}{2}$ असेल तर हवेचा काचेच्या संदर्भात अपवर्तनांक .......... असेल.'

 'ज्या रासायनिक अभिक्रियेत एकाच अभिक्रियाकारकापासून दोन किंवा अधिक उत्पादिते मिळतात, त्या अभिक्रियेला ......... अभिक्रिया असे म्हणतात.'

'आधुनिक आवर्तसारणीत अधातू ............ खंडात आहेत.'

'रासायनिक समीकरणाच्या डाव्या बाजूस'