List of top Questions asked in CBSE Class X

PQ is tangent to a circle with centre O. If \(\angle POR = 65^\circ\), then m\(\angle PTR\) is
From an external point P, a tangent PT has been drawn to a circle with centre at O and radius 3 cm, intersecting its concentric circle at A and B. If AB = 8 cm and OA = AP, the length PQ equals.
Three tennis balls are just packed in a cylindrical jar. If radius of each ball is r, volume of air inside the jar is
Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is
Observe the graph of polynomial p(x). The zeroes of the polynomial are
A circle is divided into 16 identical sectors. If radius of the circle is 7 cm, area of each sector is
The value of k for which the system of linear equations kx – y – 2 = 0 and 6x – 2y – 3 = 0 has infinitely many solutions, is (does)
An ice-cream cone of radius r and height h is completely filled by two spherical scoops of ice-cream. If radius of each spherical scoop is \(\frac{r}{2}\), then h : 2r equals
The distance between the points (a cos \(\theta\) + b sin \(\theta\), 0) and (0, a sin \(\theta\) – b cos \(\theta\)) is
Rays from the sun converge at a point 25 cm behind a convex lens. The distance at which an object be placed in front of the lens to get a virtual image, is:
Which of the following is NOT a type of motivation?
The value of x for which \( 2x, (x + 10) \) and \( (3x + 2) \) are the three consecutive terms of an A.P. is :
What is the difference between a Web Server and a Web Browser?
For acute angles A and B and \(A + 2B\) and \(2A + B\) are acute if \(\tan (A + 2B) = \sqrt{3}\) and \(\sin (2A + B) = \frac{1}{\sqrt{2}}\), then find the measures of angles A and B.}
Identify the imperative sentence:
The distance of the point \( A(4a, 3a) \) from x-axis is :
Through the mid-point Q of side CD of a parallelogram ABCD, the line AR is drawn which intersects BD at P and produced BC at R. Prove that \(AQ = QR\).
The perimeter of sector OAB of a circle with centre O and radius 5.6 cm, is 15.6 cm. Find length of the arc AB. Also find the value of \(\theta\).
Prove that : \(\frac{1}{\sec x - \tan x} - \frac{1}{\cos x} = \frac{1}{\cos x} - \frac{1}{\sec x + \tan x}\)
A kite is flying at a height of 60 m above the ground level. Ravi, standing at the roof of the house is holding the string straight and observes the angle of elevation of kite as 30º. From the bottom of the same building, the angle of elevation of kite is 45º. Find the length of the string and height of roof from the ground. (Use \(\sqrt{3} = 1.73\))

\(\alpha, \beta\) are zeroes of the polynomial p(x) = 3x\(^2\) – 6x – 5. Find the value of \(\frac{1}{\alpha^2} + \frac{1}{\beta^2}\).
A trader has three different types of oils of volume 870 l, 812 l and 638 l. Find the least number of containers of equal size required to store all the oil without getting mixed.
Assertion (A) : (\(\sqrt{3}\) + \(\sqrt{5}\)) is an irrational number.
Reason (R) : Sum of the any two irrational numbers is always irrational.
In the given figure, DE \(\parallel\) AC and DF \(\parallel\) AE. Prove that : \(\frac{BF}{FE} = \frac{BE}{EC}\).
Verify that roots of the quadratic equation (p – q)x\(^2\) + (q – r)x + (r – p) = 0 are equal when q + r = 2p.