List of top Questions asked in UK Class X

10th term of A.P. 4, 9, 14, ……. is:

In figure \( AB = 8 \, \text{cm} \) and \( PE = 3 \, \text{cm} \), then find AE. 

The table given below shows the daily expenditure on food of 25 households in a locality: 

In figure, there are shown sectors of radii 7 cm and 3.5 cm. Find the area and perimeter of the shaded region ABCD. 

Find the modal class and mode of the following data: 

A drone is flying at a height of 100 m above the ground. It observes on its right two stationary cars on a highway at angles of depression 45° and 30°. On the basis of above information, answer the following questions: If the drone rises to 150 m, find the tangent of the angle of depression of each car at the new height.
Two years ago, father was thrice as old as his daughter, and 6 years later he will be 4 years older than twice her age. How old are they now?
Prove that the parallelogram circumscribing a circle is a rhombus.
Prove the identity \( \sec^2 \theta = 1 + \tan^2 \theta \) for any right-angled triangle and use it to show that: \[ \frac{\sin \theta - \cos \theta + 1}{\sin \theta + \cos \theta - 1} = \frac{1}{\sec \theta - \tan \theta}. \]
A cylindrical block of radius 5 cm and height 9 cm is hollowed out from one end by removing a cone of radius 5 cm and slant height 10 cm. Find the total surface area and volume of the remaining solid.
Show graphically that the linear equations \( x - y = 8 \), \( 3x - 3y = 16 \) are inconsistent, i.e. it has no solution.
A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it possible to do so? If yes, at what distances from the two gates should the pole be erected?
Find a point on the Y-axis which is equidistant from the points \( A(6, 5) \) and \( B(-4, 3) \).
Find the coordinates of the points that trisect the line segment AB joining the points \( A(-1, 2) \) and \( B(2, 8) \).
If AP and DQ are medians of triangles ABC and DEF respectively, where \( \triangle ABC \sim \triangle DEF \), prove that: \[ \frac{AB}{DE} = \frac{AP}{DQ} \]
A drone is flying at a height of 100 m above the ground. It observes on its right two stationary cars on a highway at angles of depression 45° and 30°. On the basis of above information, answer the following questions: Find the distance of each car from the point on the highway just below the drone.
A drone is flying at a height of 100 m above the ground. It observes on its right two stationary cars on a highway at angles of depression 45° and 30°. On the basis of above information, answer the following questions: Find the distance between the two cars.
Form a quadratic equation, one of whose zero is \( 2 + \sqrt{5} \) and the sum of zeros is 4.
The A.P. \( 8, 10, 12, \ldots \) has 60 terms. Find the sum of the last 20 terms.
Find the area of a circle with maximum area that can be inscribed in a square of side 7 cm.
If \( \sin A + \cos A = \sqrt{2} \), find the value of \( \sin A \cos A \).
Two coins are tossed simultaneously, what is the probability of getting at least one head?
Find the value of K for which the given system of equations has infinitely many solutions: \[ Kx + 3y = K-3 \quad \text{(1)} \] \[ 12x + Ky = K \quad \text{(2)} \]
What do you understand by irrational number? Prove that \( 5 - 3\sqrt{2} \) is an irrational number.
Assertion (A): The number \(4^n\) cannot end with the digit 0, where \(n\) is a natural number.
Reason (R): A number ends with 0 if its prime factorization contains both 2 and 5.