List of top Mathematics Questions asked in Common Entrance Test Delhi Polytechnic

The area of the triangle with vertices $(0, 0)$, $(6, 0)$, and $(0, 5)$ is:
How many least number of distinct points determine a unique line ?
The perpendicular distance of the point P (6,8) from x axis is :
If \( (2K-1, K) \) is a Solution of the equation \( 10x - 9y = 12 \), then K =
If \( (x-a) \) is a factor of \( x^3 - 3x^2a + 2a^2x + b \), then the value of \( b \) is :
If \( x + \frac{1}{x} = 2 \), then \( x^3 + \frac{1}{x^3} = \)
Every point on a number line represents :

If \(\frac{5+9+13+…… \text{ to } n \text{ terms}}{7+9+11+……. \text{ to } (n+1) \text{ terms}}\) \(= \frac{17}{16}\) then\(n =\)

In the given figure \(\triangle \text{ABC}\) is an equilateral triangle of side 8 cm. A,B and C are the centres of circular arcs of radius 4 cm. Find the area of the shaded region correct upto 2 decimal places (\(\pi = 3.142, \sqrt{3} = 1.732\)): Equilateral triangle ABC. From each vertex (A, B, C), a circular sector is drawn inside the triangle.

Radius of each sector is 4 cm. Side of triangle is 8 cm. The shaded region is the area of the triangle MINUS the areas of these three sectors.

In a single throw of pair of dice, the probability of getting a multiple of 2 on one and a multiple of 3 on the other will be :
A bag contains 14 balls of which \(x\) are white. If 6 more white balls are added to the bag, the probability of drawing a white ball is \( \frac{1}{2} \). Then the value of \( x = \)
Two dice are numbered 1,2,3,4,5,6 and 1,1,2,2,3,3 respectively. They are thrown and the sum of the numbers on them is noted. The probability of getting a sum of 5 will be :
From the top of a tower \(h\) meter high, the angle of depression of two objects, which lie on either side of it are \( \alpha \) and \( \beta \). The distance between the two objects is :
If \( \alpha \) and \( \beta \) are the roots of \( 2x^2 - 4x + 1 = 0 \). Then \( \frac{1}{\alpha^2\beta} + \frac{1}{\alpha\beta^2} = \)
The exponent of 3 in the prime factorisation of 864 is :
The circumference of a circle is 100 cm. The side of a square inscribed in the circle is :
The least numbers divisible by 2,3,7 and 9 is :

In the given figure \( \angle CAB = 90^\circ \) and AD \(\perp\) BC. If AC = 25 cm, AB = 1m and BD = 96.08 cm, then find the value of AD

Visual shows triangle CAB with right angle at A. AD is perpendicular to BC, with D on BC. Labels: AC=25cm, AB=1m. BD=96.08cm is marked on the hypotenuse segment.

Graphically, the two systems of equations \(x+7=0, y-2=0\) and \(x-2=0, y+7=0\) enclose a :
Sum of all 3 digit natural numbers which are divisible by 13 :
If the equation : \( (a^2+b^2)x^2 - 2(ac+bd)x + (c^2+d^2) = 0 \) has equal roots then :
A cone, a hemisphere and a cylinder stands on equal bases and have the same height. What is the ratio of their volumes :
If \( \sin A + \sin^2 A = 1 \), then the value of \( \cos^2 A + \cos^4 A \) is :
If \(a\) and \(b\) can take values 1,2,3,4. Then the number of the equations of the form : \(ax^2+bx+1=0\) having real roots is :
If the sum of first \(n\) terms of an A.P. is \( \frac{3n^2}{2} + \frac{5n}{2} \) then its 25th term is :