List of top Mathematical Ability Questions

If \(\frac{1 + \cos \theta + \sin \theta}{2 \sin \theta} = \frac{\lambda}{1 - \cos \theta + \sin \theta}\), then \(\lambda - 1 =\)

ABC is a right-angled triangle with right angle at B. If \(AB = 2\) and \(AC = 5\), then \(\tan C + \sec C =\)

If \(k\) is the minimum value of the algebraic expression \(x^2 + 3x + 2\) attained at \(x = a\), then \((k,a)=\)

If \(\frac{x+y}{xy}=\frac{12}{35}\) and \(\frac{x-y}{xy}=\frac{2}{35}\), then \(5x+7y=\)

The cost of two mangoes and three oranges together is ₹88, and the cost of four mangoes and seven oranges together is ₹188. Then, the cost of four mangoes and three oranges together, in rupees, is:

What is the sum of all natural numbers strictly between 100 and 1000 which are multiples of 5?

In a geometric progression the difference between the fifth term and the fourth term is 576 and the difference between the second term and the first term is 9. The fifth term is:

If \(\frac{\tan 60^\circ + \cot 60^\circ + \sec 60^\circ}{\tan 60^\circ + \cos 60^\circ + \csc 60^\circ} = a + b\sqrt{3}\), then \(\frac{a}{b} + \frac{b}{a} =\)

If \(a_n = \cos 2n\), then \(a_1 \times a_2 \times \dots \times a_{45} =\)

If A and B are any two non-empty sets, then \[ [(A \cap (A \cup B)^C)] \cup [(A \cap B)\cup(A\cap B^C)] = \]

If \(\alpha, \beta,\) and \(\gamma\) are the zeros of the polynomial \(6x^3 - 29x^2 + 46x + 24\), then the polynomial whose zeros are \(\frac1\alpha,\frac1\beta,\frac1\gamma\) is:

If \(P(x)=x^3+ax^2+bx+c\) is a polynomial such that \(P(1)=0\), \(P(2)=0\), and \(P(3)=6\), then \(6a+4b+3c=\)

If the quadratic polynomial \((x^2-x-2)\) is a factor of the polynomial \((x^4-x^3+ax^2+bx+4)\), then \((a,b)=\)

The polynomial \(f(x)\) when divided by \((x-4)\) and \((x-6)\) leaves remainders 6 and 8 respectively. Then the remainder of \(f(x)\) when divided by \((x^2-10x+24)\) is:

Set A contains all 3 digit positive integers that are divisible by 5, set B contains all 3 digit positive integers that are divisible by 7 and set C contains all 3 digit positive integers divisible by 11. Then \(n(A\cup B\cup C)=\)

The length of a side of a uniform cubic shape water tank is 1.2m. This tank is completely filled with water. From this tank 64 cans of water are removed and the water remaining is a \(\frac13\) portion of the tank. If the magnitude of all containers is uniform, then the amount of water that fills a can (in litres) is:

The length and height of a godown are \(22\)m and \(6.5\)m respectively. If the area of four walls is \(442\) sq.m., then the breadth of the room in meters is:

The radius of the base of a solid cone is 6 cm and its vertical height is 8 cm. Then the curved surface area (approximate) of the cone in \(\text{cm}^2\) is:

The volume of a cuboid is twice that of the volume of a cube. The dimensions of the cuboid are 9 cm, 8 cm, and 6 cm. If it costs ₹2.50 per sq.cm. for painting, the amount required to paint the surfaces of the cube (in rupees) is:

The remainder when \(27^{325}\) is divided by 14 is:

The product of two numbers 5 and \(x\) leaves remainder 6 when divided by 11. Then the least integer \(x\) is:

What is the area of a rhombus (in sq.m.) whose perimeter is 40 m and one of its diagonals is 16 m?

The dimensions of a brick and a wall are \(20\text{ cm} \times 10\text{ cm} \times 7.5\text{ cm}\) and \(25\text{ m} \times 2\text{ m} \times 0.75\text{ m}\) respectively. How many bricks (in thousands) are required to construct the wall?

The dimensions of a rectangular park are \(75\text{ m} \times 55\text{ m}\). A walking path of breadth \(2.5\) m is laid on the outside and along the boundary of the park. The area of the path in sq. meters is:

A certain number of persons were hired to complete a job in 60 days. If 8 more persons are hired then the job could be completed in 10 days less. How many persons were hired originally?