List of top Questions asked in TG ICET

$ax^{2}-bx+c=0$ has roots $\sin60^\circ$ and $\cos60^\circ$. Then \[ \frac{ac}{b^{2}}+\frac{a+c}{b} = \ ? \]}

$(\cos^{2}0^{\circ}+\sin^{2}30^{\circ})(\tan^{2}45^{\circ}+\cot^{2}60^{\circ})(\cos^{2}180^{\circ}+\sin^{2}90^{\circ})=$

$\tan(A+B)=m$ and $\tan(A-B)=n$. Then $\tan(2A)=$

A boat sails 27 kms down stream in 3 hours but takes 9 hours to sail back the same distance up stream. Calculate the ratio of speed of boat to speed of stream.

The equation \(x^3-24x^2+\alpha x-\beta=0\) has positive integral roots \(p,q,r\). If geometric mean of the three roots is 8, then \(\alpha=\)

The polynomial \(4x^3+ax^2+bx+c\) leaves remainders 11, -3 and 41 respectively when divided by \(x+1\), \(x+2\) and \(x-2\). Then the remainder when it is divided by \(x-1\) is

A polynomial \( p(x) \) in x leaves remainder 5 and 6 when the polynomial \( p(x) \) is divided by \( x+1 \) and \( x+3 \) respectively. If it leaves remainder \( ax+b \) when divided by \( x^{2}+4x+3 \), then \( 4a+6b = \)

If \(\frac{48}{x+y}-\frac{6}{x-y}=10\) and \(\frac{15}{x+y}+\frac{4}{x-y}=9\), then \(x^{2}+y^{2}=\)

If \(x, y\) are two real numbers such that \(x+y=23\) and \(x^{2}+y^{2}=289\), then \(x^{3}+y^{3}=\)

The floor of hall of dimensions \(18\,m \times 12\,m\) is to be fixed by tiles of size \(45\,cm \times 15\,cm\). The number of tiles required for the floor of the hall is:

A solid metallic sphere of 16 cm diameter is melted and cast into smaller solid spheres of diameter 4 cm. The number of smaller spheres formed is:

Three sets A, B and C are defined as follows:
\(A=\{x|x\text{ is an even integer}\}\),
\(B=\{x|x\text{ is an integer and multiple of 5}\}\),
\(C=\{x|x\text{ is an integer and multiple of 10}\}\).
Then \(A \cap (B \cup C)=\)

If A and B are two non-empty sets, then \((A\cup B)-(A\cap B)=\)

The product of two numbers 13 and \(x\), when divided by 11 leaves remainder 7. The least positive such integer \(x\) is:

If \(793 \equiv x \pmod{29}\) and \(0 \le x < 29\), then the sum of distinct prime divisors of \(x\) is:

If \(\alpha,\beta\) are the zeroes of the polynomial \(x^2-78x+k\) and if \(\alpha=\beta-6\), then \(k=\)

In triangle ABC, \( AB=26 \) cm, \( AC=24 \) cm and \( \angle C=90^{\circ} \). If \( r_1, r_2, r_3 \) are the areas of the semi-circles with AB, AC, BC as diameters respectively, then \( \frac{1}{\pi}(r_1 + 2r_2 + 3r_3) \) (in \( cm^2 \)) is

The length of a rectangle is 8 cm more than its breadth. If the area of the rectangle is 209 \( cm^2 \), then the perimeter of the rectangle, in cm, is

If the total surface area of a cone is \(384\pi \, cm^2\) and its height is 16 cm, then volume of the cone, in \(cm^3\) is

The height of a cylinder is 7 cm and the area of its curved surface is 264 sq.cm. Then the volume of the cylinder in cu.cm. is (take value of \( \pi=\frac{22}{7} \))

The perimeter of the longest circle that can be inscribed in a rectangle of sides \(161 \, \text{cm}\) and \(296 \, \text{cm}\), in cm, is (take \( \pi \approx \frac{22}{7} \)).

160 people are employed to finish the work in 120 days. After 40 days it was found that only \(\frac{1}{5}\) of the work is completed. To complete the work in the scheduled time, how many more people are to be employed?

Two persons P and Q enter into partnership with capitals of ₹60000 and ₹45000 respectively. After three months P withdrew ₹20000 while Q invested another ₹15000. After another five months R joins the business with a capital of ₹90000. At the end of the year the difference between the profits received by P and R in a total profit of ₹32200 in rupees is

Two pipes A and B can fill a tank in 10 minutes and 15 minutes respectively. Both pipes are opened together, but after 3 minutes, pipe B is closed. How much more time will it take for pipe A to fill the remaining part of the tank?

A tank is connected with two inlet pipes A and B and one outlet pipe C. A, B independently can fill the (empty) tank in 20 hours and 30 hours respectively. If all the three pipes are opened simultaneously it takes 3 hours extra than if only A and B are opened. Then the time in hours required for the pipe C alone to empty the full tank (in hours) is