TS ICET 19th August 2021 Shift-2

If the top of a 15 meter high tower makes an angle of depression of $$60^{circ}$$ with the bottom of an electric pole and an angle of depression of $$30^{circ}$$ with the top of the pole, then the height (in meters) of that electric pole is

$$\sqrt{(x^{2} - 2x - 15)(x^{2} - 5x - 24)(x^{2} - 13x + 40)}$$

If $$\left(3a-\frac{1}{b}\right)^{2}-8\left(3a-\frac{1}{b}\right)+16+\left(c+\frac{1}{b}-2a\right)\left(3a-\frac{1}{b}-4\right)=0$$, then

A polynomial in $$x$$ leaves remainder -1 and 7, when it is divided by $$(x+ 1)$$ and $$(x - 3)$$ respectively. If the same polynomial is divided by $$x^{2} - 2x - 3$$ then the remainder is

If the remainder when the polynomial $$7x^{3} - 8x^{2} + 9x - 10$$ is divided by $$x^{2} - x - 2$$ is $$ax + b$$, then a + b =

A person has Rs.10 and Rs.20 notes in his purse. Total number of notes is 37. Total amount is Rs.510. Then the difference between the number of Rs.10 notes and Rs.20 notes is

Five pens and six pencils cost Rs.28. Six pens and five pencils cost Rs.27. Now the cost (in Rupees) of each pen and each pencil respectively?

The sum of all natural numbers between 1 and 100 which are multiples of 3 is

If the $$5^{th}$$ term of a Geometric Progression is 7, then the product of the first 9 terms is

If $$C_{0}, C_{1}, C_{2}, ... C_{n}$$, are binominal co-efficients of $$(1+x)^{n}=$$ then $$C_{0} - C_{1} + C_{2} + ... + C_{n}(-1)^{n}$$