TS ICET 1st Oct 2020 Shift-1

A man walking away from the foot of a cliff 150 meters high observes that it take 2 minutes to change the angle of elevation of the top of the cliff from $$60^{\circ}$$ to $$45^{\circ}$$. His walking speed in kmph is

If $$\alpha$$ and $$\beta$$ are two roots of the equation $$ax^{2} + bx + c = 0$$, then $$a + \beta$$ and $$\alpha \beta$$ are respectively

If $$\alpha, \beta, \gamma$$ are zeros the polynominal of $$ax^{2} + bx^{2} + cx + d$$, then the polynominal zero are $$\frac{1}{\alpha}, \frac{1}{\beta}, \frac{1}{\gamma} =$$

The remainder when $$f(x) = 4x^{3} - 3x + 9$$ is divided by $$3x - 2$$ is

If $$px^{2} + qx + 17$$ leaves remainder -5, 13 when divided by $$x - 5x + 7$$, respectively. Then $$3p -q =$$

Vishal's age is at present four times the age of Jahnavi. After 8 years, Vishal's age will be 2.5 times Jahnavi's age. In another eight years, how many times will be vishal's age, as compared to Jahnavi's age?

A rational number becomes $$\frac{1}{4}$$ when 7 is subtracted from the numerator and 3 is added to the denominator. The same number becomes 2 when 1 is added to the numerator and is subtracted from the denominator. The number is

The sum of eight terms of an A.P. is 316 and the difference between the first and the eighth terms is 91 . What is its first term?

If 5 times the $$5^{th}$$ term of an A.P. is equal to 13 times of its $$13^{th}$$ term, then the $$18^{th}$$ term of the A.P. is

What is. the number of terms the expansion of $$(a^{2} + 2ab + b^{2})^{10}$$