AP ICET 11th September 2020 Shift-1

From the top of a vertical cliff of 40m high, the angle of depression of an object that is at the base level of the cliff is $$30^{\circ}$$. If the object is at a distance $$x$$ units from the base of the cliff, then $$\frac{1}{x + 40}$$

Two polynomials $$f(x)$$ and $$g(x)$$ of degree 3 have $$2x^{2} + 7x + 5$$ as a common factor. If 1 and 2 are respectively the zeros of $$f(x)$$ and $$g(x)$$, then the zeros of the polynomial  $$\left(f(x) - g(x)\right)$$ are

When the polynomial $$5x^{4} + 7x^{2} + 2x + 5$$, divided by $$(x - 2)(x - 3)$$ if be quotient is $$ax^{2} + bx + c$$ then a + b + c =

Let $$x$$ and y be two positive integers with $$x > y$$ and when $$x$$ is divided by y, the remainder obtained is d. When y is divided by d leaves a remainder f and when dis divided by f leaves zero as remainder, then the greatest common divisor of $$x$$ and y is

If the polynomial $$f(x)$$ when divided by $$(x - 1)$$ leaves a remainder 2 and when divided by $$(x - 2)$$ leaves a remainder 1, then the remainder when $$f(x)$$ is divided by $$(x - 1)(x - 2)$$ is

For a fraction $$\frac{x}{y}$$ with $$(x, y) = 1$$, if the numerator is increased by 2 and the denominator is decreased by 3, then the fraction becomes 6. On the other hand, if the numerator is increased by 3 and the denominator is decreased by 2, then that fraction is equal to 5. Then $$\frac{x-y}{3} = $$

The number of common positive integral solutions of $$3x + 5y \leq 15$$ and $$2x + 7y \leq 14$$ is

If $$\frac{3+5+\cdot\cdot\cdot n^{th} term}{3+6+12+ \cdot\cdot\cdot n^{th} term} = \frac{16}{63}$$, then n =

If l, m, n, rare in harmonic progression and $$l > m > n > r$$, then $$\frac{l+r}{m+n}$$ = 

If the coefficients of $$x^{6}$$ and $$x^{5}$$ in the binomial expansion of $$(5 + ax)^{8}$$ are equal, then a=