NTSE SAT Mathematics Papers 17

If \(\alpha \,\,and\,\beta \)are the zeroes of the polynomial \(f(x) = {x^2} - 5x + k\)such that \(\alpha - \beta = 1\), the value of K is-

If (x+2) is a factor of the polynomial \(f(x) = {x^2} + ax + 2b\)and a+b=1, then the value of a and b are-

If \({1^3} + {2^3} + ........ + {9^3} = 2025\)then \({\left( {0.11} \right)^3} + {(0.22)^3} + ......... + {(0.99)^3}\)will be-

If \(\tan \theta + \frac{1}{{\tan \theta }} = 2\)then the value of\({\tan ^2}\theta + \frac{1}{{{{\tan }^2}\theta }}\)will be-

If Sec 2A = Cosec \(\left( {A - 42^\circ } \right)\)where 2A is acute angle then value of A is-

If \(\frac{{Cos\theta - Sin\theta }}{{Cos\theta + Sin\theta }} = \frac{{1 - \sqrt 3 }}{{1 + \sqrt 3 }}\)then \(\theta \)is

If \(Cot\theta + Co\sec \theta = 2\), then the value of \(\frac{{1 + \cos \theta }}{{1 - \cos \theta }}\)is-

In the following figure O is the centre of circle and \(\angle BAC = n^\circ ,\,\,\angle OCB = m^\circ \)then

In given figure \(AB\parallel CD,\,\angle ABE = 120^\circ ,\,\,\angle DCE = 110^\circ \,\,and\,\angle BEC = x^\circ \)then \(x^\circ \)will be-

In the following figure \(\angle PQR\)is-

If \(\overline x \)is the mean of the terms \({x_1},{x_2},{x_3},........,{x_n}\)and \(\sum\limits_{i = 1}^n x = {x_1} + {x_2} + {x_3} + ...... + {x_n}\)then the value of \(\sum\limits_{i = 1}^n x - n\overline x \)is

Point P divides the line segment joining the points A (2, 1) and B (5, -8) such that \(\frac{{AP}}{{AB}} = \frac{1}{3}\)if P lines on the line 2x + y + k=0 then the value of K is-

A copper wire 3 mm in diameter is rounded about a cylinder whose length is 1.2 m and diameter is 10 cm, so as to cover the curved surface of the cylinder. The length of the wire is-

Relation among mean, median and mode is-

The area of the figure formed by the inter section of lines x=0, y=0, x=3, y=4 will be-