NTSE SAT Mathematics Papers 16

If x percent of y is equal to 1 percent of z, y percent of z is equal to 1 percent of x and z percent of x is equal to 1 percent of y, then the value of xy + yz + zx is

The value of\(\frac{{2 + \sqrt 2 + \sqrt 6 }}{{3 + \sqrt {2 + \sqrt 3 } }} + \sqrt {2 + \sqrt 3 } + \sqrt {2 - \sqrt 3 } \)is

The unit’s digit of the product \({3^{1001}} \times {7^{1002}} \times {13^{1003}}\)is

The perimeters of a regular hexagon and a square are equal. The ratio of the area of the square of hexagon is

If \({a_1},\,{a_2},\;{a_3},...........\) is an arithmetic progression with common difference 1 and \(\sum\limits_{i = 1}^{98} {{a_1} = 137} \), then the value of \({a_2} + {a_4} + {a_6} + ... + {a_{98}}\)is

ABCD is a triangle with AD=10 cm. Semicircle are drawn on AD and BC if the shaded area is 100 \(c{m^2}\), then the shortest distance (in cm) between the semi circles is

In the figure, the area of square ABCD is \(4c{m^2}\)and E any point on AB. F, G and H and K are the mid-point of DE, CF, DG and CH respectively. The area of \(\Delta KDC\) is

If \(P + \sqrt 3 \,\,\,Q + \sqrt 5 \,\,\,\,R + \sqrt {15} \,\,\,\,\,\,S = \frac{1}{{1 + \sqrt 3 + \sqrt 5 }}\)then the value of P is

If \({\sec ^2}\theta + {\tan ^2}\theta = 2,\,\,0^\circ < \theta < 90^\circ \), then the value of \(\cos e{c^2}\theta + {\cot ^2}\theta \)is

If the roots of \(p{x^2} + 2qx + r = 0\)and\(q{x^2} - 2\sqrt {pr} \,x + q = 0\) are simultaneously real, than

If a right circular cone, with slant height l , and a right circular cylinder have the same radius r, same total surface area and heights h and \(h'\)respectively, then \(\sqrt {\frac{{l - r}}{{l + r}}} = \)

\(\Delta ABC\)has vertices A(-4, 1), B(2, -1) and C (1, k). The number of possible values for k such that the triangle is isosceles is

In a class of boys and girls, an student is chosen at random. If the probability that a boy is chosen is \(\frac{2}{3}\)of the probability that a girl is chosen, the ratio of the number of boys to the total number of students is the class is

In the figure, DB is a diagonal of rectangle ABCD and line l through A and line m through C divide DB in three equal parts each of length 1 cm and are perpendicular to DB area (in \(c{m^2}\)) of rectangle ABCD is

One of the factor of \({x^6} + 10{x^3} - 27\)is