NTSE SAT Mathematics Papers 18

If \({2^{x - 1}} + {2^{x - 1}} = 320\)then the value of x is-

If \(x + \frac{1}{x} = 2\)then \(\sqrt x + \frac{1}{{\sqrt x }}\)will be-

What is the value of P for which (a – 2) is factor of \({a^2} - 5a + P\)-

A person wishes to fit three rods together in the shape of a right angled triangle so that the hypotenuse is to be longer 4 cm than the base and 8 cm longer than the altitude. The lengths of the rods are-

If x + y = 8, xy = 15, then the value of \({x^2} + {y^2}\)will be-

If \(\frac{1}{{p + q}},\frac{1}{{q + r}},\frac{1}{{r + p}}\)are in A.P. then

For the equation \(3{x^2} + px + 3 = 0\), if one of the roots is the square of the other then p =______

The area of a rectangle is same as that of a circle of radius \(\sqrt {\frac{{35}}{{11}}} \)cm. If the length of the rectangle exceeds its breadth by 3 cm, then the length of the rectangle is

If x + y =1 then \({x^3} + {y^3} + 3xy = ...........\)

The difference between a two digit given number and the number obtained by interchanging the digits is 27. The sum of the two digits is ___________

The probability that a leap year selected will have 53 Sunday is

The probability ‘p’ of happening of an event

If \(SinA = \frac{1}{2}\left( {0^\circ < A < 90^\circ } \right)\)then \(Co{s^3}A - 3CosA = ...................\)

If \(Sin{\theta _1} + Sin{\theta _2} + Sin{\theta _3} = 3\)then \(Cos{\theta _1} + Cos{\theta _2} + Cos{\theta _3} = ............\)

If \(Sin\theta + Co\sec \theta = 2\)then \(Sin{\theta ^{100}} + Co{\sec ^{100}}\theta = .............\)