NTSE SAT Mathematics - Algebra
Exam Duration: 45 Mins Total Questions : 30
If \(\sqrt {1+ \frac{x}{169}}=\frac{14}{13}\) , then x is equal to
- (a)
5
- (b)
3
- (c)
27
- (d)
13
If \(\sqrt{3^n}\) =729, then value of n is
- (a)
6
- (b)
10
- (c)
8
- (d)
12
If y=5, then what is the value of 10y \(\sqrt{y^1-y^2}\) ?
- (a)
100
- (b)
500
- (c)
\(200\sqrt5\)
- (d)
\(50\sqrt2\)
If x = (7 - 4 \(\sqrt3\)) then the value of (x+\(\frac{1}{x}\)) is
- (a)
\(8 \sqrt3\)
- (b)
14
- (c)
\(3\sqrt3\)
- (d)
14 + \(8 \sqrt3\)
the value of \(\frac{(x-y)^3+(y-z)^2+(z-3)^3}{9(x-y)(y-z)(z-x)}\) is equal to
- (a)
\(\frac{1}{3}\)
- (b)
\(\frac{1}{9}\)
- (c)
0
- (d)
1
Find x if \(\frac{x}{5}-\frac{x}{6}=4\)
- (a)
-100
- (b)
-120
- (c)
100
- (d)
120
x = 1 - q and y = 2q + 1, then for what value of q, x is equal to y?
- (a)
0
- (b)
\(\frac{1}{2}\)
- (c)
2
- (d)
-1
1f 2x+3y=31,y-z=4 and x+2z=11, then what is the value of x+y+ z ?
- (a)
16
- (b)
15
- (c)
13
- (d)
12
If 3x-5y=5 and \(\frac{x}{x+y} = \frac{5}{7}\), then what is the value of x-y?
- (a)
9
- (b)
6
- (c)
4
- (d)
3
If 5x2-13xy+y6y2 = 0 then x:y is
- (a)
(3:5) only
- (b)
(3:5) or (2:1)
- (c)
(2:1) only
- (d)
(5:3) or (1:2)
The ratio between two numbers is 3:4 and their LCM is 180. The first number is
- (a)
45
- (b)
20
- (c)
15
- (d)
60
The third proportional to (x2-y2) and (x-y) is
- (a)
\(\frac{a-y}{x+y}\)
- (b)
\(\frac{x+y}{x-y}\)
- (c)
(x-y)
- (d)
(x+y)
If 3a+b=27 and 27a-b = 3, then which of the following is correct?
- (a)
\(\frac{5}{3},\frac{4}{3}\)
- (b)
\(\frac{2}{3},\frac{5}{3}\)
- (c)
\(\frac{4}{3},\frac{2}{3}\)
- (d)
none of these
The value of \(\frac{2^{7m+4}\times3^{2m-3n}\times5^{5m+3n+4}\times6^{m+2n-3}}{10^{2m+4n+7}15^{3m-n-3}2^{6m-2n-5}}\) is
- (a)
\(\frac{1}{2}\)
- (b)
2
- (c)
0
- (d)
1
What must be subtracted from 2x4-11x3 + 29x2-40x+29, so that the resulting polynomial is exactly divisible by x2-3x+4?
- (a)
2x+5
- (b)
-2x+5
- (c)
3x+5
- (d)
-3x+5
If α,β of the zeroes of the polynomial x2-9, Find αβ (α+β)?
- (a)
9
- (b)
3
- (c)
-3
- (d)
0
Which of the following is not a quadratic polynomial?
- (a)
x2+5x+6
- (b)
x2-5x+6
- (c)
1+(x2-2x)
- (d)
(x-2)(x+2)-(x2+5x)
The polynomial x2-5x+6 has
- (a)
no linear factor
- (b)
one linear factor
- (c)
Two linear factors
- (d)
more than two linear factors
If the product of zeroes of polynomial ax3-6x2 +11x-6 is 6, then value of a is
- (a)
0
- (b)
-1
- (c)
2
- (d)
1
Find the zeroes of quadratic polynomial \(\sqrt3x^2+10x+7\sqrt3\)
- (a)
\(\frac{7}{3},\sqrt3\)
- (b)
\(\frac{-7}{3},-\sqrt3\)
- (c)
\(\frac{4}{3},\sqrt3\)
- (d)
none of these
If 3p+q=27 and 3P-Q = 32 then p2+q2 is equal to
- (a)
4/3,2/3
- (b)
7/2,6/5
- (c)
\(\frac{1}{2},\frac{5}{2}\)
- (d)
none of these
If p(x) =x2-2x-3, then value of \((\frac{1}{4}).p(\frac{1}{4})\) is 11
- (a)
\(\frac{55}{16}\)
- (b)
\(\frac{-55}{16}\)
- (c)
\(-3\frac{7}{16}\)
- (d)
both B or C
The zeroes of x2+7x + 12 are
- (a)
4,3
- (b)
2,3
- (c)
-4,-3
- (d)
none of these
If x+y=4, y-x=8, xy=2, value of \(\frac{1}{x^2}-\frac{1}{y^2}\) will be
- (a)
2
- (b)
4
- (c)
6
- (d)
8
If 9x+y = 81 and 9x-y = \(\frac{1}{81}\)
- (a)
x=0,y=2
- (b)
x=2, y=-2
- (c)
x=3, y = -2
- (d)
none of these
x+z=8;xz = 16 then \(\frac{1}{x}+\frac{1}{z}\)is equal to
- (a)
\(\frac{1}{2}\)
- (b)
\(\frac{2}{8}\)
- (c)
\(\frac{1}{4}\)
- (d)
none of these
The value of \(\sqrt{10+\sqrt{25+\sqrt{108\sqrt{154+\sqrt{225}}}}}\) is
- (a)
6
- (b)
4
- (c)
10
- (d)
8
Rajeev's age after 15 years will be 5 times his age 5 years back. What is the present age of Rajeev?
- (a)
5 yrs
- (b)
10 yrs
- (c)
15 yrs
- (d)
none of these
Find the HCF and LCM of the polynomials (x2-3x+2) and (x2-4x+4).
- (a)
(x-3) (x-2) (x-4) (x-5)
- (b)
(x-2) (x-3) (x-4) (x-5)
- (c)
(x-1) (x-2) (x-2)
- (d)
none of these
If the polynomial 2x3-9x2+15x+p, when divided by (x-2) leaves -p as a remainder, then p is equal to
- (a)
-5
- (b)
20
- (c)
10
- (d)
-16
