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OTI365 - NTSE - X Standard
NTSE SAT Mathematics - Quadratic Equation Sample Question Paper

SAT Mathematics - Quadratic Equation

Exam Duration: 45 Mins Total Questions : 30

1 )

The product of two natural numbers is 17. Then, the sum of the reciprocals of their squares is

(a)
\(\frac { 1 }{ 289 } \)
(b)
\(\frac { 289 }{ 290 } \)
(c)
\(\frac { 290 }{ 289 } \)
(d)
289

2 )

If, \(x+\frac { 1 }{ x } =3\) then the value of x⁶+\(\frac { 1 }{ { x }^{ 6 } } \) is

(a)
927
(b)
114
(c)
364
(d)
322

3 )

ax²+bx+c=0, where a,b and c are real roots, if

(a)
c = 0
(b)
b²>3ac
(c)
a, b, c are integers
(d)
ac>0, and b is zero

4 )

The number of real roots of quadratic equation x²-3|x|-10 = 0 is

(a)
1
(b)
2
(c)
3
(d)
4

5 )

If one root of the two quadratic equations x²+ax+b=0 and x²+bx+a=0 is common, then

(a)
a + b = 1
(b)
a + b = -1
(c)
ab = 1
(d)
ab = -1

6 )

If the equation x² - kx + 1 = 0, has no real roots then

(a)
-2<k<2
(b)
-3<k<3
(c)
-4<k<4
(d)
none of these

7 )

If \(\alpha\) and \(\beta\) are the roots of quadratic equation x²-2x+1, then \(\alpha\)²+\(\beta\)² is

(a)
1
(b)
3
(c)
2
(d)
-2

8 )

Find the nature of the roots of the quadratic equation \({ 3x }^{ 2 }-4\sqrt { 3 } x+4=0\)

(a)
\(2\frac { \sqrt { 3 } }{ 3 } ,2\frac { \sqrt { 3 } }{ 3 } \)
(b)
\(2\frac { \sqrt { 3 } }{ \sqrt { 3 } } ,2\frac { \sqrt { 3 } }{ \sqrt { 3 } } \)
(c)
\(2\frac { \sqrt { 3 } }{ 3 } ,-2\frac { \sqrt { 3 } }{ 3 } \)
(d)
None of these

9 )

Solve 5^(x+1) + 5^(2-x) = 5³+1

(a)
2, -1
(b)
-2, 1
(c)
-2, -1
(d)
None of these

10 )

A total number of 324 coins of 20 paise and 25 paise makes a sum of Rs 71. The number of 25 paise coins

(a)
120
(b)
124
(c)
37
(d)
40

11 )

If the root of the equation (b-c)x² + (c-a)x+(a-b) = 0 is 1, the other root will be

(a)
1
(b)
\(\frac { b-a }{ b-c } \)
(c)
\(\frac { a-b }{ b-c } \)
(d)
None of these

12 )

If \(\alpha\) and \(\beta\) are roots of the equation x^2-k(x+1)-c=0, the values of (\(\alpha\)+1)(\(\beta\)+1) is equal to

(a)
1
(b)
1-c
(c)
0
(d)
None of these

13 )

The value of m for which the equation 3x²+(7+m) x+2-m=0 has equal roots is

(a)
-1
(b)
1
(c)
25
(d)
None of these

14 )

The nature of the roots of the quadratic equation a²b²y² + 2abcy +c² = 0,

(a)
Real and equal
(b)
Real and Distinct
(c)
No real roots
(d)
Reciprocal roots

15 )

The roots of the quadratic equation are (b+a)x²-2(b²-a²)x+(b-a)² = 0 are

(a)
Equal
(b)
Distinct
(c)
Real
(d)
None

16 )

The roots of the quadratic equation x²-x-12=0 are

(a)
4,-3
(b)
-4, 3
(c)
-4, -3
(d)
None of these

17 )

Sashankand Manav together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Represent this situation in the form of a quadratic equation

(a)
(x-5)(40-x) = 124
(b)
(x-5)(x-40) = 124
(c)
(5+x)(40-x) = 124
(d)
None of these

18 )

The sum of a number and its reciprocal is \(\frac { 5 }{ 2 } \). Represent this situation in the form of a quadratic equation

(a)
\(x+\frac { 1 }{ x } =\frac { 5 }{ 2 } \)
(b)
\(x-\frac { 1 }{ x } =\frac { 5 }{ 2 } \)
(c)
\({ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } =\frac { 5 }{ 2 } \)
(d)
\(x+\sqrt { x } =\frac { 5 }{ 2 } \)

19 )

The quadratic equation has two distinct roots if

(a)
b² = 4ac
(b)
b²>4ac
(c)
b²<4ac
(d)
b² = ac

20 )

The discriminant of the quadratic equation 2x²-4x+3 = 0 is

(a)
8
(b)
-8
(c)
4
(d)
-4

21 )

The roots of the quadratic equation 2x²-4x + 3 are

(a)
Real and distinct
(b)
Real and equal
(c)
No real roots
(d)
Reciprocal roots

22 )

Find the value of k if the roots of the quadratic equation kx(x-2) +6=0 are equal

(a)
3
(b)
4
(c)
5
(d)
6

23 )

If the sum of the roots of the quadratic equation 3x²+(2k+1)x-(k+5)=0 is equal to the product of the roots, then the value of k is

(a)
2
(b)
3
(c)
4
(d)
5

24 )

If the two roots of the two quadratic equations x² + mx + 1 = 0 and ax² + bx + \(\alpha\) = 0 are common, then the value of m is

(a)
ab
(b)
b
(c)
\(\frac { a }{ b } \)
(d)
\(\frac { b }{ a } \)

25 )

The condition that both the roots of the two quadratic equation a₁x²+b₁x+c₁=0 and a₂x²+b₂x+c₂=0 are common is

(a)
a₁a₂|b₁b₂+c₁c₂=0
(b)
\(\frac { { a }_{ 1 } }{ { a }_{ 2 } } =\frac { { b }_{ 1 } }{ { b }_{ 2 } } =\frac { { c }_{ 1 } }{ { c }_{ 2 } } \)
(c)
\({ a }_{ 1 }+{ b }_{ 1 }+{ c }_{ 1 }={ a }_{ 2 }+{ b }_{ 2 }+{ c }_{ 2 }\frac { W }{ R } \)
(d)
\({ a }_{ 1 }^{ 2 }+{ b }_{ 1 }^{ 2 }+{ c }_{ 1 }^{ 2 }={ a }_{ 2 }^{ 2 }+{ b }_{ 2 }^{ 2 }+{ c }_{ 2 }^{ 2 }\)