Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 36

MEDIUM

CAT

IMPORTANT

Earn 100

A two digit number is such that the product of its digits is $12 .$ When $9$ is addded to the number, the digits interchange their places, find the number:

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Important Questions on Theory of Equations

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CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 37

A plane left

40

minutes late due to bad weather and in order to reach its destination,

1600 km

away in time, it had to increase its speed by

400 km / hr

from its usual speed. Find the usual speed of the plane.

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CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 38

The sum of the squares to two natural consecutive odd numbers is

290

, then find the sum of the number.

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CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 8

The number of quadratic equations that are unchanged by squaring their roots is

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CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 11

If

x \in R,

and

K = \frac{(x^{2} - x + 1)}{(x^{2} + x + 1)},

then:

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CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 15

If

α, β, γ

are such that

α + β + γ = 2, α^{2} + β^{2} + γ^{2} = 6, α^{3} + β^{3} + γ^{3} = 8,

then

α^{4} + β^{4} + γ^{4}

is

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 16

The real values of a for which the quadratic equation 2x² - (a³ + 8a - 1) x + a² - 4a = 0 possesses roots of opposite signs are given by :

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 17

If

α, β

are the roots of

a x^{2} + b x + c = 0

and

α + h, β + h

are the roots of

p x^{2} + q x + r = 0,

then what is

h

equal to?

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 20

The value of

a

for which the equation

x^{2} - 2 (a - 1) x + (2 a + 1) = 0

has both roots positive is