Maths-
General
Easy

Question

For the quadratic polynomial f (x) = 4x2 – 8kx + k, the statements which hold good are

  1. there is only one integral k for which f (x) is non negative blank x blank R    
  2. for k < 0 the number zero lies between the zeros of the polynomial.    
  3. f (x) = 0 has two distinct solutions in (0, 1) for k element of left parenthesis 1 divided by 4 comma 4 divided by 7 right parenthesis
  4. Minimum value of y straight for all k element of R  is k(1 + 12k)

The correct answer is: there is only one integral k for which f (x) is non negative blank x blank R

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The graph of the quadratic polynomial y = ax2 + bx + c is as shown in the figure. Then :

The graph of the quadratic polynomial y = ax2 + bx + c is as shown in the figure. Then :

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The greatest possible number of points of intersections of 8 straight line and 4 circles is :

The students can make an error if they don’t know about the formula for calculating the number of points as mentioned in the hint which is as follows
The number point of intersection between two lines can be counted by finding the number of ways in which two lines can be selected out of the lot as two lines can intersect at most one point.
The number point of intersection between two circles can be counted by finding the number of ways in which two circles can be selected out of the lot multiplied by 2 as two circles can intersect at most two points.
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The greatest possible number of points of intersections of 8 straight line and 4 circles is :

Maths-General

The students can make an error if they don’t know about the formula for calculating the number of points as mentioned in the hint which is as follows
The number point of intersection between two lines can be counted by finding the number of ways in which two lines can be selected out of the lot as two lines can intersect at most one point.
The number point of intersection between two circles can be counted by finding the number of ways in which two circles can be selected out of the lot multiplied by 2 as two circles can intersect at most two points.
The number point of intersection between two circles can be counted by finding the number of ways in which one circle and one line can be selected out of the lot multiplied by 2 as one circle and one line can intersect at most two points.

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How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even position ?

Here we have obtained the total number of 9 digit numbers using the given digits. While finding the number of ways to arrange the odd digits in 5 even places, we have divided the 4! by 2! because the digit 3 were occurring two times and the digit 5 were occurring 2 times. Here we can make a mistake by conserving the number of even digits 4 and the number of odd digits 5, which will result in the wrong answer.

How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even position ?

Maths-General

Here we have obtained the total number of 9 digit numbers using the given digits. While finding the number of ways to arrange the odd digits in 5 even places, we have divided the 4! by 2! because the digit 3 were occurring two times and the digit 5 were occurring 2 times. Here we can make a mistake by conserving the number of even digits 4 and the number of odd digits 5, which will result in the wrong answer.

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A person predicts the outcome of 20 cricket matches of his home team. Each match can result either in a win, loss or tie for the home team. Total number of ways in which he can make the predictions so that exactly 10 predictions are correct, is equal to :

A person predicts the outcome of 20 cricket matches of his home team. Each match can result either in a win, loss or tie for the home team. Total number of ways in which he can make the predictions so that exactly 10 predictions are correct, is equal to :

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The foot of the perpendicular from the point left parenthesis 3 , 3 pi divided by 4 right parenthesis on the line r left parenthesis c o s space theta minus s i n space theta right parenthesis equals 6 square root of 2 is

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The point of intersection of the lines 2 c o s space theta plus s i n space theta equals 1 over r comma c o s space theta plus s i n space theta equals 1 over r is

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The line passing through open parentheses negative 1 comma fraction numerator pi over denominator 2 end fraction close parentheses and perpendicular to square root of 3 s i n space theta plus 2 c o s space theta equals 4 over r is

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The equation of the line passing through left parenthesis negative 1 comma pi divided by 6 right parenthesis comma left parenthesis 1 comma pi divided by 2 right parenthesis is

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The sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at a time is (repetition is not allowed) :

Alternatively, we can use the formula for the sum of numbers as
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The sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at a time is (repetition is not allowed) :

Maths-General

Alternatively, we can use the formula for the sum of numbers as
(n - 1)! cross times (sum of digits) cross times (11111 ............ntimes). We can also solve this problem by writing all the possible numbers and finding the sum of them which will be time taking and make us confused. We should know that the value of the digits is determined by the place where they were present. We should check whether there is zero in the given digits and whether there are any repetitions present in the numbers. Similarly, we can expect problems to find the sum of numbers formed by these digits with repetition allowed.

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Total number of divisors of 480, that are of the form 4n + 2, n greater or equal than 0, is equal to :

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Total number of divisors of 480, that are of the form 4n + 2, n greater or equal than 0, is equal to :

Maths-General

We can also solve this question by writing 4n + 2 = 2(2n + 1) where 2n + 1 is always an odd number. So, when all odd divisors will be multiplied by 2, we will get the divisors that we require. Hence, we can say a number of divisors of 4n + 2 form is the same as the number of odd divisors for 480.

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If 9P5 + 5 9P4 = 10Pr , then r =

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The number of proper divisors of 2 to the power of p. 6 to the power of q. 15r is-

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Ifx squared minus 11 x plus a text  and  end text x squared minus 14 x plus 2 a have a common factor then 'a' is equal to

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physics-

A block C of mass is moving with velocity and collides elastically with block of mass  and connected to another block of mass  through spring constant .What is  if  is compression of spring when velocity of  is same ?

A block C of mass is moving with velocity and collides elastically with block of mass  and connected to another block of mass  through spring constant .What is  if  is compression of spring when velocity of  is same ?

physics-General
parallel

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