Question

# For x R, let [x] denote the greatest integer x, then value of++ +…+is -

- –100
- –123
- –135
- –153

## The correct answer is: –135

### For 0 r 66, 0 <

– < – 0

– – < – – –

= –1 for 0 r 66

Also, for 67 r 100, 1

–1 – –

– – 1 – – – –

= –2 for 67 r 100

Hence, = 67(–1) + 2(–34) = –135.

### Related Questions to study

### The number of integral solutions of the equation x + y + z = 24 subjected to conditions that 1 x 5, 12 y 18, z –1

### The number of integral solutions of the equation x + y + z = 24 subjected to conditions that 1 x 5, 12 y 18, z –1

### Ravish write letters to his five friends and address the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes -

### Ravish write letters to his five friends and address the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes -

### In how many ways can we get a sum of at most 17 by throwing six distinct dice -

### In how many ways can we get a sum of at most 17 by throwing six distinct dice -

### The number of non negative integral solutions of equation 3x + y + z = 24

### The number of non negative integral solutions of equation 3x + y + z = 24

### Sum of divisors of 2^{5 }·3^{7 }·5^{3 }· 7^{2} is –

### Sum of divisors of 2^{5 }·3^{7 }·5^{3 }· 7^{2} is –

### The length of the perpendicular from the pole to the straight line is

### The length of the perpendicular from the pole to the straight line is

### The condition for the lines and to be perpendicular is

### The condition for the lines and to be perpendicular is

### If f : R →R; f(x) = sin x + x, then the value of (f^{-1} (x)) dx, is equal to

Here we used the concept of integration and the inverse functions to solve the question. Finding an antiderivative of a function is the procedure known as integration. The process of adding the slices to complete it is comparable. The process of integration is the opposite of that of differentiation. So the final answer is .

### If f : R →R; f(x) = sin x + x, then the value of (f^{-1} (x)) dx, is equal to

Here we used the concept of integration and the inverse functions to solve the question. Finding an antiderivative of a function is the procedure known as integration. The process of adding the slices to complete it is comparable. The process of integration is the opposite of that of differentiation. So the final answer is .

### The polar equation of the straight line with intercepts 'a' and 'b' on the rays and respectively is

### The polar equation of the straight line with intercepts 'a' and 'b' on the rays and respectively is

### The polar equation of the straight line parallel to the initial line and at a distance of 4 units above the initial line is

### The polar equation of the straight line parallel to the initial line and at a distance of 4 units above the initial line is

### The polar equation of axy is

### The polar equation of axy is

### If x, y, z are integers and x 0, y 1, z 2, x + y + z = 15, then the number of values of the ordered triplet (x, y, z) is -

### If x, y, z are integers and x 0, y 1, z 2, x + y + z = 15, then the number of values of the ordered triplet (x, y, z) is -

### If then the equation whose roots are

Here we used the concept of quadratic equations and solved the problem. We also understood the concept of discriminant and used it in the solution to find the intervals. Therefore, the equation is .

### If then the equation whose roots are

Here we used the concept of quadratic equations and solved the problem. We also understood the concept of discriminant and used it in the solution to find the intervals. Therefore, the equation is .

### Let p, q {1, 2, 3, 4}. Then number of equation of the form px^{2} + qx + 1 = 0, having real roots, is

Here we used the concept of quadratic equations and solved the problem. We also understood the concept of discriminant and used it in the solution to find the intervals. Therefore, total 7 seven solutions are possible so 7 equations can be formed.

### Let p, q {1, 2, 3, 4}. Then number of equation of the form px^{2} + qx + 1 = 0, having real roots, is

Here we used the concept of quadratic equations and solved the problem. We also understood the concept of discriminant and used it in the solution to find the intervals. Therefore, total 7 seven solutions are possible so 7 equations can be formed.

### ax^{2} + bx + c = 0 has real and distinct roots null. Further a > 0, b < 0 and c < 0, then –

Here we used the concept of quadratic equations and solved the problem. The concept of sum of roots and product of roots was also used here. Therefore, 0 < ∣α∣ < β.

### ax^{2} + bx + c = 0 has real and distinct roots null. Further a > 0, b < 0 and c < 0, then –

Here we used the concept of quadratic equations and solved the problem. The concept of sum of roots and product of roots was also used here. Therefore, 0 < ∣α∣ < β.