Page No 423:
Question 1:
Which of the following are quadratic equation in x ?
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)
(xi)
Answer:
(ix)
This is of the form ax2 + bx + c = 0.
Hence, the given equation is a quadratic equation.
(x)
This is not of the form ax2 + bx + c = 0.
Hence, the given equation is not a quadratic equation.
(xi)
This is not of the form ax2 + bx + c = 0.
Hence, the given equation is not a quadratic equation.
Page No 424:
Question 2:
Which of the following are the roots of ?
(i) −1
(ii)
(iii)
Answer:
Page No 424:
Question 3:
Find the value of k for which x = 1 is root of the equation .
Answer:
Page No 424:
Question 4:
Find the values of a and b for which are the roots of the equation
Answer:
Page No 424:
Question 5:
Answer:
Page No 424:
Answer:
Page No 424:
Answer:
Page No 424:
Answer:
Page No 424:
Answer:
Page No 424:
Answer:
Page No 424:
Answer:
Page No 424:
Answer:
Page No 424:
Answer:
Page No 424:
Answer:
Page No 424:
Answer:
Page No 424:
Question 16:
Answer:
Page No 424:
Question 17:
Answer:
Page No 424:
Answer:
Page No 424:
Answer:
Page No 424:
Answer:
Page No 424:
Answer:
Page No 424:
Question 22:
Answer:
Page No 424:
Question 23:
Answer:
Page No 424:
Question 24:
Answer:
Page No 424:
Answer:
Page No 424:
Question 26:
Answer:
Page No 424:
Question 27:
Answer:
Page No 424:
Question 28:
Answer:
Page No 424:
Answer:
Page No 424:
Answer:
Page No 424:
Question 31:
Answer:
Page No 424:
Question 32:
Answer:
Page No 424:
Question 33:
Answer:
Page No 424:
Question 34:
Answer:
Page No 424:
Question 35:
Answer:
Page No 424:
Question 36:
Answer:
Page No 424:
Question 37:
Answer:
Page No 424:
Question 38:
Answer:
Page No 425:
Question 39:
Answer:
Page No 425:
Question 40:
Answer:
Page No 425:
Question 41:
Answer:
Page No 425:
Question 42:
Answer:
Page No 425:
Question 43:
Answer:
Page No 425:
Question 44:
Answer:
Page No 425:
Question 45:
Answer:
Page No 425:
Question 46:
Answer:
Page No 425:
Question 47:
Answer:
Page No 425:
Question 48:
Answer:
Page No 425:
Question 49:
Answer:
Page No 425:
Question 50:
Answer:
Page No 431:
Answer:
Page No 431:
Answer:
Page No 431:
Answer:
Page No 431:
Answer:
Page No 431:
Answer:
Page No 431:
Answer:
Page No 431:
Answer:
Page No 431:
Answer:
Page No 431:
Answer:
Page No 431:
Question 10:
Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
Answer:
Page No 431:
Answer:
Page No 431:
Answer:
Page No 431:
Question 13:
Answer:
Page No 431:
Question 14:
Answer:
Page No 432:
Question 15:
Answer:
Page No 432:
Answer:
Page No 432:
Answer:
Page No 432:
Answer:
Page No 432:
Answer:
Page No 432:
Answer:
Page No 432:
Question 21:
Answer:
Page No 432:
Answer:
Page No 432:
Question 23:
Answer:
Page No 432:
Question 24:
Answer:
Page No 432:
Question 25:
Answer:
Page No 432:
Question 26:
Answer:
Page No 432:
Question 27:
, where a0 and b0
Answer:
Page No 439:
Answer:
Page No 439:
Answer:
Page No 439:
Answer:
Page No 439:
Answer:
Page No 439:
Answer:
Page No 439:
Question 6:
Answer:
Page No 439:
Question 7:
Show that the roots of the equation are real for all real value of p and q.
Answer:
Page No 439:
Question 8:
Show that the equation has real and distinct roots for all real values of a.
Answer:
Page No 439:
Question 9:
Show that the equation has no real roots.
Answer:
Page No 439:
Question 10:
Find the values of k for which the equation has real and distinct roots.
Answer:
Page No 439:
Question 11:
Determine the values of p for which the quadratic equation has real roots.
Answer:
Page No 439:
Question 12:
Find the value of α for which the equation has equal roots.
Answer:
Page No 439:
Question 13:
If the equation has equal roots, prove that
Answer:
Page No 439:
Question 14:
If the roots of the equation are real and equal, show that either
Answer:
Page No 439:
Question 15:
Find the values k for which of roots of are real and equal
Answer:
Page No 439:
Question 16:
Find the values of k for which the roots of the equation are real and equal?
Answer:
Page No 439:
Question 17:
For what values of k are the roots of the quadratic equation real and equal?
Answer:
Page No 453:
Question 1:
The sum of two numbers is 8. Determine the numbers, if the sum of their reciprocals is
Answer:
Page No 453:
Question 2:
The difference of two numbers is 4. If the difference of their reciprocals is , find the number.
Answer:
Page No 453:
Question 3:
The sum of two numbers is 18 and the sum of their reciprocals is . Find the numbers.
Answer:
Page No 453:
Question 4:
The difference of two numbers is 5 and the difference of their reciprocals is . Find the numbers.
Answer:
Page No 453:
Question 5:
The sum of a number and its reciprocal is . Find the number.
Answer:
Page No 453:
Question 6:
Divide 57 into two parts whose product is 782.
Answer:
Page No 453:
Question 7:
Find two consecutive positive multiples of 3 whose product is 270.
Answer:
Page No 453:
Question 8:
Find two consecutive positive even integers, the sum of whose squares is 340.
Answer:
Page No 453:
Question 9:
The sum of a number and its squares is . Find the number.
Answer:
Page No 454:
Question 10:
The sum of a number and its positive square root is . Find the number.
Answer:
Page No 454:
Question 11:
Two natural numbers differ by 3 and their product is 504. Find the numbers.
Answer:
Page No 454:
Question 12:
Find two consecutive positive integers, the sum of whose squares is 365.
Answer:
Page No 454:
Question 13:
The difference of the squares of two natural numbers is 45. The squares of the smaller number is four times the largest number. Find the numbers.
Answer:
Page No 454:
Question 14:
Find two natural numbers, the sum of whose squares is 25 times their sum and also equal to 50 times their difference.
Answer:
Page No 454:
Question 15:
Divide 16 into two parts such that twice the squares of the larger part exceeds the square of the smaller part by 164.
Answer:
Page No 454:
Question 16:
The denominator of a fraction is 3 more than its numerator. The sum of the fraction and its reciprocal is . Find the fraction.
Answer:
Page No 454:
Question 17:
A two-digit number is 4 times the sum of its digits and twice the product of its digit. Find the number.
Answer:
Page No 454:
Question 18:
A two-digit number is such that the product of its digits is 14. If 45 is added to the number, the digits interchange their places. Find the number.
Answer:
​​
Page No 454:
Question 19:
Out of a number of saras birds, one-fourth of the number are moving about in lots, coupled with as well as 7 times the square root of the number move on a hill, 56 birds remain in vakula trees. What is the total number of birds?
Answer:
Page No 454:
Question 20:
A teacher on attempting to arrange the students for mass drill in the form of a solid square found that 24 students were left. When he increased the size of the square by one student, he found that he was short of 25 students. Find the number of students.
Answer:
Page No 454:
Question 21:
300 apples are distributed equally among a certain number of students. Had there been 10 more students, each would have received one apple less. Find the number of student.
Answer:
Page No 454:
Question 22:
A man busy a number of pens for Rs 80. If he had bought 4 more pens for the same amount, each pen would have cost him Rs 1 less. How many pens did he buy?
Answer:
Page No 455:
Question 23:
In a class test, the sum of Kamal's marks in Mathematics and English is 40. Had he got 3 marks more in Mathematics and 4 marks less in English, the product of the marks would have been 360. Find his marks in two subjects separately.
Answer:
Page No 455:
Question 24:
A takes 10 days than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.
Answer:
Page No 455:
Question 25:
A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find its usual speed.
Answer:
Page No 455:
Question 26:
A train travels a distance of 360 km at a uniform speed. If the speed of he train is increased by 5 km an hour, the journey would have taken 1 hour less. Find the original speed of the train.
Answer:
Page No 455:
Question 27:
A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hr more, it would have taken 30 minutes less for the journey. Find the original speed of the train.
Answer:
Page No 455:
Question 28:
The distance between Mumbai and Pune is 192 km. Travelling by the Deccan Queen, it takes 48 minutes less than another train. Calculate the speed of the Deccan Queen if the speed of the two trains differ by 20 km/hr.
Answer:
Page No 455:
Question 29:
A motorboat whose speed is 9 km/hr in still water, goes 15 km downstream and comes back in a total time of 3 hours 45 minutes. Find the speed of the stream.
Answer:
Page No 455:
Question 30:
A motor boat whose speed in still water is 18 km/hr, takes 1 hour more to go 24 km upstream than o return to the same spot. Find the speed of the stream.
Answer:
Page No 455:
Question 31:
The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.
Answer:
Page No 455:
Question 32:
A sailor can row a boat 8 km downstream and return back to the starting point in 1 hour 40 minutes. If the speed of the stream is 2 kmph, find the speed of the boat in still water.
Answer:
Page No 455:
Question 33:
Two pipes running together can fill a cistern in minutes. If one pipe takes 3 minutes more than the other to fill it, find the time in which each pipe would fill the cistern.
Answer:
Page No 455:
Question 34:
One year ago, a man was 8 times old as his son. Now his age is equal to the square of his son's age. Find their present ages.
Answer:
Page No 456:
Question 35:
The sum of the ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man's age at that time. Find their present ages.
Answer:
Page No 456:
Question 36:
The product of Tanvy's age (in years) 5 years ago and her age 8 years later is 30. Find her present age.
Answer:
Page No 456:
Question 37:
The sum of the ages of a boy and his brother is 25 years, and the product of their ages in years is 126. Find their ages.
Answer:
Page No 456:
Question 38:
A rectangular field is 16 m long and 10 m wide. There is a path of uniform width all around it, having an area of 120 m2. Find the width of the path.
Answer:
Page No 456:
Question 39:
The length of a rectangle is twice its breadth and its area is 288 cm2. Find the dimensions of the rectangle.
Answer:
Page No 456:
Question 40:
The length of a rectangular field is three times its breadth. If the area of the field by 147 sq metres, find the length of the field.
Answer:
Page No 456:
Question 41:
The length of a hall is 3 metres more than its breadth. If the area of the hall is 238 square metres, calculate its length and breadth.
Answer:
Page No 456:
Question 42:
The perimeter of a rectangular plot is 62 m and its area is 228 sq metres. Find the dimensions of the plot.
Answer:
Page No 456:
Question 43:
The length of a rectangle is thrice as long as the side of a square. The side of the square is 4 cm more than width of a the rectangle. Their areas being equal, find their dimensions.
Answer:
Page No 456:
Question 44:
A farmer prepares a rectangular vegetable garden of area 180 sq metres. With 39 metres of barbed wire, he can fence the three sides of the garden, leaving one of the longer sides unfenced. Find the dimensions of the garden.
Answer:
Page No 456:
Question 45:
The area of a right-triangle is 600 cm2. If the base of the triangle exceeds the altitude by 10 cm, find the dimensions of the triangle.
Answer:
Let the altitude of the triangle be x cm.
Therefore, the base of the triangle will be (x + 10) cm.
Page No 456:
Question 46:
The area of a right-angled triangle is 96 sq metres. If the base is three times the altitude, find the base.
Answer:
Let the altitude of the triangle be x m.
Therefore, the base will be 3x m.
Area of a triangle =
The value of x cannot be negative.
Therefore, the altitude and base of the triangle are 8 m and (3 8 = 24 m), respectively.
Page No 456:
Question 47:
The area of a right-angled triangle is 165 sq metres. Determine its base and altitude if the latter exceeds the former by 7 metres.
Answer:
Let the base be m.
Therefore, the altitude will be m.
Area of a triangle =
The value of cannot be negative.
Therefore, the base is 15 m and the altitude is {(15 + 7) = 22 m}.
Page No 456:
Question 48:
The hypotenuse of a right-angled triangle is 20 metres. If the difference between the length of the other sides be 4 metres, find the other sides.
Answer:
Let one side of the right-angled triangle be m and the other side be m.
On applying Pythagoras theorem, we have:
The value of x cannot be negative.
Therefore, the base is 12 m and the other side is {(12 + 4) = 16 m}.
Page No 456:
Question 49:
The length of the hypotenuse of a right-angled triangle exceeds the length of the base by 2 cm and exceeds twice the length of the altitude by 1 cm. Find the length of each side of the triangle.
Answer:
Let the base and altitude of the right-angled triangle be and y cm, respectively.
Therefore, the hypotenuse will be cm.
Thus, the base, altitude and hypotenuse of the triangle are 15 cm, 8 cm and 17 cm, respectively.
Page No 457:
Question 50:
The hypotenuse of a right-angled triangle is 1 metre less than twice the shortest side. If the third is 1 metre more than the shortest side, find the sides of the triangle.
Answer:
Let the shortest side be m.
Therefore, according to the question:
Hypotenuse = m
Third side = m
On applying Pythagoras theorem, we get:
The length of the side cannot be 0; therefore, the shortest side is 3 m.
Therefore,
Hypotenuse = 5 m
Third side = (3 + 1) = 4 m
Page No 457:
Question 51:
The sum of the areas of two squares is 640 m2. If the difference in their perimeters be 64 m, find the sides of the two squares.
Answer:
Let the length of the side of the first and the second square be and y, respectively.
Putting the value of in (i), we get:
Page No 457:
Question 52:
The difference of squares of two numbers is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.
Answer:
Page No 457:
Question 53:
Three consecutive positive integers are such that the sum of the square of the first and the product of the other two is 46, find the integers.
Answer:
Page No 462:
Question 1:
Which of the following is a quadratic equation?
(a)
(b)
(c)
(d)
Answer:
(d)
Page No 462:
Question 2:
Which of the following is a quadratic equation?
(a)
(b)
(c)
(d) None of these
Answer:
(b)
Page No 463:
Question 3:
Which of the following is not a quadratic equation?
(a)
(b)
(c)
(d)
Answer:
(c)
Page No 463:
Question 4:
If x = 3 is a solution of the equation then k = ?
(a) 11
(b) −11
(c) 13
(d) −13
Answer:
(b) −11
Page No 463:
Question 5:
The sum of the roots of the equation is
(a) 2
(b) −2
(c) 6
(d) −6
Answer:
(c) 6
Page No 463:
Question 6:
If the product of the roots of the equation is −2, then the value of k is
(a) −2
(b) −8
(c) 8
(d) 12
Answer:
(c) 8
Page No 463:
Question 7:
If one root of the equation is 2, then a = ?
(a) 7
(b) −7
(c)
(d)
Answer:
(b) −7
Page No 463:
Question 8:
The ratio of the sum and product of the roots of the equation
(a) 7 : 12
(b) 7 : 18
(c) 2 : 3
(d) 3 : 2
Answer:
(c) 2 : 3
Page No 463:
Question 9:
The roots of the equation are
(a)
(b)
(c)
(d)
Answer:
(b)
Page No 463:
Question 10:
The root of the equation are
(a)
(b)
(c)
(d)
Answer:
(d)
Page No 463:
Question 11:
The roots of the equation = 10 are
(a) 2, 0
(b) −2, 0
(c) 3, −1
(d) −3, 1
Answer:
(b) −2, 0
Page No 463:
Question 12:
The roots of the equation are
(a)
(b)
(c)
(d)
Answer:
(b)
Page No 463:
Question 13:
The roots of the equation are
(a)
(b)
(c)
(d)
Answer:
(c)
Page No 463:
Question 14:
The roots of the equation are
(a)
(b)
(c)
(d) none of these
Answer:
(b)
Page No 464:
Question 15:
The roots of are
(a) ±4
(b) ±6
(c) ±8
(d)
Answer:
(c) ±8
Page No 464:
Question 16:
The root of a quadratic equation are 5 and −2. Then, the equation is
(a)
(b)
(c)
(d)
Answer:
(b)
Page No 464:
Question 17:
If the sum of the roots of a quadratic equation is 6 and their product is 6, the equation is
(a)
(b)
(c)
(d)
Answer:
(a)
Page No 464:
Question 18:
If one root of the equation then the other root is
(a)
(b)
(c) −3
(d) 3
Answer:
(d) 3
Page No 464:
Question 19:
The quadratic equation whose one root is is
(a)
(b)
(c)
(d)
Answer:
(b)
Page No 464:
Question 20:
If the sum of the roots of the equation is equal to their product, then the value of k is
(a)
(b)
(c)
(d)
Answer:
(d)
Page No 464:
Question 21:
If one root of be the reciprocal of the other root, then the value of k is
(a) 0
(b) 1
(c) 2
(d) 5
Answer:
(d) 5
Page No 464:
Question 22:
The roots of the equation will be reciprocal of each other if
(a) a = b
(b) b= c
(c) c = a
(d) none of these
Answer:
(c) c = a
Page No 464:
Question 23:
If the roots of the equation are equal, then then c = ?
(a)
(b)
(c)
(d)
Answer:
(d)
Page No 464:
Question 24:
If the equation has equal roots, then k = ?
(a) 2 or 0
(b) −2 or 0
(c) 2 or −2
(d) 0 only
Answer:
(c) 2 or −2
Page No 464:
Question 25:
If the equation has equal rots, then k = ?
(a) 1 or 4
(b) −1 or 4
(c) 1 or −4
(d) −1 or −4
Answer:
(a) 1 or 4
Page No 464:
Question 26:
If the equation has equal roots, then k = ?
(a)
(b)
(c)
(d)
Answer:
(d)
Page No 465:
Question 27:
If the equation has equal roots, then k = ?
(a)
(b)
(c)
(d)
Answer:
(c)
Page No 465:
Question 28:
If the equation has both roots equal, then
(a) b = ac
(b)
(c) b2 = ac
(d)
Answer:
(c) b2 = ac
Page No 465:
Question 29:
The roots of are real and unequal, if
(a) > 0
(b) = 0
(c) < 0
(d) none of these
Answer:
(a) > 0
Page No 465:
Question 30:
In the equation it is given that Then, the roots of the equation are
(a) real and equal
(b) real and unequal
(c) imaginary
(d) none of these
Answer:
(b) real and unequal
Page No 465:
Question 31:
If the equation has no real roots, then
(a)
(b)
(c)
(d) none of these
Answer:
(c)
Page No 465:
Question 32:
If the equation has no real roots, then
(a) k < −2
(b) k > 2
(c) −2 < k < 2
(d) none of these
Answer:
(c) −2 < k < 2
Page No 465:
Question 33:
The roots of the equation are
(a) real, unequal and rational
(b) real, unequal and irrational
(c) real and equal
(d) imaginary
Answer:
(d) imaginary
Page No 465:
Question 34:
The roots of the equation are
(a) real, unequal and rational
(b) real, unequal and irrational
(c) real and equal
(d) imaginary
Answer:
(b) real, unequal and irrational
Page No 465:
Question 35:
For the equation which of the following statements is incorrect?
(a) If (b2 − 4ac) < 0, the roots are imaginary.
(b) If (b2 − 4ac) = 0, the roots are real and equal.
(c) If (b2 − 4ac) > 0 and (b2 − 4ac) is a perfect square, then the roots are rational and unequal.
(d) (b2 − 4ac) < 0, the roots are irrational.
Answer:
(d) (b2 − 4ac) < 0, the roots are irrational.
Page No 465:
Question 36:
If the roots of are real and distinct, then
(a)
(b) only
(c) only
(d) either or
Answer:
(d) either or
Page No 466:
Question 37:
The root of the equation are
(a) both real and equal
(b) both real and unequal
(c) both imaginary
(d) none of these
Answer:
(c) both imaginary
Page No 466:
Question 38:
The sum of a number and its reciprocal is The number is
(a)
(b)
(c)
(d)
Answer:
(a)
Page No 466:
Question 39:
The two parts into which 57 should be divided so that their product is 782, are
(a) 43 and 14
(b) 33 and 24
(c) 34 and 23
(d) 44 and 13
Answer:
(c) 34 and 23
Page No 466:
Question 40:
The perimeter of a rectangle is 82 m and its area is 400 m2. The breadth of the rectangle is
(a) 25 m
(b) 20 m
(c) 16 m
(d) 9 m
Answer:
(c) 16 m
Page No 466:
Question 41:
Which constant should be added and subtracted to solve the quadratic equation by the method of completing the square?
(a)
(b)
(c)
(d)
Answer:
(b)
Page No 466:
Question 42:
The roots of the equation are
(a)
(b)
(c)
(d)
Answer:
(c)
Page No 466:
Question 43:
For what real values of k, the equation has real and equal roots?
(a) k = 2 or −2
(b) k = 3 or −3
(c)
(d) None of these
Answer:
(b) k = 3 or −3
Page No 466:
Question 44:
For what values of k, the equation has real roots?
(a)
(b)
(c)
(d) None of these
Answer:
(b)
Page No 466:
Question 45:
If α and β are the roots of the equation
(a)
(b)
(c) −4
(d) 4
Answer:
(c) −4
Page No 466:
Question 46:
Which of the following is not true?
(a) Every quadratic equation can have at the most two real roots.
(b) Some quadratic equations do not have any real root.
(c) Some quadratic equations may have one real root.
(d) Every quadratic equations has two real roots.
Answer:
Page No 467:
Question 47:
Consider the following statements:
I. If the roots of the equation are negative reciprocal of each other, than a + c = 0.
II. A quadratic equation can have at all most two roots.
III. If α, β are the roots of then α + β = 22 and α − β = 8.
Of these statements:
(a) I and II are true and III is false.
(b) I and III are true and II is false.
(c) II and III are true I is false.
(d) I, II and III are all true.
Answer:
(d) I, II and III are all true.
Page No 467:
Question 48:
Assertion (A)
The equation x2 + x + 1 = 0 has both real roots.
Reason (R)
The equation ax2 + bx + c = 0, (a ≠ 0) has both real roots, if (b2 − 4ac) > 0.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.
Answer:
(d) Assertion (A) is false and Reason (R) is true.
Page No 467:
Question 49:
Assertion (A)
The equation has no real roots.
Reason (R)
The equation has no real roots, if
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.
Answer:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
Page No 467:
Question 50:
Assertion (A)
If −5 is a root of has equal roots, then
Reason (R)
The equation has equal roots, if
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.
Answer:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
Page No 468:
Question 51:
Assertion (A)
The roots of
Reason (R)
If
Answer:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
Thus, Assertion (A) is true and Reason (R) is a correct explanation of Assertion (A).
Page No 468:
Question 52:
Assertion (A)
If has real roots, then
Reason (R)
The equation has no real root, if ad ≠ bc.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.
Answer:
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
Page No 468:
Question 53:
Match the following columns:
Column I |
Column II |
(a) |
(p) Real and equal |
(b) |
(q) Real, distinct and irrational |
(c) |
(r) Real distinct and rational |
(d) |
(s) Imaginary |
Answer:
Page No 475:
Question 1:
If has real roots, then
(a) p ≥ 4
(b) p ≤ 4
(c) p ≥ 5
(d) p ≤ 5
Answer:
(b) p ≤ 4
Page No 475:
Question 2:
If x = 1 is a common root of
(a) 3
(b) −3
(c) 4
(d) 6
Answer:
(a) 3
Page No 475:
Question 3:
If has a repeated root, then k = ?
(a) 1 or 4
(b) −1 or 4
(c) 1 or −4
(d) −1 or −4
Answer:
(a) 1 or 4
Page No 475:
Question 4:
If has no real root, then
(a)
(b)
(c)
(d) none of these
Answer:
(c)
Page No 476:
Question 5:
For what values of k, the roots the equation are imaginary?
Answer:
Page No 476:
Question 6:
For what values of k, the roots of the equation are real?
Answer:
For real roots, the value of k must be lesser than or equal to 4.
Page No 476:
Question 7:
For what values of k, the roots of the equation are real?
Answer:
Page No 476:
Question 8:
Solve:
Answer:
Page No 476:
Question 9:
Show that the equation has real and unequal roots.
Answer:
Page No 476:
Question 10:
Show that the equation has no real roots.
Answer:
Page No 476:
Question 11:
Solve:
Answer:
Page No 476:
Question 12:
Solve:
Answer:
Page No 476:
Question 13:
Solve:
Answer:
Page No 476:
Question 14:
Find two consecutive positive integers, the sum of whose squares is 25.
Answer:
Page No 476:
Question 15:
Solve:
Answer:
Page No 476:
Question 16:
Using quadratic formula, solve
Answer:
Page No 476:
Question 17:
The area of a right-angle triangle is 165 m2. Determine its base and altitude if the latter exceeds the former by 7 metres.
Answer:
Page No 476:
Question 18:
Solve:
Answer:
Page No 476:
Question 19:
Solve:
Answer:
Page No 476:
Question 20:
Solve: 5(x+1)+5(2−x)=126.
Answer:
View NCERT Solutions for all chapters of Class 10