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10th Class - CBSE - Mathematics - 6109 Questions - 0 Concepts

#### Important Questions

Q1 Multiple Correct Hard
If the quadratic equation $ax^{2}+2bx-4=0$ ,where $a,b,c\in R$, does not have two real & distinct roots, then
• A. $a-b>1$
• B. $2b-a\leq -4$
• C. $2b-a\geq -4$
• D. $a+b\leq 1$

1 Verified Answer | Published on 05th 09, 2020

Q2 Single Correct Hard
If $p,q$ are any two values of $k$ for which $\dfrac{\displaystyle \sum _{ r=0 }^{ k-1 }{ { x }^{ 2r } } }{\displaystyle \sum _{ r=0 }^{ k-1 }{ { x }^{ r } } }$ is a polynomial in $x$, then roots of equation $3x^2 + px + 5q = 0$ cannot be
• A. real
• B. imaginary
• C. irrational
• D. rational

1 Verified Answer | Published on 05th 09, 2020

Q3 Single Correct Hard
If, for a positive integer n, the quadratic equation, $x ( x + 1 ) + ( x + 1 ) ( x + 2 ) + \ldots + \left( x + \frac { 1 } { n - 1 } \right) ( x + n ) = 10 n$ has two consecutive integral solutions, then n is equal to
• A. 12
• B. 9
• C. 10
• D. 11

1 Verified Answer | Published on 05th 09, 2020

Q4 Single Correct Hard
A trader bought a number of articles for $Rs\ 1200$. Ten were damaged and he sold each of the remaining articles at $Rs\ 2$ more than what he paid for it, thus getting a profit of $Rs\ 60$ on the whole transaction. Taking no. of articles he bought as $x$, find $x$.
• A. $92$
• B. $85$
• C. $56$
• D. $100$

1 Verified Answer | Published on 05th 09, 2020

Q5 One Word Hard
The hypotenuse of a right triangle is $2$ centimeters more than the longer of the side containing the right angle. The shorter of the side containing the right angle is $7$ centimeters less than the longer side containing the right angle. Find the length of the hypotenuse.

1 Verified Answer | Published on 05th 09, 2020

Q6 Single Correct Hard
The sum of a number and its reciprocal is $\dfrac {82}{9}$. Find the number.
• A. $x=8$ and $x=\dfrac {1}{8}$
• B. $x=10$ and $x=\dfrac {1}{10}$
• C. $x=0.9$ and $x=\dfrac {1}{0.9}$
• D. $x=9$ and $x=\dfrac {1}{9}$

1 Verified Answer | Published on 05th 09, 2020

Q7 Single Correct Hard
The values of $\lambda$ for which the equation
$(x^{2}+3x+5)^{2}-(\lambda -3)(x^{2}+3x+4)(x^{2}+3x+5)+(\lambda -4)(x^{2}+3x+4)^{2}=0$
has at least one real root are
• A. $\left ( 5,\dfrac{39}{7} \right )$
• B. $\left ( 5,\dfrac{39}{7} \right ]$
• C. $\left [ 5,\dfrac{39}{7} \right )$
• D. $\left [ 5,\dfrac{39}{7} \right ]$

1 Verified Answer | Published on 05th 09, 2020

Q8 Single Correct Hard
If each pair among the equations $x^{2} + qr =0$, $x^{2} +qx +rp=0$ and $x^{2} + rx+pq=0$ have a common root then the product of these common roots is
• A. $-pq^{2}$
• B. $pq (p+q)$
• C. $-(pq^{2} +pq^{2})$
• D. $2pqr$

1 Verified Answer | Published on 05th 09, 2020

Q9 Assertion & Reason Hard
##### ASSERTION

If the roots of the equations ${ x }^{ 2 }-bx+c=0$ and ${ x }^{ 2 }-cx+b=0$ differ by the same quantity, then $b+c$ is equal to $-4$

##### REASON

If $\alpha, \beta$ are the roots of the equation $A{ x }^{ 2 }+Bx+C=0$, then $\displaystyle \alpha -\beta =\frac { \sqrt { { B }^{ 2 }-4AC } }{ A }$

• A. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• B. Assertion is correct but Reason is incorrect
• C. Assertion is incorrect but Reason is correct
• D. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

1 Verified Answer | Published on 05th 09, 2020

Q10 Single Correct Hard
If the quadratic equation $ax^{2}+bx+a^{2}+b^{2}+c^{2}-ab-bc-ca=0$, where $a, b, c$ are distinct real numbers, has imaginary roots, then
• A. $2\left ( a-b \right )+\left ( a-b \right )^{2}+\left ( b-c \right )^{2}+\left ( c-a \right )^{2}< 0$
• B. $2\left ( a-b \right )+\left ( a-b \right )^{2}+\left ( b-c \right )^{2}+\left ( c-a \right )^{2}= 0$
• C. none of these
• D. $2\left ( a-b \right )+\left ( a-b \right )^{2}+\left ( b-c \right )^{2}+\left ( c-a \right )^{2}> 0$